IEEE Transactions on Information Theory最新文献

{"title":"Simultaneous Computation and Communication Over MAC","authors":"Matthias Frey;Igor Bjelaković;Michael C. Gastpar;Jingge Zhu","doi":"10.1109/TIT.2025.3542673","DOIUrl":"https://doi.org/10.1109/TIT.2025.3542673","url":null,"abstract":"We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver with vanishing error probability. Analog transmitters hold sequences of analog values. Some functions of these distributed values (but not the values themselves) need to be conveyed to the receiver, subject to a fidelity criterion such as mean squared error (MSE) or a certain maximum error with given confidence. For the case in which the computed function for the analog transmitters is a sum of values in <inline-formula> <tex-math>$[-1,1]$ </tex-math></inline-formula>, we derive inner and outer bounds for the tradeoff of digital and analog rates of communication under peak and average power constraints for digital transmitters and a peak power constraint for analog transmitters. We then extend the achievability result to a class of functions that includes all linear and some non-linear functions. This extended scheme works over fading channels as long as full channel state information is available at the transmitter. The practicality of our proposed communication scheme is shown in channel simulations that use a version of the scheme based on low density parity check (LDPC) coding. We evaluate the system performance for different block lengths and Gaussian as well as non-Gaussian noise distributions.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3644-3665"},"PeriodicalIF":2.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constructing (h, d) Cooperative MSR Codes With Sub-Packetization (d − k + h)(d − k + 1)⌈n/2⌉","authors":"Zihao Zhang;Guodong Li;Sihuang Hu","doi":"10.1109/TIT.2025.3542118","DOIUrl":"https://doi.org/10.1109/TIT.2025.3542118","url":null,"abstract":"We address the multi-node failure repair challenges for MDS array codes. Presently, two primary models are employed for multi-node repairs: the centralized model where all failed nodes are restored in a singular data center, and the cooperative model where failed nodes acquire data from auxiliary nodes and collaborate amongst themselves for the repair process. This paper focuses on the cooperative model, and we provide explicit constructions of optimal MDS array codes with <italic>d</i> helper nodes under this model. The sub-packetization level of our new codes is <inline-formula> <tex-math>$(d-k+h)(d-k+1)^{lceil n/2 rceil }$ </tex-math></inline-formula> where <italic>h</i> is the number of failed nodes, <italic>k</i> the number of information nodes, and <italic>n</i> the code length. This improves upon recent constructions by Liu et al. (IEEE Transactions on Information Theory, Vol. 69, 2023).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2505-2516"},"PeriodicalIF":2.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fundamental Limits of Covert Communication Over Classical-Quantum Channels","authors":"Michael S. Bullock;Azadeh Sheikholeslami;Mehrdad Tahmasbi;Robert C. Macdonald;Saikat Guha;Boulat A. Bash","doi":"10.1109/TIT.2025.3537970","DOIUrl":"https://doi.org/10.1109/TIT.2025.3537970","url":null,"abstract":"We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a of <italic>n</i> input states is used: <inline-formula> <tex-math>$L_{mathrm { SRL}}sqrt {n}+o(sqrt {n})$ </tex-math></inline-formula> covert bits (but no more) can be reliably transmitted in <italic>n</i> uses of classical-quantum channel, where <inline-formula> <tex-math>$L_{mathrm { SRL}}gt 0$ </tex-math></inline-formula> is a channel-dependent constant that we call <italic>covert capacity</i>. We also show that ensuring covertness requires <inline-formula> <tex-math>$J_{mathrm { SRL}}sqrt {n}+o(sqrt {n})$ </tex-math></inline-formula> bits secret key shared by the communicating parties prior to transmission, where <inline-formula> <tex-math>$J_{mathrm { SRL}}geq 0$ </tex-math></inline-formula> is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on all <italic>n</i> channel uses. We determine the single-letter expressions for <inline-formula> <tex-math>$L_{mathrm { SRL}}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$J_{mathrm { SRL}}$ </tex-math></inline-formula>, and establish conditions when <inline-formula> <tex-math>$J_{mathrm { SRL}}=0$ </tex-math></inline-formula> (i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2741-2762"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Random Staircase Generator Matrix Codes: Coding Theorem, Performance Analysis, and Code Design","authors":"Qianfan Wang;Yiwen Wang;Yixin Wang;Jifan Liang;Xiao Ma","doi":"10.1109/TIT.2025.3541734","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541734","url":null,"abstract":"In this paper, we present a class of codes, referred to as random staircase generator matrix codes (SGMCs), which have staircase-like generator matrices. In the infinite-length region, we prove that the random SGMC is capacity-achieving over binary-input output-symmetric (BIOS) channels. In the finite-length region, we propose the generalized representative ordered statistics decoding with local constraints (LC-ROSD) algorithm for the SGMCs. The most distinguished feature of the SGMCs with LC-ROSD is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE), avoiding the serial GE of conventional OSD and supporting a potential low decoding latency, as implied from simulations. To analyze the performance of random SGMCs in the finite-length region, we derive the ensemble weight spectrum and invoke the conventional union bound. We also derive a partially random coding union (RCU) bound, which is tighter than the conventional one and is used as a criterion to design the SGMCs. Staircase-like generator matrices allow us to derive a series of (tighter and tighter) lower bounds based on the second-order Bonferroni inequality with the incremental number of codewords. The numerical results show that the decoding performance can match well with the proposed partially RCU bound for different code rates and different profiles. The numerical results also show that the tailored SGMCs with the LC-ROSD algorithm can approach the finite-length performance bound, outperforming the 5G low-density parity-check (LDPC) codes, 5G polar codes, and Reed-Muller (RM) codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3497-3509"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variable-Length Feedback Codes Over Known and Unknown Channels With Non-Vanishing Error Probabilities","authors":"Recep Can Yavas;Vincent Y. F. Tan","doi":"10.1109/TIT.2025.3541629","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541629","url":null,"abstract":"We study variable-length feedback (VLF) codes with noiseless feedback for discrete memoryless channels. We present a novel non-asymptotic bound, which analyzes the average error probability and average decoding time of our modified Yamamoto-Itoh scheme. We then optimize the parameters of our code in the asymptotic regime where the average error probability <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> remains a constant as the average decoding time <italic>N</i> approaches infinity. Our second-order achievability bound is an improvement of Polyanskiy et al.’s (2011) achievability bound. We also develop a universal VLF code that does not rely on the knowledge of the underlying channel parameters. Our universal VLF code employs the empirical mutual information as its decoding metric and universalizes the code by Polyanskiy et al. (2011). We derive a second-order achievability bound for universal VLF codes. Our results for both VLF and universal VLF codes are extended to the additive white Gaussian noise channel with an average power constraint. The former yields an improvement over Truong and Tan’s (2017) achievability bound. The proof of our results for universal VLF codes uses a refined version of the method of types and an asymptotic expansion from the nonlinear renewal theory literature.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3271-3286"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Comprehensive Study on Ziv-Zakai Lower Bounds on the MMSE","authors":"Minoh Jeong;Alex Dytso;Martina Cardone","doi":"10.1109/TIT.2025.3541987","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541987","url":null,"abstract":"This paper explores Bayesian lower bounds on the minimum mean squared error (MMSE) that belong to the well-known Ziv-Zakai family. The Ziv-Zakai technique relies on connecting the bound to an <inline-formula> <tex-math>$mathsf M$ </tex-math></inline-formula>-ary hypothesis testing problem. There are three versions of the Ziv-Zakai bound (ZZB): the first version relies on the so-called <italic>valley-filling function</i>, the second one is a relaxation of the first bound which omits the valley-filling function, and the third one, namely the single-point ZZB (SZZB), replaces the integration present in the first two bounds with a single point maximization. The first part of this paper focuses on providing the most general version of the bounds. It is shown that these bounds hold without any assumption on the distribution of the estimand. This makes the bounds applicable to discrete and mixed distributions. Then, the SZZB is extended to an <inline-formula> <tex-math>$mathsf M$ </tex-math></inline-formula>-ary setting and a version of it that holds for the multivariate setting is provided. In the second part, general properties of these bounds are provided. First, unlike the Bayesian <italic>Cramér-Rao bound</i>, it is shown that all the versions of the ZZB <italic>tensorize</i>. Second, a characterization of the <italic>high-noise</i> asymptotic is provided, which is used to argue about the tightness of the bounds. Third, a complete <italic>low-noise</i> asymptotic is provided under the assumptions of mixed-input distributions and Gaussian additive noise channels. In the low-noise, it is shown that the ZZB is generally tight, but there are examples for which the SZZB is not tight. In the third part, the tightness of the bounds is evaluated. First, it is shown that in the low-noise regime the ZZB without the valley-filling function, and, therefore, also the ZZB with the valley-filling function, are tight for mixed-input distributions and Gaussian additive noise channels. Second, for discrete inputs it is shown that the ZZB with the valley-filling function is always sub-optimal, and equal to zero without the valley-filling function. Third, unlike for the ZZB, an example is shown for which the SZZB is tight to the MMSE for discrete inputs. Fourth, sufficient and necessary conditions for the tightness of the bounds are provided. Finally, some examples are provided in which the bounds in the Ziv-Zakai family outperform other well-known Bayesian lower bounds, namely the Cramér-Rao bound and the maximum entropy bound.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"3214-3236"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blind Interference Alignment for MapReduce: Exploiting Side-Information With Reconfigurable Antennas","authors":"Yuxiang Lu;Syed A. Jafar","doi":"10.1109/TIT.2025.3541808","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541808","url":null,"abstract":"In order to explore how blind interference alignment (BIA) schemes may take advantage of side-information in computation tasks, we study the degrees of freedom (DoF) of a <italic>K</i> user wireless network setting that arises in full-duplex wireless MapReduce applications. In this setting the receivers are assumed to have reconfigurable antennas and channel knowledge, while the transmitters have neither, i.e., the transmitters lack channel knowledge and are only equipped with conventional antennas. The central ingredient of the problem formulation is the message structure arising out of the Shuffle phase of MapReduce, whereby each transmitter has a subset of messages that need to be delivered to various receivers, and each receiver has a subset of messages available to it in advance as side-information. We approach this problem by decomposing it into distinctive stages that help identify key ingredients of the overall solution. The novel elements that emerge from the first stage, called broadcast with groupcast messages, include an outer maximum distance separable (MDS) code structure at the transmitter, and an algorithm for iteratively determining groupcast-optimal reconfigurable antenna switching patterns at the receiver to achieve intra-message (among the symbols of the same message) alignment. The next stage, called unicast with side-information, reveals optimal inter-message (among symbols of different messages) alignment patterns to exploit side-information, and by a relabeling of messages, connects to the desired MapReduce setting.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2604-2625"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Joint Message Detection and Channel Estimation for Unsourced Random Access in Cell-Free User-Centric Wireless Networks","authors":"Burak Çakmak;Eleni Gkiouzepi;Manfred Opper;Giuseppe Caire","doi":"10.1109/TIT.2025.3541281","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541281","url":null,"abstract":"We consider unsourced random access (uRA) in a cell-free (CF) user-centric wireless network, where a large number of potential users compete for a random access slot, while only a finite subset is active. The random access users transmit codewords of length <italic>L</i> symbols from a shared codebook, which are received by <italic>B</i> geographically distributed radio units (RUs), each equipped with <italic>M</i> antennas. Our goal is to devise and analyze a <italic>centralized</i> decoder to detect the transmitted messages (without prior knowledge of the active users) and estimate the corresponding channel state information. A specific challenge lies in the fact that, due to the geographically distributed nature of the CF network, there is no fixed correspondence between codewords and large-scale fading coefficients (LSFCs). This makes current activity detection approaches which make use of this fixed LSFC-codeword association not directly applicable. To overcome this problem, we propose a scheme where the access codebook is partitioned in location-based subcodes, such that users in a particular location make use of the corresponding subcode. The joint message detection and channel estimation is obtained via a novel <italic>Approximated Message Passing</i> (AMP) algorithm for a linear superposition of matrix-valued sources corrupted by noise. The statistical asymmetry in the fading profile and message activity leads to <italic>different statistics</i> for the matrix sources, which distinguishes the AMP formulation from previous cases. In the regime where the codebook size scales linearly with <italic>L</i>, while <italic>B</i> and <italic>M</i> are fixed, we present a rigorous high-dimensional (but finite-sample) analysis of the proposed AMP algorithm. Exploiting this, we then present a precise (and rigorous) large-system analysis of the message missed-detection and false-alarm rates, as well as the channel estimation mean-square error. The resulting system allows the seamless formation of user-centric clusters and very low latency beamformed uplink-downlink communication without explicit user-RU association, pilot allocation, and power control. This makes the proposed scheme highly appealing for low-latency random access communications in CF networks.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3614-3643"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Covering Radii and Deep Holes of Two Classes of Extended Twisted GRS Codes and Their Applications","authors":"Yang Li;Shixin Zhu;Zhonghua Sun","doi":"10.1109/TIT.2025.3541799","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541799","url":null,"abstract":"Maximum distance separable (MDS) codes that are not monomially equivalent to generalized Reed-Solomon (GRS) codes are called non-GRS MDS codes, which have important applications in communication and cryptography. Covering radii and deep holes of linear codes are closely related to their decoding problems. In the literature, the covering radii and deep holes of GRS codes have been extensively studied, while little is known about non-GRS MDS codes. In this paper, we study two classes of extended twisted generalized Reed-Solomon (ETGRS) codes involving their non-GRS MDS properties, covering radii, and deep holes. In other words, we obtain two classes of non-GRS MDS codes with known covering radii and deep holes. As applications, we further directly derive more non-GRS MDS codes, and get some results on the existence of their error-correcting pairs. As a byproduct, we find some connections between the well-known Roth-Lempel codes and these two classes ETGRS codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3516-3530"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MDS Variable Generation and Secure Summation With User Selection","authors":"Yizhou Zhao;Hua Sun","doi":"10.1109/TIT.2025.3541551","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541551","url":null,"abstract":"A collection of <italic>K</i> random variables are called <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS if any <italic>n</i> of the <italic>K</i> variables are independent and determine all remaining variables. In the MDS variable generation problem, <italic>K</i> users wish to generate variables that are <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS using a randomness variable owned by each user. We show that to generate 1 bit of <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS variables for each <inline-formula> <tex-math>$n in {1,2,cdots , K}$ </tex-math></inline-formula>, the minimum size of the randomness variable at each user is <inline-formula> <tex-math>$1 + 1/2 + cdots + 1/K$ </tex-math></inline-formula> bits. An intimately related problem is secure summation with user selection, where a server may select an arbitrary subset of <italic>K</i> users and securely compute the sum of the inputs of the selected users. We show that to compute 1 bit of an arbitrarily chosen sum securely, the minimum size of the key held by each user is <inline-formula> <tex-math>$1 + 1/2 + cdots + 1/(K-1)$ </tex-math></inline-formula> bits, whose achievability uses the generation of <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS variables for <inline-formula> <tex-math>$n in {1,2,cdots ,K-1}$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"3129-3141"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}