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In this paper, capacity bounds for the two-user interference channels with cooperative receivers via conferencing links of finite capacities are investigated. Capacity results known for these communication scenarios are limited to a very few special cases of the one-sided channels. One of the challenges in obtaining capacity limits of such cooperative networks is how to establish efficient capacity outer bounds for them. In this paper, by applying new techniques, novel capacity outer bounds are established for the interference channels with conferencing receivers. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A conferencing link (between receivers) may be utilized to provide a receiver with “information about its desired signal” or “information about its interfering signal”. It is demonstrated that both strategies can be helpful to achieve capacity. Finally, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse. [ABSTRACT FROM AUTHOR]

In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this paper, using quantum mass functions, we discuss the realization of measurements in terms of unitary interactions and marginalizations. It follows that classical measurement results strictly belong to local models, i.e., marginals of more detailed models. Classical variables that are created by marginalization do not exist in the unmarginalized model, and different marginalizations may yield incompatible classical variables. These observations are illustrated by the Frauchiger–Renner paradox, which is analyzed (and resolved) in terms of quantum mass functions. Throughout, the paper uses factor graphs to represent quantum systems/models with multiple measurements at different points in time. [ABSTRACT FROM AUTHOR]

Boolean functions, coding theory and $t$ -designs have close connections and interesting interplay. A standard approach to constructing $t$ -designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the automorphism groups are two ways for proving that a code has sufficient regularity for supporting $t$ -designs. However, some linear codes hold $t$ -designs, although they do not satisfy the conditions in the Assmus-Mattson Theorem and do not admit a $t$ -transitive or $t$ -homogeneous group as a subgroup of their automorphisms. The major objective of this paper is to develop a theory for explaining such codes and obtaining such new codes and hence new $t$ -designs. To this end, a general theory for punctured and shortened codes of linear codes supporting $t$ -designs is established, a generalized Assmus-Mattson theorem is developed, and a link between 2-designs and differentially $\delta $ -uniform functions and 2-designs is built. With these general results, binary codes with new parameters and explicit weight distributions are obtained, new 2-designs and Steiner system $S(2, 4, 2^{n})$ are produced in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we first present two systematic constructions of bent functions by modifying the truth tables of Rothaus’s bent function and Maiorana-McFarland’s bent function respectively. The number of the newly constructed bent functions by modifying the truth table of Rothaus’s bent function is also determined. The methods of constructing self-dual bent functions are then given after the dual functions of these bent functions being determined. Finally, as an application, two constructions of 2-rotation symmetric bent functions are presented in this paper. [ABSTRACT FROM AUTHOR]

This paper studies the Pliable Index CODing problem (PICOD), which models content-type distribution networks. In the PICOD $({t})$ problem there are ${m}$ messages, ${n}$ users and each user has a distinct message side information set, as in the classical Index Coding problem (IC). Differently from IC, where each user has a pre-specified set of messages to decode, in the PICOD $({t})$ a user is “pliable” and is satisfied if it can decode any ${t}$ messages that are not in its side information set. The goal is to find a code with the shortest length that satisfies all the users. This flexibility in determining the desired message sets makes the PICOD $({t})$ behave quite differently compared to the IC, and its analysis even more challenging. This paper mainly focuses on the complete– ${S}$ PICOD $({t})$ with ${m}$ messages, where the set ${S}\subset [{m}]$ contains the sizes of the side information sets, and the number of users is ${n}=\sum _{s\in {S}}\binom {m} {s}$ , with no two users having the same side information set. Capacity results are shown for: (i) the consecutive complete– ${S}$ PICOD $({t})$ , where ${S}=[{s}_{\text {min}}:{s}_{\text {max}}]$ for some $0 \leqslant {s}_{\text {min}}\leqslant {s}_{\text {max}} \leqslant {m}-{t}$ , and (ii) the complement-consecutive complete– ${S}$ PICOD $({t})$ , where ${S}=[0: {m}-{t}]\backslash [{s}_{\text {min}}:{s}_{\text {max}}]$ , for some $0 < {s}_{\text {min}}\leqslant {s}_{\text {max}} < {m}-{t}$. The novel converse proof is inspired by combinatorial design techniques and the key insight is to consider all messages that a user can eventually decode successfully, even those in excess of the ${t}$ required ones. This allows one to circumvent the need to consider all possible desired message set assignments at the users in order to find the one that leads to the shortest code length. The core of the novel proof is to solve the critical complete– ${S}$ PICOD $({t})$ with ${m} = 2{s}+{t}$ messages and ${S}=\{{s}\}$ , by showing the existence of a user who can decode ${s}+{t}$ messages regardless of the desired message set assignment. All other tight converse results for the complete– ${S}$ PICOD $({t})$ can be deduced from this critical case. The converse results show the information theoretic optimality of simple linear coding schemes. By similar reasoning, all complete– ${S}$ PICOD $({t})$ where the number of messages is ${m}\leqslant 5$ can be fully characterized. In addition, tight converse results are also shown for the PICOD(1) with circular-arc network topology hypergraph. [ABSTRACT FROM AUTHOR]

The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In this paper, we prove that in order to determine a pair of generic signals uniquely, up to trivial ambiguities, the number of phaseless measurements one needs to collect is, at most, five times the number of parameters required to describe the signals. This result improves significantly upon previous papers, which required the number of measurements to be quadratic in the number of parameters rather than linear. In addition, we consider the simpler problem of recovering a pair of generic signals from their blind short-time Fourier transform, when the phases are known. In this setting, which can be understood as a special case of the blind deconvolution problem, we show that the number of measurements required to determine the two signals, up to trivial ambiguities, equals exactly the number of parameters to be recovered. As a side result, we study the classical phase retrieval problem—that is, recovering a signal from its Fourier magnitudes—when some entries of the signal are known a priori. We derive a bound on the number of required measurements as a function of the size of the set of known entries. Specifically, we show that if most of the signal’s entries are known, then only a few Fourier magnitudes are necessary to determine a signal uniquely. [ABSTRACT FROM AUTHOR]

Let $\mathbb {F}_{q}$ be the finite field of $q$ elements. In this paper we obtain bounds on the following counting problem: given a polynomial $f(x)\in \mathbb {F}_{q} [x]$ of degree $k+m$ and a non-negative integer $r$ , count the number of polynomials $g(x)\in \mathbb {F}_{q} [x]$ of degree at most $k-1$ such that $f(x)+g(x)$ has exactly $r$ roots in $\mathbb {F}_{q}$. Previously, explicit formulas were known only for the cases $m=0, 1, 2$. As an application, we obtain an asymptotic formula on the list size of the standard Reed-Solomon code $[q, k, q-k+1]_{q}$. [ABSTRACT FROM AUTHOR]

The MAC-IC-MAC is a class of multiple-access interference channels consisting of two multiple-access channels (MACs) that are mutually interfering but in which there is interference only from one transmitter of each MAC to the receiver of the other MAC. Two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete-memoryless semi-deterministic MAC-IC-MAC were obtained in a previous companion work by the authors using inner and outer bounds that are unions of polytopes over admissible random coding distributions. In this paper, we obtain single-distribution—and hence explicit—inner and outer bounds that characterize the capacity region of the MIMO Gaussian MAC-IC-MAC to within a constant gap. We also evaluate and study the generalized degrees of freedom (GDoF) region via multidimensional signal-level partitioning for MIMO networks. Through its lens, the achievability of the key vertices of the GDoF region are examined. This analysis as well as the symmetric GDoF curve reveal that, at high SNR, when the ratio of the interference-to-noise to the signal-to-noise ratios, both taken in dB, is within a certain range, non-interfering transmitters in that cell can fully occupy the receivers’ signal partitions in one or more dimensions that cannot otherwise be utilized by the interfering transmitter alone. This extends the same finding in the companion paper which established the results of this work for the scalar Gaussian MAC-IC-MAC. [ABSTRACT FROM AUTHOR]

This paper studies an $n$ -dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, when $n=1$ the capacity-achieving input distribution is discrete with finitely many mass points, and when $n>1$ the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, not even a bound on the exact number of mass points/shells was available. This paper provides an alternative proof of the finiteness of the number mass points/shells of the capacity-achieving input distribution while producing the first firm bounds on the number of mass points and shells, paving an alternative way for approaching many such problems. The first main result of this paper is an order tight implicit bound which shows that the number of mass points in the capacity-achieving input distribution is within a factor of two from the number of zeros of the downward shifted capacity-achieving output probability density function. Next, this implicit bound is utilized to provide a first firm upper on the support size of optimal input distribution, an $O(\mathsf {A}^{2})$ upper bound where $\mathsf {A}$ denotes the constraint on the input amplitude. The second main result of this paper generalizes the first one to the case when $n>1$ , showing that, for each and every dimension $n\ge 1$ , the number of shells that the optimal input distribution contains is $O(\mathsf {A}^{2})$. Finally, the third main result of this paper reconsiders the case $n=1$ with an additional average power constraint, demonstrating a similar $O(\mathsf {A}^{2})$ bound. [ABSTRACT FROM AUTHOR]

This paper aims to provide an optimization framework for coded caching that accounts for various heterogeneous aspects of practical systems. An optimization theoretic perspective on the seminal work on the fundamental limits of caching by Maddah-Ali and Niesen is first developed, whereas it is proved that the coded caching scheme presented in that work is the optimal scheme among a large, non-trivial family of possible caching schemes. The optimization framework is then used to develop a coded caching scheme capable of handling simultaneous non-uniform file length, non-uniform file popularity, and non-uniform user cache size. Although the resulting full optimization problem scales exponentially with the problem size, this paper shows that tractable simplifications of the problem that scale as a polynomial function of the problem size can still perform well compared to the original problem. By considering these heterogeneities both individually and in conjunction with one another, evidence of the effect of their interactions and influence on optimal cache content is obtained. [ABSTRACT FROM AUTHOR]

Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user’s local cache memory, even without knowledge of user’s later demands. Maddah-Ali and Niesen proposed a two-phase (placement phase and delivery phase) coded caching strategy for broadcast channels with cache-aided users. This paper investigates the same model under the constraint that content is placed uncoded within the caches, that is, when bits of the files are simply copied within the caches. When the cache contents are uncoded and the users’ demands are revealed, the caching problem can be connected to an index coding problem. This paper focuses on deriving fundamental performance limits for the caching problem by using tools for the index coding problem that were either known or are newly developed in this work. First, a converse bound for the caching problem under the constraint of uncoded cache placement is proposed based on the “acyclic index coding converse bound.” This converse bound is proved to be achievable by the Maddah-Ali and Niesen’s scheme when the number of files is not less than the number of users, and by a newly derived index coding achievable scheme otherwise. The proposed index coding achievable scheme is based on distributed source coding and strictly improves on the widely used “composite (index) coding” achievable bound and its improvements, and is of independent interest. An important consequence of the findings of this paper is that advancements on the coded caching problem posed by Maddah-Ali and Niesen are thus only possible by considering strategies with coded placement phase. A recent work by Yu et al has however shown that coded cache placement can at most half the network load compared to the results presented in this paper. [ABSTRACT FROM AUTHOR]

Given a ${q}$ -ary frequency hopping sequence set of length ${n}$ and size ${M}$ with Hamming correlation ${H}$ , one can obtain a ${q}$ -ary (nonlinear) cyclic code of length ${n}$ and size nM with Hamming distance n-H. Thus, every upper bound on the size of a code from coding theory gives an upper bound on the size of a frequency hopping sequence set. Indeed, all upper bounds from coding theory have been converted to upper bounds on frequency hopping sequence sets. On the other hand, a lower bound from coding theory does not automatically produce a lower bound for frequency hopping sequence sets. In particular, the most important lower bound, the Gilbert-Varshamov bound in coding theory, has not been transformed to a valid lower bound on frequency hopping sequence sets. The purpose of this paper is to transform the Gilbert-Varshamov bound from coding theory to frequency hopping sequence sets by establishing a connection between a special family of cyclic codes (which are called hopping cyclic codes in this paper) and frequency hopping sequence sets. We provide two proofs of the Gilbert-Varshamov bound. One is based on a probabilistic method that requires advanced tool–martingale. This proof covers the whole rate region. Another proof is purely elementary but only covers part of the rate region. [ABSTRACT FROM AUTHOR]

The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate freely without taxing the system bandwidth, and that the only information transmission that counts is the one between the racks. This assumption implies that the nodes within each of the racks can collaborate before providing information to the failed node. The main emphasis of the paper is on code construction for this storage model. We present an explicit family of maximum distance separable (MDS) array codes that support recovery of a single failed node from any number of helper racks using the minimum possible amount of inter-rack communication(such codes are said to provide optimal repair). The codes are constructed over finite fields of size comparable to the code length. We also derive a bound on the number of symbols accessed at helper nodes for the purposes of repair, and construct a code family that approaches this bound, while still maintaining the optimal repair property. Finally, we present a construction of scalar Reed-Solomon codes that support optimal repair for the rack-oriented storage model. [ABSTRACT FROM AUTHOR]

Motivated by the recent studies on $\mathbb {Z}_{2}\mathbb {Z}_{4}$ -additive cyclic codes, $\mathbb {Z}_{2}\mathbb {Z}_{2}[u]$ -cyclic codes and $\mathbb {Z}_{2}\mathbb {Z}_{2^{s}}$ -additive codes have been introduced by Aydogdu et al.. In this paper, we study $\mathbb {Z}_{q}R$ -linear cyclic codes where $R=\mathbb {Z}_{q}+u\mathbb {Z}_{q}, q$ is a prime number and $u^{2}=0$. There are two major ingredients in this paper. The first is to investigate the algebraic structure of cyclic codes and their duals over ring $\mathbb {Z}_{q}R$ , the spanning sets, the types and sizes of $\mathbb {Z}_{q}R$ -cyclic codes and their duals as well. Based on this, the second ingredient is to present an infinite family of MDSS codes and obtain some illustrative examples of $q$ -ary cyclic codes with optimal parameters derived from the $\mathbb {Z}_{q}R$ -cyclic codes. [ABSTRACT FROM AUTHOR]

Signal recovery from unitarily invariant measurements is investigated in this paper. A message-passing algorithm is formulated on the basis of expectation propagation (EP). A rigorous analysis is presented for the dynamics of the algorithm in the large system limit, where both input and output dimensions tend to infinity while the compression rate is kept constant. The main result is the justification of state evolution (SE) equations conjectured by Ma and Ping. This result implies that the EP-based algorithm achieves the Bayes-optimal performance that was originally derived via a non-rigorous tool in statistical physics and proved partially in a recent paper, when the compression rate is larger than a threshold. The proof is based on an extension of a conventional conditioning technique for the standard Gaussian matrix to the case of the Haar matrix. [ABSTRACT FROM AUTHOR]

Locally repairable codes, or locally recoverable codes (LRC for short), are designed for applications in distributed and cloud storage systems. Similar to classical block codes, there is an important bound called the Singleton-type bound for locally repairable codes. In this paper, an optimal locally repairable code refers to a block code achieving this Singleton-type bound. Like classical MDS codes, optimal locally repairable codes carry some very nice combinatorial structures. Since the introduction of the Singleton-type bound for locally repairable codes, people have put tremendous effort into construction of optimal locally repairable codes. There are a few constructions of optimal locally repairable codes in the literature. Most of these constructions are realized via either combinatorial or algebraic structures. In this paper, we apply automorphism group of the rational function field to construct optimal locally repairable codes by considering the group action on projective lines over finite fields. Due to various subgroups of the projective general linear group, we are able to construct optimal locally repairable codes with flexible locality as well as smaller alphabet size comparable to the code length. In particular, we produce new families of $q$ -ary locally repairable codes, including codes of length $q+1$ via cyclic groups. [ABSTRACT FROM AUTHOR]

In the classical model for (information theoretically secure) Private Information Retrieval (PIR) due to Chor, Goldreich, Kushilevitz and Sudan, a user wishes to retrieve one bit of a database that is stored on a set of ${n}$ servers, in such a way that no individual server gains information about which bit the user is interested in. The aim is to design schemes that minimise the total communication between the user and the servers. More recently, there have been moves to consider more realistic models where the total storage of the set of servers, or the per server storage, should be minimised (possibly using techniques from distributed storage), and where the database is divided into ${R}$ -bit records with ${R}>1$ , and the user wishes to retrieve one record rather than one bit. When ${R}$ is large, downloads from the servers to the user dominate the communication complexity and so the aim is to minimise the total number of downloaded bits. Work of Shah, Rashmi and Ramchandran shows that at least ${R}+1$ bits must be downloaded from servers in the worst case, and provides PIR schemes meeting this bound. Sun and Jafar have considered the download cost of a scheme, defined as the ratio of the message length ${R}$ and the total number of bits downloaded. They determine the best asymptotic download cost of a PIR scheme (as ${R}\rightarrow \infty $) when a database of ${k}$ messages is stored by ${n}$ servers. This paper provides various bounds on the download complexity of a PIR scheme, generalising those of Shah et al. to the case when the number ${n}$ of servers is bounded, and providing links with classical techniques due to Chor et al. The paper also provides a range of constructions for PIR schemes that are either simpler or perform better than previously known schemes. These constructions include explicit schemes that achieve the best asymptotic download complexity of Sun and Jafar with significantly lower upload complexity, and general techniques for constructing a scheme with good worst case download complexity from a scheme with good download complexity on average. [ABSTRACT FROM AUTHOR]

Blind deconvolution is a ubiquitous problem aiming to recover a convolution kernel $\boldsymbol a_{0}\in \mathbb R ^{k}$ and an activation signal $\boldsymbol x_{0}\in \mathbb R ^{m}$ from their convolution $\boldsymbol y\in \mathbb R ^{m}$. Unfortunately, this is an ill-posed problem in general. This paper focuses on the short and sparse blind deconvolution problem, where the convolution kernel is short ($k\ll m$) and the activation signal is sparsely and randomly supported ($\left \|{ \boldsymbol x_{0} }\right \|_{0}\ll m$). This variant captures the structure of the convolutional signals in several important application scenarios. In this paper, we normalize the convolution kernel to have unit Frobenius norm and then cast the blind deconvolution problem as a nonconvex optimization problem over the kernel sphere. We demonstrate that (i) in a certain region of the sphere, every local optimum is close to some shift truncation of the ground truth, and (ii) for a generic unit kernel $\boldsymbol a_{0}$ , when the sparsity of activation signal satisfies $\theta \lesssim k^{-2/3}$ and number of measurements $m\gtrsim \mathop {\mathrm {poly}}\nolimits \left ({k }\right) $ , the proposed initialization method together with a descent algorithm which escapes strict saddle points recovers some shift truncation of the ground truth kernel. [ABSTRACT FROM AUTHOR]

Content delivery networks store information distributed across multiple servers, so as to balance the load and avoid unrecoverable losses in case of node or disk failures. Coded caching has been shown to be a useful technique which can reduce peak traffic rates by pre-fetching popular content at the end users and encoding transmissions so that different users can extract different information from the same packet. On one hand, distributed storage limits the capability of combining content from different servers into a single message, causing performance losses in coded caching schemes. But, on the other hand, the inherent redundancy existing in distributed storage systems can be used to improve the performance of those schemes through parallelism. This paper designs coded caching and delivery schemes tailored towards systems where the library is distributed across multiple servers, possibly with some redundancy in the form of maximum distance separable (MDS) erasure codes. Different schemes are proposed based on the capacity of the users’ caches, as well as the number of parity servers. The main focus is on scenarios with one (RAID-4) or two (RAID-6) parity servers, but the paper also includes simple extensions for cases with more than two or no parity servers at all. The proposed schemes are shown to reduce the worst case latency, or equivalently the peak transmission rate from any server, below that of state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem, the optimum mean codeword length of variable-length codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold. In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds, we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. Finally, we apply the general formula derived in this paper to the case of stationary memoryless sources. [ABSTRACT FROM AUTHOR]

Mean hitting time for random walks on a network, defined as the average of hitting times over all possible pairs of nodes, has found a large variety of applications in many areas. In this paper, we first prove that among all $N$ -node networks, the complete graph has the minimum mean hitting time $N-1$ , which scales linearly with network size. We then study a random walk mobility model with location heterogeneity, modeled by scale-free networks, which are ubiquitous in realistic systems such as P2P networks. For this purpose, we consider random walks on two sparse scale-free small-world networks. By using the connection between random walks and electrical networks, we derive explicit formulas about mean hitting time for both networks, the dominant scaling of which exhibits the same behavior as that of complete graphs. This paper demonstrates that heterogeneous sparse networks can have low-mean hitting time with a behavior similar to that of dense complete graphs, which is instrumental in designing networks, where search is fast between any pair of nodes. [ABSTRACT FROM AUTHOR]

We investigate a probabilistic model for routeing in a multihop ad hoc communication network, where each user sends a message to the base station. Messages travel in hops via other users, used as relays. Their trajectories are chosen at random according to a Gibbs distribution, which favors trajectories with low interference, measured in terms of signal-to-interference ratio. This model was introduced in our earlier paper, where we expressed, in the limit of a high density of users, the typical distribution of the family of trajectories in terms of a law of large numbers. In this paper, we derive its qualitative properties. We analytically identify the emerging typical scenarios in three extreme regimes. We analyze the typical number of hops and the typical length of a hop and the deviation of the trajectory from the straight line, regime 1 in the limit of a large communication area and large distances and regime 2 in the limit of a strong interference weight. In both the regimes, the typical trajectory approaches a straight line quickly, in regime 1 with equal hop lengths. Interestingly, in regime 2, the typical length of a hop diverges logarithmically in the distance of the transmitter to the base station. We further analyze (regime 3) local and global repulsive effects of a densely populated subarea on the trajectories. [ABSTRACT FROM AUTHOR]

This paper studies the downlink of a cloud radio access network (C-RAN) in which a centralized processor (CP) communicates with mobile users through base stations (BSs) that are connected to the CP via finite-capacity fronthaul links. Information theoretically, the downlink of a C-RAN is modeled as a two-hop broadcast-relay network. Among the various transmission and relaying strategies for such model, this paper focuses on the compression strategy, in which the CP centrally encodes the signals to be broadcast jointly by the BSs, then compresses and sends these signals to the BSs through the fronthaul links. We characterize an achievable rate region for a generalized compression strategy with Marton’s multicoding for broadcasting and multivariate compression for fronthaul transmission. We then compare this rate region with the distributed decode-forward (DDF) scheme, which achieves the capacity of the general relay networks to within a constant gap, and show that the difference lies in that DDF performs Marton’s multicoding and multivariate compression jointly as opposed to successively as in the compression strategy. A main result of this paper is that under the assumption that the fronthaul links are subject to a sum capacity constraint, this difference is immaterial; so, for the Gaussian network, the compression strategy based on successive encoding can already achieve the capacity region of the C-RAN to within a constant gap, where the gap is independent of the channel parameters and the power constraints at the BSs. As a further result, for C-RAN under individual fronthaul constraints, this paper also establishes that the compression strategy can achieve to within a constant gap to the sum capacity. [ABSTRACT FROM AUTHOR]

This paper investigates the construction of rank-metric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension of a rank-metric code with given specified Ferrers diagram shape and rank distance. While the conjecture in its generality is wide open, several cases have been established in the literature. This paper contributes further cases of Ferrers diagrams and ranks for which the conjecture holds true. In addition, the proportion of maximal Ferrers diagram codes within the space of all rank-metric codes with the same shape and dimension is investigated. Special attention is being paid to MRD codes. It is shown that for growing field size the limiting proportion depends highly on the Ferrers diagram. For instance, for $[m\times 2]$ -MRD codes with rank 2 this limiting proportion is close to $1/e$. [ABSTRACT FROM AUTHOR]

There has been much recent interest in private information retrieval (PIR) in models where a database is stored across several servers using coding techniques from distributed storage, rather than being a simply replicated. In particular, a recent breakthrough result of Fazelli, Vardy, and Yaakobi introduces the notion of a PIR code and a PIR array code, and uses this notion to produce efficient PIR protocols. In this paper, we are interested in designing PIR array codes. We consider the case when we have $m$ servers, with each server storing a fraction $(1/s)$ of the bits of the database; here $s$ is a fixed rational number with $s > 1$. A PIR array code with the $k$ -PIR property enables a $k$ -server PIR protocol (with $k\leq m$) to be emulated on $m$ servers, with the overall storage requirements of the protocol being reduced. The communication complexity of a PIR protocol reduces as $k$ grows, so the virtual server rate, defined to be $k/m$ , is an important parameter. We study the maximum virtual server rate of a PIR array code with the $k$ -PIR property. We present upper bounds on the achievable virtual server rate, some constructions, and ideas how to obtain the PIR array codes with the highest possible virtual server rate. In particular, we present constructions that asymptotically meet our upper bounds and the exact largest virtual server rate is obtained when $1 < s \leq 2$. A $k$ -PIR code (and similarly a $k$ -PIR array code) is also a locally repairable code with symbol availability $k-1$. Such a code ensures $k$ parallel reads for each information symbol. So the virtual server rate is very closely related to the symbol availability of the code when used as a locally repairable code. The results of this paper are discussed also in this context where subspace codes also have an important role. [ABSTRACT FROM AUTHOR]

The problem of universal source coding for binary trees is considered. Zhang, Yang, and Kieffer derived upper bounds on the average-case redundancy of codes based on directed acyclic graph (DAG) compression for binary tree sources with certain properties. In this paper, a natural class of binary tree sources is presented such that the demanded properties are fulfilled. Moreover, for both subclasses considered in the paper of Zhang, Yang, and Kieffer, their result is improved by deriving bounds on the maximal pointwise redundancy (or worst-case redundancy) instead of the average-case redundancy. Finally, using context-free tree grammars instead of DAGs, upper bounds on the maximal pointwise redundancy for certain binary tree sources are derived. This yields universal codes for new classes of binary tree sources. [ABSTRACT FROM AUTHOR]

This paper studies the operation of multi-agent networks engaged in binary decision tasks, and derives performance expressions and performance operating curves under challenging conditions with some revealing insights. One of the main challenges in the analysis is that agents are only allowed to exchange one-bit messages, and the information at each agent therefore consists of both continuous and discrete components. Due to this mixed nature, the steady-state distribution of the state of each agent cannot be inferred from direct application of central limit arguments. Instead, the behavior of the continuous component is characterized in integral form by using a log-characteristic function, while the behavior of the discrete component is characterized by means of an asymmetric Bernoulli convolution. By exploiting these results, this paper derives reliable approximate performance expressions for the network nodes that match well with the simulated results for a wide range of system parameters. The results also reveal an important interplay between continuous adaptation under constant step-size learning and the binary nature of the messages exchanged with neighbors. [ABSTRACT FROM AUTHOR]

This paper presents a new approach, called perturb-max, for high-dimensional statistical inference in graphical models that is based on applying random perturbations followed by optimization. This framework injects randomness into maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic result from extreme value statistics asserts that perturb-max operations generate unbiased samples from the Gibbs distribution using high-dimensional perturbations. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. However, when the perturbations are of low dimension, sampling the perturb-max prediction is as efficient as MAP optimization. This paper shows that the expected value of perturb-max inference with low dimensional perturbations can be used sequentially to generate unbiased samples from the Gibbs distribution. Furthermore the expected value of the maximal perturbations is a natural bound on the entropy of such perturb-max models. A measure concentration result for perturb-max values shows that the deviation of their sampled average from its expectation decays exponentially in the number of samples, allowing effective approximation of the expectation. [ABSTRACT FROM AUTHOR]

This paper addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research which can be viewed as demonstrating qualitative advantage of quantum communication in the three most common communication “layouts”: two-way interactive communication, one-way communication and simultaneous message passing (SMP). I demonstrate a functional problem $ { \widetilde {cEq}_{T}}$ , whose communication complexity is $O\left ({(\log n)^{2}}\right)$ in the quantum version of the SMP and $\tilde \Omega \left ({ \sqrt {n}}\right)$ in the classical (randomized) version of SMP. Second, this paper contributes to understanding the power of the weakest commonly studied regime of quantum communication–SMP with quantum messages and without shared randomness (the latter restriction can be viewed as a somewhat artificial way of making the quantum model “as weak as possible”). Our function $ { \widetilde {cEq}_{T}}$ has an efficient solution in this regime as well, which means that even lacking shared randomness, quantum SMP can be exponentially stronger than its classical counterpart with shared randomness. [ABSTRACT FROM AUTHOR]

Reed-Solomon (RS) codes are widely used in distributed storage systems. In this paper, we study the repair bandwidth and sub-packetization size of RS codes. The repair bandwidth is defined as the amount of transmitted information from surviving nodes to a failed node. The RS code can be viewed as a polynomial over a finite field $GF(q^\ell)$ evaluated at a set of points, where $\ell $ is called the sub-packetization size. Smaller bandwidth reduces the network traffic in distributed storage, and smaller $\ell $ facilitates the implementation of RS codes with lower complexity. Recently, Guruswami and Wootters proposed a repair method for RS codes when the evaluation points are the entire finite field. While the sub-packetization size can be arbitrarily small, the repair bandwidth is higher than the minimum storage regenerating (MSR) bound. Tamo, Ye, and Barg achieved the MSR bound but the sub-packetization size grows faster than the exponential function of the number of the evaluation points. In this paper, we present code constructions and repair schemes that extend these results to accommodate different sizes of the evaluation points. In other words, we design schemes that provide points in between. These schemes provide a flexible tradeoff between the sub-packetization size and the repair bandwidth. In addition, we generalize our schemes to manage multiple failures. [ABSTRACT FROM AUTHOR]

In this paper, a general framework of constructing the optimal frequency-hopping sequence (FHS) sets is presented based on the designated direct product. Under this framework, we obtain infinitely many new optimal FHS sets by combining some one-coincide (OC) sequence sets that are newly constructed in this paper with some known optimal FHS sets. Our constructions are also based on extension method. However, our constructions give new and flexible parameters due to the free choice of OC sequence set. As a result, our constructions allow a great flexibility of choosing parameters of FHS sets for a given frequency-hopping spread spectrum system. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over $\mathbb {F}_{q}$ exists. This problem is completely solved for the case where $q$ is even. For $q$ is odd, some $q$ -ary MDS Euclidean self-dual codes were obtained in the literature. In this paper, we construct six new classes of $q$ -ary MDS Euclidean self-dual codes by using generalized Reed–Solomon (GRS for short) codes and extended GRS codes. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of quantum measurement compression with side information in the one-shot setting with shared-randomness. In this problem, Alice shares a pure quantum state with Bob and the reference system. She performs a measurement on her registers and wishes to communicate the outcome to Bob using shared-randomness and classical communication. The outcome that Bob receives must be correctly correlated with the reference system and his own registers. Our goal is to concurrently minimize the classical communication and shared-randomness cost. The suggested protocol presented in this paper is based on convex-split and position based decoding. The communication is upper bounded in terms of smooth max and hypothesis testing relative entropies. A second protocol addresses the task of strong randomness extraction in the presence of quantum side information. The protocol provides an error guarantee in terms of relative entropy (as opposed to trace distance) and extracts close to the optimal number of uniform bits. As an application, we provide a new achievability result for the task of quantum measurement compression without feedback, in which Alice does not need to know the outcome of the measurement. The result achieves the optimal number of bits communicated and the required number of bits of shared-randomness, for the same task in the asymptotic and i.i.d. setting. [ABSTRACT FROM AUTHOR]

In 2007, Carlet and Ding introduced two parameters, denoted by $Nb_{F}$ and $NB_{F}$ , quantifying respectively the balancedness of general functions $F$ between finite Abelian groups and the (global) balancedness of their derivatives $D_{a} F(x)=F(x+a)-F(x)$ , $a\in G\setminus \{0\}$ (providing an indicator of the nonlinearity of the functions). These authors studied the properties and cryptographic significance of these two measures. They provided inequalities relating the nonlinearity $\mathcal {NL}(F)$ to $NB_{F}$ for S-box and specifically obtained an upper bound on the nonlinearity that unifies Sidelnikov-Chabaud-Vaudenay’s bound and the covering radius bound. At the Workshop WCC 2009 and in its postproceedings in 2011, a further study of these parameters was made; in particular, the first parameter was applied to the functions $F+L$ , where $L$ is affine, providing more nonlinearity parameters. In 2010, motivated by the study of Costas arrays, two parameters called ambiguity and deficiency were introduced by Panario et al. for permutations over finite Abelian groups to measure the injectivity and surjectivity of the derivatives, respectively. These authors also studied some fundamental properties and cryptographic significance of these two measures. Further studies followed without comparing the second pair of parameters to the first one. In this paper, we observe that ambiguity is the same parameter as $NB_{F}$ up to additive and multiplicative constants (i.e., up to rescaling). We perform the necessary work of comparison and unification of the results on $NB_{F}$ and on ambiguity, which have been obtained in the five papers devoted to these parameters. We generalize some known results to any finite Abelian groups. More importantly, we derive many new results on these parameters. [ABSTRACT FROM AUTHOR]

Motivated by systems, where the information is represented by a graph such as neural networks, associative memories, and distributed systems. In this paper, we present a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of undirected or directed complete graphs, and a code over graphs is a set of graphs. A node failure is the event, where all edges in the neighborhood of the erased node have been erased. We say that a code over graphs can tolerate $\rho $ node failures, if it can correct the erased edges of any $\rho $ failed nodes in the graph. While the construction of optimal codes over graphs can be easily accomplished by MDS codes, their field size has to be at least ${\mathcal{ O}}(n^{2})$ , when $n$ is the number of nodes in the graph. In this paper, we present several constructions of codes over graphs with smaller field size. To accomplish this task, we use constructions of product codes and rank metric codes. Furthermore, we present optimal codes over graphs correcting two node failures over the binary field, when the number of nodes in the graph is a prime number. Last, we also provide upper bound on the number of nodes for optimal codes. [ABSTRACT FROM AUTHOR]

BCH codes are an important class of cyclic codes which have applications in satellite communications, DVDs, disk drives, and two-dimensional bar codes. Although BCH codes have been widely studied, their parameters are known for only a few special classes. Recently, Ding et al. made some new progress in BCH codes. However, we still have very limited knowledge on the dimension of BCH codes, not to mention the weight distribution of BCH codes. In this paper, we generalize the results on BCH codes from several previous papers. 1) The dimension of narrow-sense BCH codes of length $((q^{m}-1)/{\lambda })$ with designed distance $2\leq \delta \leq (({q^{\lceil (m+1)/2 \rceil }-1})/(\lambda)+1)$ is settled, where $\lambda $ is any factor of $(q-1)$. 2) The weight distributions of two classes of narrow-sense BCH codes of length $(({q^{m}-1})/2)$ with designed distance $\delta =(({(q-1)q^{m-1}-q^{\lfloor (m-1)/2\rfloor }-1})/2)$ and $\delta =(({(q-1)q^{m-1}-q^{\lfloor (m+1)/2\rfloor }-1})/2)$ are determined. 3) The weight distribution of a class of BCH codes of length $((q^{m}-1)/({q-1}))$ is determined. In particular, a subclass of this class of BCH codes is optimal with respect to the Griesmer bound. Some optimal linear codes obtained from this class of BCH codes are characterized. [ABSTRACT FROM AUTHOR]

This paper studies the continuous-time Poisson channel whose dark current is random and may change for every $\tau $ -second time interval, where the actual values of the dark current are known to the transmitter as channel-state information (CSI). In the limit where $\tau $ tends to zero, the capacity gain provided by both causal and noncausal CSI is shown to vanish linearly with $\tau $ , so CSI at the transmitter provides almost no capacity improvement. The paper also considers a related problem of the state-dependent very noisy channel. In the very noisy limit, the capacity gain provided by noncausal CSI is shown to be the same as that provided by causal CSI. [ABSTRACT FROM AUTHOR]

Modern communication and computation systems often consist of large networks of unreliable nodes. Still, it is well known that such systems can provide aggregate reliability via redundancy. While duplication may increase the load on a system, it can lead to significant performance improvement when combined with the judicious management of extra system resources. Prime examples of this abstract paradigm include multi-path routing across communication networks, content access from multiple caches in delivery networks, and master/slave computations on compute clusters. Several recent contributions in the area establish bounds on the performance of redundant systems, characterizing the latency-redundancy tradeoff under specific load profiles. Following a similar line of research, this paper introduces new analytical bounds and approximation techniques for the latency-redundancy tradeoff for a range of system loads and a class of symmetric redundancy schemes, under the assumption of Poisson arrivals, exponential service-rates, and fork-join scheduling policy. The proposed approach can be employed to efficiently approximate the latency distribution of a queueing system at equilibrium. Various metrics can subsequently be derived for this system, including the mean and variance of the sojourn time, and the tail decay rate of the stationary distribution. This paper also establishes the stability region in terms of arrival rates for redundant systems with certain symmetries. Finally, it offers selection guidelines for design parameters to provide latency guarantees based on the proposed approximations. Findings are substantiated by numerical results. [ABSTRACT FROM AUTHOR]

Most codes with an algebraic decoding algorithm are derived from Reed-Solomon codes. They are obtained by taking equivalent codes, for example, generalized Reed-Solomon codes, or by using the so-called subfield subcode method, which leads to alternant codes over the underlying prime field, or over some intermediate subfield. The main advantage of these constructions is to preserve both the minimum distance and the decoding algorithm of the underlying Reed-Solomon code. In this paper, we explore in detail the subspace subcodes construction. This kind of codes was already studied in the particular case of cyclic Reed-Solomon codes. We extend this approach to any linear code over the extension of a finite field. We are interested in additive codes who are deeply connected to subfield subcodes. We characterize the duals of subspace subcodes. We introduce the notion of generalized subspace subcodes. We apply our results to generalized Reed-Solomon codes which leads to codes with interesting parameters, especially over a large alphabet. To conclude this paper, we discuss the security of the use of generalized subspace subcodes of Reed-Solomon codes in a cryptographic context. [ABSTRACT FROM AUTHOR]

Ovoids in ${\mathrm {PG}}(3, {\mathrm {GF}}(q))$ have been an interesting topic in coding theory, combinatorics, and finite geometry for a long time. So far only two families of ovoids are known. The first is the elliptic quadrics and the second is the Tits ovoids. It is known that an ovoid in ${\mathrm {PG}}(3, {\mathrm {GF}}(q))$ corresponds to a $[q^{2}+1, 4, q^{2}-q]$ code over ${\mathrm {GF}}(q)$ , which is called an ovoid code. The objectives of this paper are to develop the general theories of subfield codes and to study the subfield codes of the two families of ovoid codes. The dimensions, minimum weights, and the weight distributions of the subfield codes of the elliptic quadric codes and Tits ovoid codes are settled. The parameters of the duals of these subfield codes are also studied. Some of the codes presented in this paper are optimal, and some are distance-optimal. The parameters of the subfield codes are new. [ABSTRACT FROM AUTHOR]

The main goal in group testing is to recover a small subset of defective items from a larger population while efficiently reducing the total number of (possibly noisy) required tests/measurements. Under the assumption that the input-output statistical relationship (i.e., channel law) is known to the recovery algorithm, the fundamental as well as the computational limits of the group testing problem are relatively better understood than when these statistical relationships are unknown. Practical considerations, however, render this assumption inapplicable, and “blind” recovery/estimation procedures, independent of the input-output statistics, are desired. In this paper, we analyze the fundamental limits of a general noisy group testing problem, when this relationship is unknown. Specifically, in the first part of this paper, we propose an efficient scheme, based on the idea of separate-decoding of items (where each item is recovered separately), for which we derive sufficient conditions on the number of tests required for exact recovery. The difficulty in obtaining these conditions stems from the fact that we allow the number of defective items to grow with the population size, which in turn requires delicate concentration analysis of certain probabilities. Furthermore, we show that in several scenarios, our proposed scheme achieves the same performance as that of the corresponding non-blind recovery algorithm (where the input-output statistics are known), implying that the proposed blind scheme is robust/universal. Finally, in the second part of this paper, we propose also an inefficient combinatorial-based scheme (or, “joint-decoding”), for which we derive similar sufficient conditions. [ABSTRACT FROM AUTHOR]

We investigate the list decodability of symbol-pair codes in this paper. First, we show that the list decodability of every symbol-pair code does not exceed the Gilbert–Varshamov bound. On the other hand, we are able to prove that with high probability, a random symbol-pair code can be list decoded up to the Gilbert–Varshamov bound. Our second result of this paper is to derive the Johnson-type bound, i.e., a lower bound on list decoding radius in terms of minimum distance. Finally, we present a list decoding algorithm of Reed–Solomon codes beyond the Johnson-type bound in the pair metric. 1 A symbol-pair code is referred to a code in the pair metric. [ABSTRACT FROM AUTHOR]

This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with ${\mathsf{K}}_{w} $ weak receivers and ${\mathsf {K}}_{s} $ strong receivers, where weak receivers and strong receivers have the same erasure probabilities and cache sizes, respectively. The lower bounds are achieved by the schemes that meticulously combine joint cache-channel coding with wiretap coding and key-aided one-time pads. The presented upper bound holds more generally for arbitrary degraded BCs and arbitrary cache sizes. When only weak receivers have cache memories, upper and lower bounds coincide for small and large cache memories, thus providing the exact secrecy capacity-memory tradeoff for this setup. The derived bounds further allow us to conclude that the secrecy capacity is positive even when the eavesdropper is stronger than all the legitimate receivers with cache memories. Moreover, they show that the secrecy capacity-memory tradeoff can be significantly smaller than its non-secure counterpart, but it grows much faster when cache memories are small. This paper also presents a lower bound on the global secrecy capacity-memory tradeoff where one is allowed to optimize the cache assignment subject to a total cache budget. It is close to the best known lower bound without secrecy constraint. For small total cache budget, the global secrecy capacity-memory tradeoff is achieved by assigning all the available cache memory uniformly over all the receivers if the eavesdropper is stronger than all the legitimate receivers, and it is achieved by assigning the cache memory uniformly only over the weak receivers if the eavesdropper is weaker than the strong receivers. [ABSTRACT FROM AUTHOR]

This paper considers secret-key generation between several agents and a base station that observe independent and identically distributed realizations of correlated random variables. Each agent wishes to generate the longest possible individual key with the base station by means of public communication. All keys must be jointly kept secret from all external entities. In this many-to-one secret-key generation setting, it can be shown that the agents can take advantage of a collective protocol to increase the sum rate of their generated keys. However, when each agent is only interested in maximizing its own secret-key rate, agents may be unwilling to participate in a collective protocol. Furthermore, when such a collective protocol is employed, how to fairly allocate individual key rates arises as a valid issue. This paper studies the tension between cooperation and self-interest with a game-theoretic treatment. This paper establishes that cooperation is in the best interest of all individualistic agents and that there exist individual secret-key rate allocations that incentivize the agents to follow the protocol. In addition, an explicit coding scheme that achieves such allocations is proposed. [ABSTRACT FROM AUTHOR]

In a paper by Guruswami et al., it was shown that the length $n$ of a $q$ -ary linear locally recoverable code with distance $d \geqslant 5$ is upper bounded by $O(dq^{3})$. Thus, it is a challenging problem to construct $q$ -ary locally recoverable codes with distance $d \geqslant 5$ and length approaching the upper bound. The same paper also gave an algorithmic construction of $q$ -ary locally recoverable codes with locality $r$ and length $n=\Omega _{r}(q^{2})$ for $d=5$ and 6, where $\Omega _{r}$ means that the implicit constant depends on locality $r$. In this paper, we present an explicit construction of $q$ -ary locally recoverable codes of distance $d= 5$ and 6 via binary constant weight codes. It turns out that 1) our construction is simpler and more explicit and 2) the length of our codes is greater than previously known. [ABSTRACT FROM AUTHOR]

In frequency hopping (FH) communication systems, frequency hopping sequences (FHSs) are crucial in determining the system’s anti-jamming performance. If FHSs can ensure a wide-gap between two adjacent frequency points to avoid the frequency points with high interference probability, it will significantly improve the FH communication system’s anti-interference ability. Moreover, if each frequency point appears at the same number of times in a sequence period, the system’s anti-electromagnetic interference will be enhanced. Therefore, it is desirable to employ FHSs with low Hamming autocorrelation, wide frequency-hopping gap, and good uniformity in practical applications. However, to the best of our knowledge, no such infinite classes of FHSs have been reported in the literature to date. This paper aims to present two constructions of uniform wide-gap frequency-hopping sequences (WGFHSs) by concatenating two or three adequately designed sequences. For the first time, we obtain two infinite classes of WGFHSs, which are optimal with respect to the well-known Lempel-Greenberger bound. [ABSTRACT FROM AUTHOR]

In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by pooling their shares, and (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with participants through a one-way, authenticated, rate-limited, and public channel. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants. Our main result is a closed-form characterization of the fundamental trade-off between secret rate and public communication rate. [ABSTRACT FROM AUTHOR]

The $k\text {-means}$ clustering problem concerns finding a partition of the data points into $k$ clusters such that the total within-cluster squared distance is minimized. This optimization objective is non-convex, and not everywhere differentiable. In general, there exist spurious local solutions other than the global optimum. Moreover, the simplest and most popular algorithm for $k\text {-means}$ , namely Lloyd’s algorithm, generally converges to such spurious local solutions both in theory and in practice. In this paper, we investigate the structures of these spurious local solutions under a probabilistic generative model with $k$ ground truth clusters. As soon as $k=3$ , spurious local minima provably exist, even for well-separated clusters. One such local minimum puts two centers at one true cluster, and the third center in the middle of the other two true clusters. We prove that this is essentially the only type of spurious local minima under a separation condition. In particular, any local minimum solution only involves a configuration that puts multiple centers at a true cluster, and one center in the middle of multiple true clusters. Our results pertain to the $k\text {-means}$ formulation for mixtures of Gaussians or bounded distributions, and hold in the over- and under-parametrization regimes where the number of centers in $k\text {-means}$ may not equal to the number of true clusters. Our theoretical results corroborate existing empirical observations and provide justification for popular heuristics for $k\text {-means}$ clustering. [ABSTRACT FROM AUTHOR]

The deterministic identification (DI) capacity is developed in multiple settings of channels with power constraints. A full characterization is established for the DI capacity of the discrete memoryless channel (DMC) with and without input constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness at the encoder, resulting in a double exponential number of messages in the block length $n$. In the deterministic setup, the number of messages scales exponentially, as in Shannon’s transmission paradigm, but the achievable identification rates are higher. An explicit proof was not provided for the deterministic setting. In this paper, a detailed proof is presented for the DMC. Furthermore, Gaussian channels with fast and slow fading are considered, when channel side information is available at the decoder. A new phenomenon is observed as we establish that the number of messages scales as $2^{n\log (n)R}$ by deriving lower and upper bounds on the DI capacity on this scale. Consequently, the DI capacity of the Gaussian channel is infinite in the exponential scale and zero in the double exponential scale, regardless of the channel noise. [ABSTRACT FROM AUTHOR]

This paper examines the average age minimization problem where only a fraction of the network users can transmit simultaneously over unreliable channels. Finding the optimal scheduling scheme, in this case, is known to be challenging. Accordingly, the Whittle’s index policy was proposed in the literature as a low-complexity heuristic to the problem. Although simple to implement, characterizing this policy’s performance is recognized to be a notoriously tricky task. In the sequel, we provide a new mathematical approach to establish its optimality in the many-users regime for specific network settings. Contrary to previous works in the literature that use restrictive mathematical assumptions, which can be challenging to verify, our novel approach is based on intricate techniques and it is free of any strong mathematical assumptions. These findings showcase that the Whittle’s index policy has analytically provable asymptotic optimality for the AoI minimization problem. Finally, we lay out numerical results that corroborate our theoretical findings and demonstrate the policy’s notable performance in the many-users regime. [ABSTRACT FROM AUTHOR]