Information Theory (cs.IT)

Abstract: Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed $(r,\delta)$-LRCs with unbounded code length and optimal minimum distance when $\delta+1 \leq d \leq 2\delta$ from the parity-check matrix equipped with the Vandermonde structure, but the block length is limited by the size of $\mathbb{F}_q$. In this paper, we propose a more general construction of $(r,\delta)$-LRCs through the parity-check matrix. Furthermore, with the help of MDS codes, we give three classes of explicit constructions of optimal $(r,\delta)$-LRCs with block length beyond $q$. It turns out that 1) our general construction extends the results of Ge et al. and 2) our explicit constructions yield some optimal $(r,\delta)$-LRCs with new parameters.

Abstract: In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance matrices, without knowledge of the true covariance matrix. In this study, we demonstrate that this minimization problem is equivalent to minimizing the loss of information between the true population covariance and the rotational invariant estimator for normal multivariate variables. However, for Student's t distributions, the minimal Frobenius norm does not necessarily minimize the information loss in finite-sized matrices. Nevertheless, such deviations vanish in the asymptotic regime of large matrices, which might extend the applicability of random matrix theory results to Student's t distributions. These distributions are characterized by heavy tails and are frequently encountered in real-world applications such as finance, turbulence, or nuclear physics. Therefore, our work establishes a connection between statistical random matrix theory and estimation theory in physics, which is predominantly based on information theory.

Abstract: We study the Chernoff-Stein exponent of the following binary hypothesis testing problem: Associated with each hypothesis is a set of channels. A transmitter, without knowledge of the hypothesis, chooses the vector of inputs to the channel. Given the hypothesis, from the set associated with the hypothesis, an adversary chooses channels, one for each element of the input vector. Based on the channel outputs, a detector attempts to distinguish between the hypotheses. We study the Chernoff-Stein exponent for the cases where the transmitter (i) is deterministic, (ii) may privately randomize, and (iii) shares randomness with the detector that is unavailable to the adversary. It turns out that while a memoryless transmission strategy is optimal under shared randomness, it may be strictly suboptimal when the transmitter only has private randomness.

Abstract: Simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) have been attracting significant attention in both academia and industry for their advantages of achieving 360{\deg} coverage and enhanced degrees of freedom. This article first identifies the fundamentals of STAR-RIS, by discussing the hardware models, channel models, and signal models. Then, three representative categorizing approaches for STAR-RIS are introduced from phase-shift, directional, and energy consumption perspectives. Furthermore, the beamforming design of STAR-RIS is investigated for both independent and coupled phase-shift cases. A general optimization framework is proposed as the recent advances, which has high compatibility and provable optimality regardless of the application scenarios. As a further advance, several promising applications are discussed to demonstrate the potential benefits of applying STAR-RIS in the sixth-generation wireless network. Lastly, a few future directions and research opportunities are highlighted for motivating future work.

Abstract: The mutual information is analyzed as a function of the input distribution using an identity due to Tops\o{e} for channels with (possibly multiple) linear cost constraints and finite input and output sets. The mutual information is bounded above by a function decreasing quadratically with the distance to the set of all capacity-achieving input distributions for the case when the distance is less than a certain threshold. The closed-form expressions for the threshold and the coefficient of the quadratic decrease are derived. A counter-example demonstrating the non-existence of such a quadratic bound in the case of infinitely many linear cost constraints is provided. Implications of these observations for the channel coding problem and applications of the proof technique to related problems are discussed.

Abstract: Low-density parity-check (LDPC) codes are specified by graphs, and are the error correction technique of choice in many communications and data storage contexts. Message passing decoders diffuse information carried by parity bits into the payload, and this paper measures the value of engineering parity bits to be more reliable than message bits. We consider the binary symmetric channel (BSC) and measure the impact of unequal data protection on the threshold of a regular LDPC code. Our analysis also includes doping where the parity bits are known to the decoder. We investigate BSC with Gallager-A decoder, with a $3$-level-alphabet decoder, and with a full belief propagation decoder. We demonstrate through theoretical analysis and simulation that non-equiprobable inputs lead to significant improvements both in the threshold and in the speed with which the decoder converges. We also show that all these improvements are possible even with a simple $3$-level-alphabet decoder.

Abstract: In this work, we propose a versatile feedback scheme which can be deployed for both single- and multi-user multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems. Particularly, we propose to use a Gaussian mixture model (GMM) with a reduced number of parameters for codebook construction, feedback encoding, and precoder design. The GMM is fitted offline at the base station (BS) to uplink (UL) training samples to approximate the channel distribution of all possible mobile terminals (MTs) located inside the BS cell. Afterwards, a codebook is constructed, where each codebook entry is based on one GMM component. By extracting directional information of the constructed codebook, the proposed GMM-based feedback approach allows to jointly design the precoders of a multi-user MIMO (MU-MIMO) system using common precoding algorithms. Alternatively, the GMM's sample generation ability can be utilized to design the precoders using a state-of-the-art stochastic iterative algorithm. After offloading the GMM to the MTs, they determine their feedback simply as the index of the GMM component with the highest responsibility for their received pilot signal. This strategy exhibits low complexity and allows for parallelization. Simulation results show that the proposed approach outperforms conventional methods, especially for a reduced number of pilots.

Abstract: Low-density parity-check codes together with belief propagation (BP) decoding are known to be well-performing for large block lengths. However, for short block lengths there is still a considerable gap between the performance of the BP decoder and the maximum likelihood decoder. Different ensemble decoding schemes such as, e.g., the automorphism ensemble decoder (AED), can reduce this gap in short block length regime. We propose a generalized AED (GAED) that uses automorphisms according to the definition in linear algebra. Here, an automorphism of a vector space is defined as a linear, bijective self-mapping, whereas in coding theory self-mappings that are scaled permutations are commonly used. We show that the more general definition leads to an explicit joint construction of codes and automorphisms, and significantly enlarges the search space for automorphisms of existing linear codes. Furthermore, we prove the concept that generalized automorphisms can indeed be used to improve decoding. Additionally, we propose a code construction of parity check codes enabling the construction of codes with suitably designed automorphisms. Finally, we analyze the decoding performances of the GAED for some of our constructed codes.

Abstract: Private information retrieval (PIR) is a privacy setting that allows a user to download a required message from a set of messages stored in a system of databases without revealing the index of the required message to the databases. PIR was introduced under computational privacy guarantees, and is recently re-formulated to provide information-theoretic guarantees, resulting in \emph{information theoretic privacy}. Subsequently, many important variants of the basic PIR problem have been studied focusing on fundamental performance limits as well as achievable schemes. More recently, a variety of conceptual extensions of PIR have been introduced, such as, private set intersection (PSI), private set union (PSU), and private read-update-write (PRUW). Some of these extensions are mainly intended to solve the privacy issues that arise in distributed learning applications due to the extensive dependency of machine learning on users' private data. In this article, we first provide an introduction to basic PIR with examples, followed by a brief description of its immediate variants. We then provide a detailed discussion on the conceptual extensions of PIR, along with potential research directions.