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We consider the problem of communicating over a channel that randomly “tears” the message block into small pieces of different sizes and shuffles them. For the binary torn-paper channel with block length $n$ and pieces of length ${\mathrm{ Geometric}}(p_{n})$ , we characterize the capacity as $C = e^{-\alpha }$ , where $\alpha = \lim _{n\to \infty } p_{n} \log n$. Our results show that the case of ${\mathrm{ Geometric}}(p_{n})$ -length fragments and the case of deterministic length- $(1/p_{n})$ fragments are qualitatively different and, surprisingly, the capacity of the former is larger. Intuitively, this is due to the fact that, in the random fragments case, large fragments are sometimes observed, which boosts the capacity. [ABSTRACT FROM AUTHOR]

Teaching outdoors is an obligatory part of physical education (PE) in most countries; therefore, PE holds great potential to contribute to learning about nature, the environment and environmental sustainability (ES). This paper reports the investigation of whether Swedish PE teachers perceive ES as part of their subject, and if so, how do they implement it? Drawing on 60 PE teachers’ answers to five opened questions (53 written answers and 7 oral interviews), and using British sociologist Basil Bernstein’s concepts of classification and codes, this study have asked the following research questions: 1. What influences the position and legitimisation of ES in PE? 2. How does the subject culture of Swedish PE influence the introduction of ES? The result from the study shows a complexity regarding the strength of the boundaries that surround ES in PE and what this complexity might offer in terms of enablers and constraints. The result also displays a strong connection between outdoor education and its potential for teaching ES. Various options are discussed with regard to where (in what content areas in PE) and how to implement ES. [ABSTRACT FROM AUTHOR]

Let I be the commutative non-unital ring of order 4 defined by generators and relations. I = a , b ∣ 2 a = 2 b = 0 , a 2 = b , a b = 0. Alahmadi et al. have classified QSD codes, Type IV codes (QSD codes with even weights) and quasi-Type IV codes (QSD codes with even torsion code) over I up to lengths n = 6 , and suggested two building-up methods for constructing QSD codes. In this paper, we construct more QSD codes, Type IV codes and quasi-Type IV codes for lengths n = 7 and 8, and describe five new variants of the two building-up construction methods. We find that when n = 8 there is at least one QSD code with minimun distance 4, which attains the highest minimum distance so far, and we give a generator matrix for the code. We also describe some QSD codes, Type IV codes and quasi-Type IV codes with new weight distributions. [ABSTRACT FROM AUTHOR]

Thematic analysis is a highly popular technique among qualitative researchers for analyzing qualitative data, which usually comprises thick descriptive data. However, the application and use of thematic analysis has also involved complications due to confusion regarding the final outcome's presentation as a conceptual model. This paper develops a systematic thematic analysis process for creating a conceptual model from qualitative research findings. It explores the adaptability of the proposed process across various research methodologies, including constructivist methodologies, positivist methodologies, grounded theory, and interpretive phenomenology, and justifies their application. The paper distinguishes between inductive and deductive coding approaches and emphasizes the merits of each. It suggests that the derived systematic thematic analysis model is valuable across multiple disciplines, particularly in grounded theory, ethnographic approaches, and narrative approaches, while also being adaptable to more descriptive, positivist-based methodologies. By providing a methodological roadmap, this study enhances the rigor and replicability of thematic analysis and offers a comprehensive strategy for theoretical conceptualization in qualitative research. The contribution of this paper is a systematic six-step thematic analysis process that leads to the development of a conceptual model; each step is described in detail and examples are given. [ABSTRACT FROM AUTHOR]

The management of existing structures is raising a number of pertinent questions to the owners and engineers. Many structures built more than 50 years ago (even those built hundreds of years ago) usually no longer comply with safety requirements of current codes, which are typically addressed in new structures. This is not necessarily only caused by a poor original design or degradation with time, but it may be, for example, the consequence of increase in actions, reducing the level of reliability of a structure. This paper focuses on strategies to be adopted for existing structures which do not comply with code requirements for new constructions (e.g., to repair, to demolish, to rebuild, etc.) on the basis of a more holistic approach that includes economic, social, and environmental considerations. To that aim, first, a brief review of the background concepts on the reliability of structures is presented, highlighting the differences for new and existing structures. Following this analysis, suitable values for the reliability index (including sustainability considerations) are proposed, as well as tailored maintenance strategies. Finally, the paper presents a case study based on a real project to emphasize the benefits of adopting such a holistic perspective. [ABSTRACT FROM AUTHOR]

In a previous paper, the second and third named authors introduced the concept of the complete cycle index and discussed a relation with the complete weight enumerator in coding theory. In this paper, we introduce the concept of the complete joint cycle index and the average complete joint cycle index, and discuss a relation with the complete joint weight enumerator and the average complete joint weight enumerator, respectively, in coding theory. Moreover, the notion of the average intersection numbers is given, and we discuss a relation with the average intersection numbers in coding theory. [ABSTRACT FROM AUTHOR]

Thematic analysis is a highly popular technique among qualitative researchers for analyzing qualitative data, which usually comprises thick descriptive data. However, the application and use of thematic analysis has also involved complications due to confusion regarding the final outcome's presentation as a conceptual model. This paper develops a systematic thematic analysis process for creating a conceptual model from qualitative research findings. It explores the adaptability of the proposed process across various research methodologies, including constructivist methodologies, positivist methodologies, grounded theory, and interpretive phenomenology, and justifies their application. The paper distinguishes between inductive and deductive coding approaches and emphasizes the merits of each. It suggests that the derived systematic thematic analysis model is valuable across multiple disciplines, particularly in grounded theory, ethnographic approaches, and narrative approaches, while also being adaptable to more descriptive, positivist-based methodologies. By providing a methodological roadmap, this study enhances the rigor and replicability of thematic analysis and offers a comprehensive strategy for theoretical conceptualization in qualitative research. The contribution of this paper is a systematic six-step thematic analysis process that leads to the development of a conceptual model; each step is described in detail and examples are given. [ABSTRACT FROM AUTHOR]

Linear codes achieving or nearly achieving the Singleton bound are interesting in both theory and practice. The objective of this paper is to construct several infinite families of MDS, near MDS and almost MDS codes from some special cyclic subgroups of ${\mathbb {F}}_{q^{2}}^{*}$. To this end, the augmentation and extension techniques are used. The codes in this paper have flexible parameters and their lengths could be large. The minimum linear locality of the codes constructed in this paper is also studied. Some infinite families of optimal linearly locally recoverable codes are obtained. Besides, some codes in this paper are proved to be proper for error detection. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive performance comparison between a current robust military waveform; namely, MIL-STD-188-110D, Waveform 0, and a filter bank multicarrier spread-spectrum (FBMC-SS) waveform proposed for communications through ionospheric/skywave HF channels. Waveform 0 is effectively a direct sequence spread spectrum waveform that uses Walsh multi-codes to enhance the information transmission rate. It may thus be referred to as Walsh-DSSS. FBMC-SS, on the other hand, makes use of filter banks to provide excellent performance when the received signal is subject to partial band interference. Successful application of FBMC-SS for communications across skywave HF channels has been previously demonstrated, both theoretically and through experimental work. However, very little has been done to contrast FBMC-SS against Walsh-DSSS. The goal of this paper is to first add new features to FBMC-SS to bring it on par with Walsh-DSSS. These features include: (i), introduction of multi-codes that achieve a comparable (or better) data rate to Walsh-DSSS; and (ii), addition of a scrambling step applied to the multi-codes to make the receiver detection robust against widely spread multipaths. With this established, in the second part of the paper, we examine the performance of the developed FBMC-SS against Walsh-DSSS when both are applied for communications across skywave HF channels. The two waveforms are compared both through a theoretical study and through experimental works across several skywave channels ranging from hundreds to thousands of kilometers. [ABSTRACT FROM AUTHOR]

The number-theoretic code is a class of codes defined by single or multiple congruences. These codes are mainly used for correcting insertion and deletion errors, and for correcting asymmetric errors. This paper presents a formula for a generalization of the complete weight enumerator for the number-theoretic codes. This formula allows us to derive the weight enumerators and cardinalities for the number-theoretic codes. As a special case, this paper provides the Hamming weight enumerators and cardinalities of the non-binary Tenengolts’ codes, correcting single insertion or deletion. Moreover, we show that the formula deduces the MacWilliams identity for the linear codes over the ring of integers modulo $r$. [ABSTRACT FROM AUTHOR]

In this paper, we consider variable-length coding over the memoryless binary asymmetric channel (BAC) with full noiseless feedback, including the binary symmetric channel (BSC) as a special case. In 2012, Naghshvar et al. introduced a coding scheme, which we refer to as the small-enough-difference (SED) coding scheme. For symmetric binary-input channels, the deterministic variable-length feedback (VLF) code constructed with the SED coding scheme asymptotically achieves both capacity and Burnashev’s optimal error exponent. Building on the work of Naghshvar et al., this paper extends the SED coding scheme to the BAC and develops a non-asymptotic VLF achievability bound that is shown to achieve both capacity and the optimal error exponent. For the specific case of the BSC, we develop an additional non-asymptotic VLF achievability bound using a two-phase analysis that leverages both a submartingale synthesis and a Markov chain time of first passage analysis. Numerical evaluations show that both new VLF achievability bounds outperform Polyanskiy’s achievability bound for variable-length stop-feedback codes. [ABSTRACT FROM AUTHOR]

With increasing the use of ultra-high performance fiber reinforced concrete (UHPFRC) in recent years, torsional design of UHPFRC beams has become of great importance. This paper presents an experimental and numerical study to investigate the torsional behavior of UHPFRC shallow and deep beams with fcu equal to 190.2 MPa. Ten UHPFRC beams with steel fibers volume fraction of 1.5% subjected to pure torsion were investigated. The provided torsional web reinforcement ratio, the area of longitudinal bars and the tested span to total height ratio (L/h = 6.0, 4.0, 2.0 and 1.0) were the studied parameters. A numerical model has been proposed to predict the torsional response of tested beams. Experimental results showed that increasing stirrups' spacing for the beams of the same L/h ratio (to be 235% of the maximum given by ACI 318-2019 code), reduced the experimental ultimate torsional strength by only 6.7%. The torsional web reinforcement ratio of UHPFRC shallow and deep beams can be safely taken to be 40% of the minimum required by ACI 318-2019. The maximum stirrups spacing can be safely taken the lesser of twice the beam width or 300 mm. The equation used by ACI 318-2019 and ECP-203-2020 for calculating the cracking strength in torsion has been modified to be suitable for UHPFRC beams by taking into consideration the L/h ratio and steel fibers percent. The proposed 3-D numerical model showed good predictions for the torsional strength of tested UHPFRC shallow and deep beams. [ABSTRACT FROM AUTHOR]

A functional $k$ -batch code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. Any multiset request of size $k$ of linear combinations (or requests) of the information bits can be recovered by $k$ disjoint subsets of the servers. The goal under this paradigm is to find the minimum number of servers for given values of $s$ and $k$. A recent conjecture states that for any $k=2^{s-1}$ requests the optimal solution requires $2^{s}-1$ servers. This conjecture is verified for $s \leqslant 5$ but previous work could only show that codes with $n=2^{s}-1$ servers can support a solution for $k=2^{s-2} + 2^{s-4} + \left \lfloor{ \frac { 2^{s/2}}{\sqrt {24}} }\right \rfloor $ requests. This paper reduces this gap and shows the existence of codes for $k=\lfloor \frac {5}{6}2^{s-1} \rfloor - s$ requests with the same number of servers. Another construction in the paper provides a code with $n=2^{s+1}-2$ servers and $k=2^{s}$ requests, which is an optimal result. These constructions are mainly based on extended Simplex codes and equivalently provide constructions for parallel Random I/O (RIO) codes. [ABSTRACT FROM AUTHOR]

Timing-based side and covert channels in processor caches continue to be a threat to modern computers. This work shows for the first time, a systematic, large-scale analysis of Arm devices and the detailed results of attacks the processors are vulnerable to. Compared to x86, Arm uses different architectures, microarchitectural implementations, cache replacement policies, etc., which affects how attacks can be launched, and how security testing for the vulnerabilities should be done. To evaluate security, this paper presents security benchmarks specifically developed for testing Arm processors and their caches. The benchmarks are evaluated with sensitivity tests, which examine how sensitive the benchmarks are to having a correct configuration in the testing phase. Further, to evaluate a large number of devices, this work leverages a novel approach of using a cloud-based Arm device testbed for architectural and security research on timing channels and runs the benchmarks on 34 different physical devices. In parallel, there has been much interest in secure caches to defend the various attacks. Consequently, this paper also investigates secure cache architectures using proposed benchmarks. Especially, this paper implements and evaluates secure PL and RF caches, showing the security of PL and RF caches, but also uncovers new weaknesses. [ABSTRACT FROM AUTHOR]

This report analyzes the reproducibility of the paper “MemXCT: Memory-Centric X-ray CT Reconstruction with Massive Parallelization” by Hidayetoğlu et al. in the cloud as part of the SC20 Virtual Student Cluster Competition (VSCC). To reproduce the results from the original work, the ETH Zürich SC20 VSCC team performed a series of CT reconstructions and performed a scaling study using three provided sinograms. All experimental runs were performed during the SC20 VSCC on an HPC cluster hosted in the Microsoft Azure CycleCloud. In this paper, we describe discrepancies in results as a factor of the differences in experiment environments and insufficient parameter tuning. We successfully reproduce the single device performance and partially reproduce the strong scaling behavior. Digital artifacts from these experiments are available at: 10.5281/zenodo.5598108. [ABSTRACT FROM AUTHOR]

In 1991, Wei proved a duality theorem that established an interesting connection between the generalized Hamming weights of a linear code and those of its dual code. Wei’s duality theorem has since been extensively studied from different perspectives and extended to other settings. In this paper, we re-examine Wei’s duality theorem and its various extensions, henceforth referred to as Wei-type duality theorems, from a new Galois connection perspective. Our approach is based on the observation that the generalized Hamming weights and the dimension/length profiles of a linear code form a Galois connection. The central result of this paper is a general Wei-type duality theorem for two Galois connections between finite subsets of $\mathbb {Z}$ , from which all the known Wei-type duality theorems can be recovered. As corollaries of our central result, we prove new Wei-type duality theorems for $w$ -demi-matroids defined over finite sets and $w$ -demi-polymatroids defined over modules with a composition series, which further allows us to unify and generalize all the known Wei-type duality theorems established for codes endowed with various metrics. [ABSTRACT FROM AUTHOR]

For fixed integers $n$ and $b\geq k$ , let $A(b,k,n)$ the largest size of a subset of $\{1,2,\ldots,b\}^{n}$ such that, for any $k$ distinct elements in the set, there is a coordinate where they all differ. Bounding $A(b,k,n)$ is a problem of relevant interest in information theory and computer science, relating to the zero-error capacity with list decoding and to the study of $(b, k)$ -hash families of functions. It is known that, for fixed $b$ and $k$ , $A(b,k,n)$ grows exponentially in $n$. In this paper, we determine new exponential upper bounds for different values of $b$ and $k$. A first bound on $A(b,k,n)$ for general $b$ and $k$ was derived by Fredman and Komlós in the ’80s and improved for certain $b\neq k$ by Körner and Marton and by Arikan. Only very recently better bounds were derived for general $b$ and $k$ by Guruswami and Riazanov, while stronger results for small values of $b=k$ were obtained by Arikan, by Dalai, Guruswami and Radhakrishnan, and by Costa and Dalai. In this paper, we strengthen the bounds for some specific values of $b$ and $k$. Our contribution is a new computational method for obtaining upper bounds on the values of a quadratic form defined over discrete probability distributions in arbitrary dimensions, which emerged as a central ingredient in recent works. The proposed method reduces an infinite-dimensional problem to a finite one, which we manage to further simplify by means of a series of optimality conditions. [ABSTRACT FROM AUTHOR]

Predictive Maintenance technologies are particularly appealing for Industrial Equipment producers, as they pave the way to the selling of high added-value services and customized maintenance plans. However, standard Predictive Maintenance approaches assume the availability of sensor measurements, and the costs associated with adding sensors or remotely accessing sensor readings may discourage the development of such technologies. In this context, Alarm Forecasting can be very useful as it represents a low-cost alternative or helpful support to sensor-based Predictive Maintenance. In this work, we propose a new formulation for the Alarm Forecasting problem, framed as a multi-label classification task. We present a novel deep learning-based approach called FORMULA (alarm FORecasting in MUlti-LAbel setting). FORMULA leverages Transformer, a popular Neural Network architecture in the field of Natural Language Processing. To cope with alarm imbalance, we draw inspiration from Segmentation and Object Detection. Thus, FORMULA is trained by minimizing the Weighted Focal Loss, which turns out to be very effective in predicting rare alarms. These alarms, even if they are difficult to predict by nature, often are business-critical. We assess the proposed approach on a representative real-world problem from the packaging industry. In particular, we show that it outperforms not only classic multilabel techniques but also models based on recurrent neural networks. As regards the latter, the proposed approach also exhibits a lower computational burden, both in terms of training time and model size. To foster research in the field and reproducibility, we also publicly share the alarm logs dataset and the code used to perform the experiments. Note to Practitioners—This paper was motivated by the problem of monitoring equipment in the scenario of dairy products packaging, under the mild assumption that logs of the alarm generated by the packaging machines are available. This paper proposes an alarm forecasting algorithm. Its goal is to predict if any alarm will occur in the future, based only on past alarm logs. The limits of the considered future window can be defined arbitrarily, so there is enough time to perform corrective actions. Thus, the proposed approach aims to prevent unexpected downtime that would not only hinder productivity but also imply significant material waste. The proposed approach leverages methodologies from Natural Language Processing and Object Detection to deal with rare alarms that are often very informative in the industrial scenario. Besides, both the code and the real-world industrial datasets used to evaluate the methodology are available publicly. Currently, the proposed approach only uses alarm logs. Especially in the context of Industry 4.0, where many sensory data may be available, this is a limitation. Thus, the described approach might be extended by integrating alarm logs with sensory data. This integration is expected to improve the estimation of equipment health state. The results described in this paper may find application not only in the manufacturing sector but also in different areas such as Cyber Security, where log files keep activity records of each process performed. [ABSTRACT FROM AUTHOR]

Recently, subfield codes of geometric codes over large finite fields ${\mathrm {GF}}(q)$ with dimension 3 and 4 were studied and distance-optimal subfield codes over ${\mathrm {GF}}(p)$ were obtained, where $q=p^{m}$. The key idea for obtaining very good subfield codes over small fields is to choose very good linear codes over an extension field with small dimension. This paper first presents a general construction of $[q+1, 2, q]$ MDS codes over ${\mathrm {GF}}(q)$ , and then studies the subfield codes over ${\mathrm {GF}}(p)$ of some of the $[q+1, 2,q]$ MDS codes over ${\mathrm {GF}}(q)$. Two families of dimension-optimal codes over ${\mathrm {GF}}(p)$ are obtained, and several families of nearly optimal codes over ${\mathrm {GF}}(p)$ are produced. Several open problems are also proposed in this paper. [ABSTRACT FROM AUTHOR]

A common method for reading information stored in DNA molecules is shotgun sequencing. This method outputs a histogram of the frequencies of all the molecules’ substrings of a given length $\ell $. To protect against noisy readings, the rank-modulation scheme encodes the information in the relative ranking of the substring frequencies, instead of their absolute values. However, the best rank-modulation codes for shotgun sequencing have low rates which are asymptotically vanishing. In this paper we propose new constructions of rank-modulation codes for shotgun sequencing. The first code construction is systematic, allowing the user to arbitrarily set the frequencies of a large subset of the substrings, which the encoder then completes to a permutation that may be realized by a DNA molecule. The construction is then improved by allowing the user to set the frequencies of additional substrings, at the cost of imposing constraints on the frequencies. The resulting codes have higher, non-vanishing rates, compared with previously known codes. As an example, for histograms of substrings of length $\ell =2$ , and an alphabet of size 4 (as in DNA molecules), we are able to construct a code with rate $\approx 0.909$ , whereas previously, the best construction resulted in a code with rate $\approx 0.654$. Additionally, the encoded information in our construction may be written to shorter DNA molecules than possible before. We also prove that the systematic codes constructed in this paper are the largest possible among all systematic codes. [ABSTRACT FROM AUTHOR]

Linear codes generated by component functions of perfect nonlinear (PN for short) and almost perfect nonlinear (APN for short) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper is to investigate some binary shortened codes of two families of linear codes from APN functions and some $p$ -ary shortened codes associated with PN functions. The weight distributions of these shortened codes and the parameters of their duals are determined. The parameters of these binary codes and $p$ -ary codes are flexible. Many of the codes presented in this paper are optimal or almost optimal. The results of this paper show that the shortening technique is very promising for constructing good codes. [ABSTRACT FROM AUTHOR]

This paper proposes a new probabilistic amplitude shaping (PAS) approach for concatenated two-level multi-level coding (MLC). The proposed system is based on a concatenated forward error correction (FEC) scheme where outer codes are serially concatenated with inner two-level MLC. This concatenated two-level MLC scheme has recently been shown to have a potential for achieving better performance-complexity trade-offs than the conventional bit-interleaved coded modulation (BICM). Meanwhile, PAS has recently been demonstrated to offer remarkable performance gains as well as rate adaptivity. However, the majority of existing works on PAS assume the use of the binary reflected Gray code as a bit-labeling, and its application to coded modulation schemes with other bit-labelings, such as two-level MLC, may not be straightforward. In this paper, we devise a bit-labeling scheme and propose a new PAS structure for an efficient integration of PAS with two-level MLC systems. More specifically, we propose to generate signed amplitude symbols with the distribution matcher (DM) for maximizing both coding and shaping gains achieved by two-level MLC and PAS, respectively, while the conventional PAS generates unsigned amplitude symbols. It is demonstrated by simulation results that, with 256QAM and inner polar codes, the proposed two-level MLC with PAS simultaneously offers 75% reduction in the number of required inner encoding and soft-decision (SD) decoding operations for given outer and inner FEC code lengths, and up to 0.3 dB performance gain over the conventional PAS scheme. [ABSTRACT FROM AUTHOR]

In this paper, we propose an optimization method for protograph-based spatially coupled low-density parity-check (SC-LDPC) codes under window decoding (WD). Previous works on constructing SC-LDPC codes for WD typically focused on optimizing asymptotic performance metrics such as the WD threshold. However, in this paper, it is observed that the WD threshold is not an appropriate metric to sufficiently explain the finite-length behavior of SC-LDPC codes under WD. Thus, we propose a new performance metric, called the window mean parameter, based on a scaling analysis to capture the WD performance more accurately and formulate a code optimization algorithm that optimizes the proposed performance metric. Since the proposed metric depends on the window size, the optimization algorithm can provide a code family of SC-LDPC codes optimized for various target window sizes. Simulation results confirm that the improvement in the proposed metric leads to a finite-length performance improvement, resulting in one to two orders of the frame error rate gain over the conventional SC-LDPC codes for a wide range of window sizes. Furthermore, we investigate structural characteristics of the proposed codes to provide a supplementary explanation for the performance improvement, which also promotes a better understanding of SC-LDPC codes for WD. [ABSTRACT FROM AUTHOR]

Linear codes with few weights have applications in consumer electronics, communications, data storage systems, secret sharing, authentication codes, and association schemes. As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure computation of data between two parties. The construction of minimal linear codes with new and desirable parameters is an interesting research topic in coding theory and cryptography. Recently, Mesnager et.al. stated that “constructing linear codes with good parameters from non-weakly regular bent functions is an interesting problem.” The goal of this paper is to construct linear codes with two or three weights from non-weakly regular bent functions over finite fields and analyze the minimality of the constructed linear codes. In doing so, we draw inspiration from a paper by Mesnager in which she constructed linear codes with small weights from weakly regular bent functions based on a generic construction method. First, we recall the definitions of the subsets $B_{+}(f)$ and $B_{-}(f)$ associated with a non-weakly regular bent function $f$. Next, we construct two- or three-weight linear $p$ -ary codes on these sets using duals of the non-weakly regular bent functions that are also bent. We note that the constructed linear codes are minimal in almost all cases. Moreover, when $f$ is a non-weakly regular bent function in a certain subclass of Generalized Maiorana-McFarland bent functions, we determine the weight distributions of the corresponding linear codes. As far as we know, the construction of linear codes from non-weakly regular bent functions over finite fields is first studied in the literature by the second author in his dissertation. [ABSTRACT FROM AUTHOR]

The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. They are widely used in data storage and communication systems. A subclass of attractive BCH codes is the narrow-sense BCH codes over the Galois field ${\mathrm {GF}}(q)$ with length $q+1$ , which are closely related to the action of the projective general linear group of degree two on the projective line. Despite its interest, not much is known about this class of BCH codes. This paper aims to study some of the codes within this class and specifically narrow-sense antiprimitive BCH codes (these codes are also linear complementary duals (LCD) codes that have interesting practical recent applications in cryptography, among other benefits). We shall use tools and combine arguments from algebraic coding theory, combinatorial designs, and group theory (group actions, representation theory of finite groups, etc.) to investigate narrow-sense antiprimitive BCH Codes and extend results from the recent literature. Notably, the dimension, the minimum distance of some $q$ -ary BCH codes with length $q+1$ , and their duals are determined in this paper. The dual codes of the narrow-sense antiprimitive BCH codes derived in this paper include almost MDS codes. Furthermore, the classification of ${\mathrm {PGL}}(2, p^{m})$ -invariant codes over ${\mathrm {GF}}(p^{h})$ is completed. As an application of this result, the $p$ -ranks of all incidence structures invariant under the projective general linear group ${\mathrm {PGL}}(2, p^{m})$ are determined. Furthermore, infinite families of narrow-sense BCH codes admitting a 3-transitive automorphism group are obtained. Via these BCH codes, a coding-theory approach to constructing the Witt spherical geometry designs is presented. The BCH codes proposed in this paper are good candidates for permutation decoding, as they have a relatively large group of automorphisms. [ABSTRACT FROM AUTHOR]

As the focus on embodied carbon within the built environment has grown in the U.S., local jurisdictional codes have increasingly proposed and implemented code language that requires the use of concrete mixtures that have reduced environmental impacts. This paper provides details about the various ways that localized sustainable concrete provisions have been proposed and implemented in the U.S., including limits on cement content and Global Warming Potential (GWP). These laws and code revisions vary in their measurement of low-carbon concrete and their exemptions and incentives. While the current version of the ACI Building Code, ACI 318-19, does allow for the consideration of sustainability in concrete design, specifics about how the relative sustainability of concrete mixtures and systems are to be measured and compared are not included. This paper addresses how the changing landscape of local jurisdictional codes is driving the development of future ACI 318 provisions to play a part in providing more consistency in the application of sustainable design practices in the United States. [ABSTRACT FROM AUTHOR]

Several sources of total cross sections for e+e− pair production by photon interaction with matter, used by major Monte Carlo codes for particle transport, are quantitatively evaluated with respect to experimental measurements collected from the literature. They include data libraries deriving from theoretical calculations and analytical formulae representing empirical fits to tabulations. Although most of these sources of cross sections are based on one theoretical reference, the statistical data analysis documented in this paper highlights differences in their compatibility with experiment. The cross sections collected in the 1997 version of the Evaluated Photon Data Library (EPDL) exhibit the lowest incompatibility with experiment; the paper details the validation results for all the examined cross section sources. The scarcity of experimental data does not allow the validation process to discern pair production in the field of the nucleus and in the field of atomic electrons; nevertheless, this paper documents relevant clues regarding the contribution of the latter to reproduce experimental measurements. [ABSTRACT FROM AUTHOR]

Conventional design methods of polar-coded modulation schemes aim to minimize the block error rate (BLER) under successive cancellation (SC) decoding. However, codes designed by conventional methods are not competitive under successive cancellation list (SCL) decoding. This paper presents a new design method based on the BLER upper bound under maximum-likelihood (ML) decoding (ML-BLER upper bound). The ML-BLER upper bound depends on the weight enumerating function (WEF) of the polar-coded modulation scheme over the squared Euclidean distance. In this paper, the polar-coded modulation is randomized by the concept of interleaved polar (i-polar) codes, and the WEF averaged over the ensemble of the polar-coded modulation schemes can be derived. Three polar-coded modulation schemes are considered, i.e., the bit-interleaved polar-coded modulation with a single interleaver (BIPCM-SI), the bit-interleaved polar-coded modulation with multiple interleavers (BIPCM-MI), and the multi-level polar-coded modulation (MLPCM). A new bit channel selection algorithm for polar-coded modulation schemes is proposed, which takes the polarization effect and the ML-BLER upper bound as design criteria. Design examples show that, under SCL decoding, the polar-coded modulation schemes (without CRC) with the proposed channel selection algorithm outperform those with conventional algorithms and are competitive as compared to the state-of-the-art 5G LDPC codes. [ABSTRACT FROM AUTHOR]

It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of antiprimitive BCH codes are given. The BCH codes presented in this paper have good parameters in general, containing many optimal linear codes. In particular, two open problems about the minimum distance of BCH codes of this type are partially solved in this paper. [ABSTRACT FROM AUTHOR]

This paper derives the optimal test channel distribution and the complete characterization of the classical Gorbunov and Pinsker (1973), Gorbunov and Pinsker (1974) nonanticipatory epsilon entropy of multivariate Gaussian Markov sources with square-error fidelity, which remained an open problem since 1974. The paper also formulates a state dependent nonanticipatory epsilon entropy, in which past reproductions are available to the decoder and not to the encoder, the test channel is specified with respect to an auxiliary (state) random process, and the reproduction process is a causal function of past reproduction and the auxiliary random process. This variation is analogous to the Wyner and Ziv (1976) and Wyner (1978) rate distortion function (RDF), of memoryless sources. It is shown that the operational rate of zero-delay codes, with past reproductions available to the decoder but not to the encoder is bounded below by the state dependent nonanticipatory epsilon entropy rate. For the case of multivariate Gaussian Markov sources with square-error fidelity, the optimal test channel distribution and the complete characterization of the state dependent of nonanticipatory epsilon entropy are derived, and also shown that that the two nonanticipatory epsilon entropies coincide. The derivations are new; they are based on structural properties of the stochastic realizations of the reproduction process that induce the optimal test channel distributions. They are derived using, achievable lower bounds on information theoretic measures, properties of mean-square estimation theory, Hadamard’s inequality, and canonical correlation coefficients of a tuple of multivariate jointly Gaussian random processes. Applications of the nonanticipatory epsilon entropy and its state dependent variation are discussed to the areas of control of unstable Gaussian systems over limited memory channels, design of causal estimators for Gaussian Markov sources with a fidelity criterion, computation of the rate loss of causal and zero-delay codes of Gaussian Markov sources with respect to non-causal codes. [ABSTRACT FROM AUTHOR]

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the users’ local caches. For the shared-link network with end-user-caches, Maddah-Ali and Niesen proposed a two-phase coded caching strategy. In practice, users may communicate with the server through intermediate relays. This paper studies the tradeoff between the memory size ${\mathsf M}$ and the network load ${\mathsf R}$ for the networks where a server with ${\mathsf N}$ files is connected to ${\mathsf H}$ relays (without caches), which in turn are connected to ${\mathsf K}$ users equipped with caches of ${\mathsf M}$ files. When each user is connected to a different subset of ${\mathsf r}$ relays, i.e., ${\mathsf K}= \binom {\mathsf H}{\mathsf r}$ , the system is referred to as a combination network with end-user-caches. In this work, converse bounds are derived for the practically motivated case of uncoded cache contents, that is, bits of the various files are directly pushed into the user caches without any coding. In this case, once the cache contents and the users’ demands are known, the problem reduces to a general index coding problem. This paper shows that relying on a well-known “acyclic index coding converse bound” results in converse bounds that are not tight for combination networks with end-user-caches. A novel converse bound that leverages the network topology is proposed, which is the tightest converse bound known to date. As a result of independent interest, an inequality that generalizes the well-known sub-modularity of entropy is derived. Several novel caching schemes are proposed, based on the Maddah-Ali and Niesen cache placement. These schemes leverage the structure of the combination network or/and perform interference elimination at the end-users. The proposed schemes are proved: (i) to be (order) optimal for some $({\mathsf N}, {\mathsf M}, {\mathsf H}, {\mathsf r})$ parameters regimes under the constraint of uncoded cache placement, and (ii) to outperform the state-of-the-art schemes in numerical evaluations. [ABSTRACT FROM AUTHOR]

A latest coding scheme named polarization‐adjusted convolutional (PAC) codes is shown to approach the dispersion bound for the code (128,64) under list decoding. However, to achieve the near‐bound performance, the list size of list decoding needs to be excessively large, which leads to insufferable time complexity. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. Four types of constituent nodes are defined and fast list decoding algorithms are provided for each of them. Simulation results present that fast list decoding with three types of constituent nodes can yield exactly the same error‐correction performance as list decoding, and reduce more than 50% time steps for the code (128,64). Moreover, fast list decoding with four types of constituent nodes can further reduce decoding complexity with negligible performance degradation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized pair weights of an $[n, k]$ -linear code over the finite field $\mathbb {F}_{q}$ and the notion of pair $r$ -equiweight codes, where $1\le r\le k-1$. Some basic properties of generalized pair weights of linear codes over finite fields are derived. We obtain a necessary and sufficient condition for an $[n,k]$ -linear code to be a pair equiweight code, and we characterize pair $r$ -equiweight codes for any $1\le r\le k-1$. A necessary and sufficient condition for a linear isomorphism to preserve pair weights between two linear codes is obtained. At the end of this paper, an application of generalized pair weights of linear codes to symbol-pair read wire-tap channels of type II is introduced. [ABSTRACT FROM AUTHOR]

In general coding theory, we often assume that error is observed in transferring or storing encoded symbols, while the process of encoding itself is error-free. Motivated by recent applications of coding theory, in this paper, we consider the case where the process of encoding is distributed and prone to error. We introduce the problem of distributed encoding, comprised of a set of $K \in \mathbb {N}$ isolated source nodes and $N \in \mathbb {N}$ encoding nodes. Each source node has one symbol from a finite field, which is sent to each of the encoding nodes. Each encoding node stores an encoded symbol from the same field, as a function of the received symbols. However, some of the source nodes are controlled by the adversary and may send different symbols to different encoding nodes. Depending on the number of the adversarial nodes, denoted by $\beta \in \mathbb {N}$ , and the cardinality of the set of symbols that each one generates, denoted by $v \in \mathbb {N}$ , the process of decoding from the encoded symbols could be impossible. Assume that a decoder connects to an arbitrary subset of $t \in \mathbb {N}$ encoding nodes and wants to decode the symbols of the honest nodes correctly, without necessarily identifying the sets of honest and adversarial nodes. An important characteristic of a distributed encoding system is $t^{*} \in \mathbb {N}$ , the minimum of such $t$ , which is a function of $K$ , $N$ , $\beta $ , and $v$. In this paper, we study the distributed linear encoding system, i.e. one in which the encoding nodes use linear coding. We show that $t^{*}_{\textrm {Linear}}=K+2\beta (v-1)$ , if $N\ge K+2\beta (v-1)$ , and $t^{*}_{\textrm {Linear}}=N$ , if $N\le K+2\beta (v-1)$. In order to achieve $t^{*}_{\textrm {Linear}}$ , we use random linear coding and show that in any feasible solution that the decoder finds, the messages of the honest nodes are decoded correctly. In order to prove the converse of the fundamental limit, we show that when the adversary behaves in a particular way, it can always confuse the decoder between two feasible solutions that differ in the message of at least one honest node. [ABSTRACT FROM AUTHOR]

This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n \times n$ array can experience deletions of rows and columns. These deletion errors are referred to as $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletions if ${t_{\mathrm {r}}}$ rows and ${t_{\mathrm {c}}}$ columns are deleted, while a code correcting these deletion patterns is called a $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletion correction code. The definitions for criss-cross insertions are similar. It is first shown that when $t_{r}=t_{c}$ the problems of correcting criss-cross deletions and criss-cross insertions are equivalent. The focus of this paper lies on the case of (1, 1)-criss-cross deletions. A non-asymptotic upper bound on the cardinality of (1, 1)-criss-cross deletion correction codes is shown which assures that the redundancy is at least $2n-3+2\log n$ bits. A code construction with an existential encoding and an explicit decoding algorithm is presented. The redundancy of the construction is at most $2n+4 \log n + 7 +2 \log e$. A construction with explicit encoder and decoder is presented. The explicit encoder adds an extra $5\log n + 5$ bits of redundancy to the construction. [ABSTRACT FROM AUTHOR]

Traces of MPI communications are used by many performance analysis and visualization tools. Storing exhaustive traces of large-scale MPI applications is infeasible, however, because of their large volume. Aggregated or lossy MPI traces are smaller but provide much less information. In this paper we present Pilgrim, a near-lossless MPI tracing tool that, by using sophisticated compression techniques, generates small trace files at large scales and incurs only moderate overheads. We perform comprehensive studies of various compression techniques used for storing timestamps associated with each call. This timing information is essential for analysis purposes such as skews study. To demonstrate the usefulness of the detailed information stored by Pilgrim, we present a proxy application generator that can generate proxy apps that preserve original communication patterns from the Pilgrim traces. [ABSTRACT FROM AUTHOR]

Despite being widely used as a performance measure for visual detection tasks, Average Precision (AP) is limited in (i) reflecting localisation quality, (ii) interpretability and (iii) robustness to the design choices regarding its computation, and its applicability to outputs without confidence scores. Panoptic Quality (PQ), a measure proposed for evaluating panoptic segmentation (Kirillov et al., 2019), does not suffer from these limitations but is limited to panoptic segmentation. In this paper, we propose Localisation Recall Precision (LRP) Error as the average matching error of a visual detector computed based on both its localisation and classification qualities for a given confidence score threshold. LRP Error, initially proposed only for object detection by Oksuz et al. (2018), does not suffer from the aforementioned limitations and is applicable to all visual detection tasks. We also introduce Optimal LRP (oLRP) Error as the minimum LRP Error obtained over confidence scores to evaluate visual detectors and obtain optimal thresholds for deployment. We provide a detailed comparative analysis of LRP Error with AP and PQ, and use nearly 100 state-of-the-art visual detectors from seven visual detection tasks (i.e. object detection, keypoint detection, instance segmentation, panoptic segmentation, visual relationship detection, zero-shot detection and generalised zero-shot detection) using ten datasets to empirically show that LRP Error provides richer and more discriminative information than its counterparts. Code available at: https://github.com/kemaloksuz/LRP-Error. [ABSTRACT FROM AUTHOR]

Despite being widely used as a performance measure for visual detection tasks, Average Precision (AP) is limited in (i) reflecting localisation quality, (ii) interpretability and (iii) robustness to the design choices regarding its computation, and its applicability to outputs without confidence scores. Panoptic Quality (PQ), a measure proposed for evaluating panoptic segmentation (Kirillov et al., 2019), does not suffer from these limitations but is limited to panoptic segmentation. In this paper, we propose Localisation Recall Precision (LRP) Error as the average matching error of a visual detector computed based on both its localisation and classification qualities for a given confidence score threshold. LRP Error, initially proposed only for object detection by Oksuz et al. (2018), does not suffer from the aforementioned limitations and is applicable to all visual detection tasks. We also introduce Optimal LRP (oLRP) Error as the minimum LRP Error obtained over confidence scores to evaluate visual detectors and obtain optimal thresholds for deployment. We provide a detailed comparative analysis of LRP Error with AP and PQ, and use nearly 100 state-of-the-art visual detectors from seven visual detection tasks (i.e. object detection, keypoint detection, instance segmentation, panoptic segmentation, visual relationship detection, zero-shot detection and generalised zero-shot detection) using ten datasets to empirically show that LRP Error provides richer and more discriminative information than its counterparts. Code available at: https://github.com/kemaloksuz/LRP-Error. [ABSTRACT FROM AUTHOR]

Neuroimaging experiments in general, and EEG experiments in particular, must take care to avoid confounds. A recent TPAMI paper uses data that suffers from a serious previously reported confound. We demonstrate that their new model and analysis methods do not remedy this confound, and therefore that their claims of high accuracy and neuroscience relevance are invalid. [ABSTRACT FROM AUTHOR]

Edge systems are required to autonomously make real-time decisions based on large quantities of input data under strict power, performance, area, and other constraints. Meeting these constraints is only possible by specializing systems through hardware accelerators purposefully built for machine learning and data analysis algorithms. However, data science evolves at a quick pace, and manual design of custom accelerators has high non-recurrent engineering costs: general solutions are needed to automatically and rapidly transition from the formulation of a new algorithm to the deployment of a dedicated hardware implementation. Our solution is the SOftware Defined Architectures (SODA) Synthesizer, an end-to-end, multi-level, modular, extensible compiler toolchain providing a direct path from machine learning tools to hardware. The SODA Synthesizer frontend is based on the multilevel intermediate representation (MLIR) framework; it ingests pre-trained machine learning models, identifies kernels suited for acceleration, performs high-level optimizations, and prepares them for hardware synthesis. In the backend, SODA leverages state-of-the-art high-level synthesis techniques to generate highly efficient accelerators, targeting both field programmable devices (FPGAs) and application-specific circuits (ASICs). In this paper, we describe how the SODA Synthesizer can also assemble the generated accelerators (based on the finite state machine with datapath model) in a custom system driven by a distributed controller, building a coarse-grained dataflow architecture that does not require a host processor to orchestrate parallel execution of multiple accelerators. We show the effectiveness of our approach by automatically generating ASIC accelerators for layers of popular deep neural networks (DNNs). Our high-level optimizations result in up to 74x speedup on isolated accelerators for individual DNN layers, and our dynamically scheduled architecture yields an additional 3x performance improvement when combining accelerators to handle streaming inputs. [ABSTRACT FROM AUTHOR]

In this work, we consider the leakage-resilience of algebraic-geometric (AG for short) codes based ramp secret sharing schemes extending the analysis on the leakage-resilience of linear threshold secret sharing schemes over prime fields that is done by Benhamouda et al. in the effort to construct linear leakage-resilient secret sharing schemes with constant share size. Since there does not exist any explicit efficient construction of AG codes over prime fields with constant field size, we consider constructions over prime fields with the help of concatenation method and constructions of codes over field extensions. Extending the Fourier analysis done by Benhamouda et al., one can show that concatenated algebraic geometric codes over prime fields do produce some nice leakage-resilient secret sharing schemes. One natural and curious question is whether AG codes over extension fields produce better leakage-resilient secret sharing schemes than the construction based on concatenated AG codes. Such construction provides several advantage compared to the construction over prime fields using concatenation method. It is clear that AG codes over extension fields give secret sharing schemes with a smaller reconstruction threshold for a fixed privacy parameter $t$. In this work, it is also confirmed that indeed AG codes over extension fields have stronger leakage-resilience under some reasonable assumptions. Furthermore, we also show that AG codes over extension fields may provide strong multiplicative property which may be used in its application to the study of multiparty computation. In contrast, the same cannot be said for constructions based on concatenated AG codes, even when we are considering multiplication friendly embeddings. These advantages strongly motivate the study of secret sharing schemes from AG codes over extension fields. The current paper has two main contributions: (i) we obtain leakage-resilient secret sharing schemes with constant share sizes and unbounded numbers of players. Some of the schemes constructed without the use of concatenation also possesses strong multiplicative property (ii) via Fourier Analysis, we analyze the leakage-resilience of secret sharing schemes from codes over extension fields. This is of its own theoretical interest independent of its application to secret sharing schemes from algebraic geometric codes over extension fields. [ABSTRACT FROM AUTHOR]

The binary quadratic-residue codes and the punctured Reed-Muller codes ${\mathcal {R}}_{2}((m-1)/2, m))$ are two families of binary cyclic codes with parameters $[n, (n+1)/2, d \geq \sqrt {n}]$. These two families of binary cyclic codes are interesting partly due to the fact that their minimum distances have a square-root bound. The objective of this paper is to construct two families of binary cyclic codes of length $2^{m}-1$ and dimension near $2^{m-1}$ with good minimum distances. When $m \geq 3$ is odd, the codes become a family of duadic codes with parameters $[2^{m}-1, 2^{m-1}, d]$ , where $d \geq 2^{(m-1)/2}+1$ if $m \equiv 3 \pmod {4}$ and $d \geq 2^{(m-1)/2}+3$ if $m \equiv 1 \pmod {4}$. The two families of binary cyclic codes contain some optimal binary cyclic codes. [ABSTRACT FROM AUTHOR]

We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $P $ and $N $ respectively, the list decoding capacity is equal to $\frac {1}{2}\log \frac {P}{N}$. Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain conjecture that originates in analytic number theory is true, then the list size grows as a polynomial function of the gap-to-capacity. [ABSTRACT FROM AUTHOR]

Twisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are non-equivalent to generalized Reed-Solomon (GRS) codes. In this paper, we characterize a sufficient and necessary condition that a twisted Reed-Solomon (TRS) code with two twists is MDS; give a sufficient and necessary condition that a TGRS code with two twists is self-dual, and present some constructions of self-dual TGRS codes. These self-dual codes are MDS, NMDS or 2-MDS. Furthermore, we study the non-GRS properties of TGRS codes with two twists and prove that these codes are non-GRS in most cases. [ABSTRACT FROM AUTHOR]

In he past decade, object detection has achieved significant progress in natural images but not in aerial images, due to the massive variations in the scale and orientation of objects caused by the bird’s-eye view of aerial images. More importantly, the lack of large-scale benchmarks has become a major obstacle to the development of object detection in aerial images (ODAI). In this paper, we present a large-scale Dataset of Object deTection in Aerial images (DOTA) and comprehensive baselines for ODAI. The proposed DOTA dataset contains 1,793,658 object instances of 18 categories of oriented-bounding-box annotations collected from 11,268 aerial images. Based on this large-scale and well-annotated dataset, we build baselines covering 10 state-of-the-art algorithms with over 70 configurations, where the speed and accuracy performances of each model have been evaluated. Furthermore, we provide a code library for ODAI and build a website for evaluating different algorithms. Previous challenges run on DOTA have attracted more than 1300 teams worldwide. We believe that the expanded large-scale DOTA dataset, the extensive baselines, the code library and the challenges can facilitate the designs of robust algorithms and reproducible research on the problem of object detection in aerial images. [ABSTRACT FROM AUTHOR]

Android malware is an ongoing threat to billions of smart devices’ security, ranging from mobile phones to car infotainment systems. Despite numerous approaches and previous studies to develop solutions for detecting and preventing Android malware, the rapid continuous development of new malware variants requires a careful reconsideration and the development of effective methods to identify malware families given a meager number of malware instances. In this paper, we present DroidMalVet, a novel Android malware family classification and detection approach that does not require to perform complex program analyses or utilize large feature sets. DroidMalVet is the first to use a promising, diverse, and small set of software metrics as features in a supervised learning platform to classify and detect various Android malware families. Our extensive empirical evaluations on two large public malware datasets show that DroidMalVet accurately detects both small and large malware families with F-Score accuracy of 94.4% and 96%, and AUC equal to 99.5% and 99.7% on the malware families in Drebin and AMD datasets, respectively. Moreover, our results demonstrate the superior performance of DroidMalVet in detecting small families (i.e., families with few samples). DroidMalVet complements existing approaches and presents an early warning tool for detecting known and emerging malware families. [ABSTRACT FROM AUTHOR]

The growing number of Internet of Thing (IoT) and Ultra-Reliable Low Latency Communications (URLCC) use cases in next generation communication networks calls for the development of efficient Forward Error Correction (FEC) mechanisms. These use cases usually imply using short to mid-sized information blocks and requires low-complexity and/or fast decoding procedures. This paper investigates the joint learning of short to mid block-length coding schemes and associated Belief-Propagation (BP) like decoders using Machine Learning (ML) techniques. An interpretable auto-encoder (AE) architecture is proposed, ensuring scalability to block sizes currently challenging for ML-based linear block code design approaches. By optimizing a coding scheme w.r.t. the targeted decoder, the proposed system offers a good complexity/performance trade-off compared to various codes from literature with length up to 128 bits. [ABSTRACT FROM AUTHOR]

The problem of computing the Hamming weight distribution of linear codes is considered in this paper. A novel method to enumerate all codewords up to a certain Hamming weight for binary linear block codes in general and in particular for the punctured, shortened, precoded polar codes is introduced. The proposed approach performs a recursive decomposition of the codes using construction X4 that is typically used to combine codes of different lengths. This allows to enumerate the low-weight codewords of the overall code as combinations of the low-weight codewords of the component codes. Numerical results show that the proposed approach can efficiently compute the exact partial weight distribution of the 5G New Radio punctured/shortened polar codes with CRC11 and pure polar codes. In the former and latter cases, the low-weight codeword number is up to 106 and 108, respectively. Besides, randomly punctured and shortened polar codes and randomly precoded polar codes are also considered. To the best of the authors’ knowledge, this is the first method able to solve these problems. [ABSTRACT FROM AUTHOR]

This paper studies low-latency streaming codes for the multi-hop network. The source transmits a sequence of messages to a destination through a chain of relays, and requires the destination to reconstruct each message by its deadline. We assume that each communication link is subjected to a certain maximum number of packet erasures. The case of a single relay (a three-node network) was considered in Fong et al. (2020). A coding scheme known as symbol-wise decode and forward was proposed. In the present work, we propose an alternative scheme that is different from Fong et al. (2020) and still achieves the same rate as in Fong et al. (2020) for the one hop case as the field-size goes to infinity. Furthermore, our proposed scheme naturally generalizes to the case of multiple-relay nodes yielding new achievable rates for this setting. The main difference with Fong et al. (2020) is that our proposed scheme exploits the ability of the relay nodes to adapt the transmission based on the erasures on the previous link. Hence, we refer to our scheme as “state-dependent” and contrast it with the scheme in Fong et al. (2020) that is state-independent. Our scheme requires the relay nodes to append a header to the transmitted packets, and we show that the size of the header does not depend on the field-size of the code. We also derive an upper bound on the maximal streaming rate achievable over a network with an arbitrary number of relays. We show that this upper bound matches our achievable rate in the special case when the maximal number of erasures on the first link is greater than or equal to the maximal number of erasures on each of the following links, and the field size goes to infinity. [ABSTRACT FROM AUTHOR]

An $(m,n,a,b)$ -tensor code consists of $m\times n$ matrices whose columns satisfy ‘ $a$ ’ parity checks and rows satisfy ‘ $b$ ’ parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in distributed storage because a single erasure can be corrected quickly either by reading its row or column. Maximally Recoverable (MR) Tensor Codes, introduced by Gopalan et al., are tensor codes which can correct every erasure pattern that is information theoretically possible to correct. The main questions about MR Tensor Codes are characterizing which erasure patterns are correctable and obtaining explicit constructions over small fields. In this paper, we study the important special case when $a=1$ , i.e., the columns satisfy a single parity check equation. We introduce the notion of higher order MDS codes ($\mathrm {MDS}(\ell)$ codes) which is an interesting generalization of the well-known MDS codes, where $\ell $ captures the order of genericity of points in a low-dimensional space. We then prove that a tensor code with $a=1$ is MR if the row code is an $\mathrm {MDS}(m)$ code. We then show that $\mathrm {MDS}(m)$ codes satisfy some weak duality. Using this characterization and duality, we prove that $(m,n,a=1,b)$ -MR tensor codes require fields of size $q=\Omega _{m,b}(n^{\min \{b,m\}-1})$. Our lower bound also extends to the setting of $a>1$. We also give a deterministic polynomial time algorithm to check if a given erasure pattern is correctable by the MR tensor code (when $a=1$). [ABSTRACT FROM AUTHOR]