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In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O([M.sup.-1]), while such ratio for the original greedy scheduler is O(M), where Mis the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible. Index Terms--Efficient greedy scheduler, multiple-input multiple-output (MIMO), vector Gaussian broadcast channel (GBC), zero-forcing dirty-paper coding (ZF-DPC), QR factorization by Householder transformation.

Recently, there has been a lot of success in using the deterministic approach to provide approximate characterization of Gaussian network capacity. In this paper, we take a deterministic view and revisit the problem of wiretap channel with side information. A precise characterization of the secrecy capacity is obtained for a linear deterministic model, which naturally suggests a coding scheme which we show to achieve the secrecy capacity of the degraded Gaussian model (dubbed as “secret writing on dirty paper”) to within half a bit. [ABSTRACT FROM PUBLISHER]

Abstract: Costa''s dirty paper coding (DPC) offers a good framework for precoding for transmission over additive Gaussian channels with additive states non-causally known at the transmitter but not at the receiver. In this paper, rate calculation, error probability analysis and code design for DPC are investigated from a practical point-of-view. Based on Monte-Carlo numerical integration and simulations, we first show that the gap to the full AWGN capacity can be partially bridged using some finite-dimensional lattices with good packing and quantizing properties. Then the difficult problem of codebook selection is addressed through some illustrative examples. Analysis sheds light on the dual roles of “packing” and “shaping” as well as on their inter-connection at finite-dimensional coding, by opposition to the asymptotic case (i.e., infinite dimension) where the two coding components are decoupled. [Copyright &y& Elsevier]

This paper examines near-capacity dirty-paper code designs based on source-channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat-accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity. [ABSTRACT FROM AUTHOR]

The "writing on dirty paper"-channel model offers an information-theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter. It indicates that lossless precoding is theoretically possible at any signal-to-noise ratio (SNR), and thus dirty-paper coding may serve as a basic building block in both single-user and multiuser communication systems. We design an end-to-end coding realization of a system materializing a significant portion of the promised gains. We employ multidimensional quantization based on trellis shaping at the transmitter. Coset decoding is implemented at the receiver using "virtual bits." Combined with iterative decoding of capacity-approaching codes we achieve an improvement of 2 dB over the best scalar quantization scheme. Code design is done using the EXIT chart technique. [ABSTRACT FROM AUTHOR]

We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme. [ABSTRACT FROM PUBLISHER]

This paper investigates an optimization of the conventional relay selection for multirelay environments. In contrast with previously reported selection schemes, where a selected relay accesses the channel in a dedicated cooperative slot, the proposed scheme recovers the bandwidth loss of the half-duplex constraint by allowing two relays to simultaneously access the channels. Based on an appropriate dirty-paper coding (DPC) technique among relays, the proposed scheme enables a relay to establish communication with the destination at the same time that another relay forwards the data from the source. It is proven that the interplay between relay selection and the superposition DPC weight factor provides a tradeoff between relaying and new data performance. Hence, an appropriate codesign of the superposition DPC parameter and opportunistic relay selection can achieve efficient communication for the new data without affecting the relaying performance. The proposed scheme is compared with conventional relaying approaches, and its enhancements are provided through theoretical studies and numerical results. [ABSTRACT FROM AUTHOR]

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper, we elaborate on the implication of these parameters and devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes, our bound is often tight. Furthermore, for these codes, the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights. [ABSTRACT FROM AUTHOR]

We derive the capacity region of the two-user dirty-paper Gaussian multiaccess channel (MAC) with conferencing encoders. In this MAC, prior to each transmission block, the transmitters can hold a conference in which they can communicate with each other over error-free bit pipes of given capacities. The received signal suffers not only from additive Gaussian noise but also from additive interference, which is known noncausally to the transmitters but not to the receiver. The additive interference is modeled as Gaussian or uniform over a sphere. We show that the interference can be perfectly mitigated, i.e., that the capacity region without interference can also be achieved in its presence. This holds irrespective of whether the transmitters learn the interference before or after the conference. It follows as a corollary that also for the MAC with degraded message sets, the interference can be perfectly mitigated if it is known noncausally to the transmitters. To derive our results, we generalize Costa's single-user writing-on-dirty-paper achievability result to channels with dependent interference and not-necessarily Gaussian noise. [ABSTRACT FROM AUTHOR]

A dirty-paper channel is considered, where the transmitter knows the interference sequence up to a constant multiplicative factor, known only to the receiver. Lower bounds on the achievable rate of communication are derived by proposing a coding scheme that partially compensates for the imprecise channel knowledge. We focus on a communication scenario where the signal-to-noise ratio is high. Our approach is based on analyzing the performance achievable using lattice-based coding schemes. When the power of the interference is finite, we show that the achievable rate of this lattice-based coding scheme may be improved by a judicious choice of the scaling parameter at the receiver. We further show that the communication rate may be improved, for finite as well as infinite interference power, by allowing randomized scaling at the transmitter. [ABSTRACT FROM AUTHOR]

In the paper Patterson – Wiedemann construction revisited by Gangopadhyay et al. (2006), modifying an idempotent function f : G F ( 2 21 ) → G F ( 2 ) , which corresponds to a ( 337 , ( 127 ) ( 49 ) ) -interleaved sequence whose columns are either all 0’s or 1’s, a balanced function h having Δ h < 2 21 + 1 2 is obtained. In this short note, we find that Δ f is computed incorrectly in their paper (leading to Δ h ≮ 2 21 + 1 2 ) and correct their result by disproving the related conjecture for the 21-variable balanced functions. [ABSTRACT FROM AUTHOR]

The authors propose a joint dirty-paper coding (DPC) and beamforming scheme for use in multiuser multiple-input multiple-output (MIMO) systems. Unlike conventional maximum likelihood (ML)-based DPC schemes, this joint DPC and beamforming precoding scheme is intended as a suboptimal strategy in that it cancels only causal interference, thus offering a practical implementation option. In addition, a signal-to-interference plus noise ratio (SINR)-based ordering strategy that can be readily applied to conventional DPC schemes is also proposed as a way of improving the performance of the joint precoding scheme. The proposed schemes markedly improve classical spatial division multiple access (SDMA), and achieve the same data rates as spatial multiplexing (SM) for all users, but with significantly superior performance/diversity gain. When the number of active users per sector is much greater than the number of transmit antennas, the proposed schemes are able to achieve enough multiuser diversity to asymptotically approach the optimal DPC capacity. In addition, unlike BLAST, the receivers do not need to know each other's vector channels. Simulation results confirm that the proposed schemes provide significant gain over conventional zero-forcing SDMA in terms of average sector throughput for downlink multi-cell multiuser systems and symbol error rate as well. Finally, the proposed interference cancellation strategies at the transmitter can be expandable to MIMO systems with any number of multiple antennas. [ABSTRACT FROM AUTHOR]

Focuses on the article "Cones, Curves, Shells, Towers: He Made Paper Jump to Life," by Margaret Wertheim, published in the June 22, 2004 issue of "The New York Times." Twists on the ancient art of origami; Contemporary field of computational origami which include computational geometry, number theory, coding theory and linear algebra.

The purpose of this study is to review journal papers on educational big data research published from 2010 to 2018. A total of 143 papers were selected. The papers were characterized based on three dimensions: (a) educational goals; (b) educational problems addressed; and (c) big data analytical techniques used. A qualitative content analysis approach was conducted to develop a coding scheme for analyzing the selected papers. The results identified four types of educational goals, with a clear predominance of quality assurance. The identification of the most mentioned educational problems resulted in four main concerns: the lack of detecting student behavior modeling and waste of resources; inappropriate curricula and teaching strategies; oversights of quality assurance; and privacy and ethical issues. Concerning the most mentioned big data analytical techniques, the coding scheme revealed that the majority of the papers focused on the educational data mining technique followed by the learning analytics technique. The visual analytics technique was mentioned in a few papers. The results also indicated that the educational data mining technique is the most suitable technique to use for quality assurance and to provide potential solutions for the lack of detecting student behavior modeling and the waste of resources in institutions. [ABSTRACT FROM AUTHOR]

The paper lists the main open questions left in the area both theoretically and practically, mainly related with the inherent tension between communication efficiency and quality of assumptions in proof systems. This special issue of Designs, Codes and Cryptography on the topic Mathematics of Zero-Knowledge aims at encouraging mathematicians and computer scientists with a strong interest in Mathematics to contribute to the burgeoning topic of zero-knowledge proofs. [Extracted from the article]

Purpose: There is a growing need for methodological plurality in advancing operations management (OM), especially with the emergence of machine learning (ML) techniques for analysing extensive textual data. To bridge this knowledge gap, this paper introduces a new methodology that combines ML techniques with traditional qualitative approaches, aiming to reconstruct knowledge from existing publications. Design/methodology/approach: In this pragmatist-rooted abductive method where human-machine interactions analyse big data, the authors employ topic modelling (TM), an ML technique, to enable constructivist grounded theory (CGT). A four-step coding process (Raw coding, expert coding, focused coding and theory building) is deployed to strive for procedural and interpretive rigour. To demonstrate the approach, the authors collected data from an open-source professional project management (PM) website and illustrated their research design and data analysis leading to theory development. Findings: The results show that TM significantly improves the ability of researchers to systematically investigate and interpret codes generated from large textual data, thus contributing to theory building. Originality/value: This paper presents a novel approach that integrates an ML-based technique with human hermeneutic methods for empirical studies in OM. Using grounded theory, this method reconstructs latent knowledge from massive textual data and uncovers management phenomena hidden from published data, offering a new way for academics to develop potential theories for business and management studies. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the simple current orbifold of a rational Narain CFT (Narain RCFT). This is a method of constructing other rational CFTs from a given rational CFT, by 'orbifolding' the global symmetry formed by a particular primary fields (called the simple current). Our main result is that a Narain RCFT satisfying certain conditions can be described in the form of a simple current orbifold of another Narain RCFT, and we have shown how the discrete torsion in taking that orbifold is obtained. Additionally, the partition function can be considered a simple current orbifold with discrete torsion, which is determined by the lattice and the B-field. We establish that the partition function can be expressed as a polynomial, with the variables substituted by certain q -series. In a specific scenario, this polynomial corresponds to the weight enumerator polynomial of an error-correcting code. Using this correspondence to the code theory, we can relate the B-field, the discrete torsion, and the B-form to each other. [ABSTRACT FROM AUTHOR]

In this paper, we extend the localized error correction code introduced by L. A. Bassalygo and coworkers from Hamming space to projective space. For constant dimensional localized error correction codes in projective space, we have a lower bound and an upper bound of the capacity, which are asymptotically tight when z< x\leq n-z\over 2, where x, z, and n are dimensions of codewords, error configurations, and the ground space, respectively. We determine the capacity of nonconstant dimensional localized error correction codes when z < n\over 3. [ABSTRACT FROM PUBLISHER]

Explores several studies on convolutional codes which claim different codes to be optimum under the optimum distance spectrum criterion. Definitions and search criterion; Inconsistencies in the studies by Bocharova and Kudryashov and Chang, Hwang and Lin.

Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory. [ABSTRACT FROM AUTHOR]

The article focuses on the dirty-paper coding (DPC) problem of Max Costa in network information theory. It offered a notation showing the capacity of the Gel'fand-Pinsker channel. Also illustrated is the Gaussian version of the problem known as writing on dirty paper. It also listed the different steps showing the proof sketch of the theorem namely codebook generation, encoding, decoding, and analysis of error probability.

In 1998 Crandall introduced a method based on coding theory to secretly embed a message in a digital support such as an image. Later, in 2005, Fridrich et al. improved this method to minimize the distortion introduced by the embedding; a process called wet paper. However, as previously emphasized in the literature, this method can fail during the embedding step. Here we and sufficient and necessary conditions to guarantee a successful embedding, by studying the dual distance of a linear code. Since these results are essentially of combinatorial nature, they can be generalized to systematic codes, a large family containing all linear codes. We also compute the exact number of embedding solutions and point out the relationship between wet paper codes and orthogonal arrays. [ABSTRACT FROM AUTHOR]

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In image steganography, a pixel can carry secret bits by choosing adding/subtracting one to/from the gray value. This kind of"±1 steganography" can hide a longer message than simple LSB embedding. We propose a double-layered embedding method for implementing "±1 steganography," in which binary covering codes and wet paper codes are used to hide messages in the LSB plane and the second LSB plane, respectively. We show that this method can achieve the upper bound on the embedding efficiency of"±1 steganography" when the employed binary covering codes reach the upper bound on that of LSB steganography. Applications using random and structured covering codes show that the new method outperforms previous ones and can approach the upper bound. [ABSTRACT FROM AUTHOR]

Recently, the vector dirty paper coding (DPC) achievable rate region has been shown to be the capacity region of a multiple-input multiple-output Gaussian broadcast channel (MIMO GBC). With DPC, the multiuser interference noncausally known at the transmitter can be completely removed. In this paper, we present a vector DPC structure for MIMO GBC. It is a generalization of the single antenna superposition dirty paper coding for the scalar Gaussian dirty paper problem proposed by Bennatan et al. In a theoretical random code setting, this construction is shown to be able to achieve the promised rate performance of the MIMO GBC. We also implement it with existing vector quantizer and capacity-achieving channel coding. "Combined with iterative decoding, a design example validates the effectiveness of our methods. [ABSTRACT FROM AUTHOR]