IEEE Transactions on Information Theory最新文献_第3页

Optimal Online Bookmaking for Binary Games 二进制游戏的最佳在线博彩

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-18 DOI: 10.1109/TIT.2026.3694366

Alankrita Bhatt;Or Ordentlich;Oron Sabag

引用次数: 0

Pragmatic Lossless Compression: Fundamental Limits and Universality 实用无损压缩：基本限制和普遍性

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-07 DOI: 10.1109/TIT.2026.3691268

Andreas Theocharous;Lampros Gavalakis;Ioannis Kontoyiannis

{"title":"Pragmatic Lossless Compression: Fundamental Limits and Universality","authors":"Andreas Theocharous;Lampros Gavalakis;Ioannis Kontoyiannis","doi":"10.1109/TIT.2026.3691268","DOIUrl":"https://doi.org/10.1109/TIT.2026.3691268","url":null,"abstract":"The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability is required to be exponentially small in the blocklength. Accurate nonasymptotic expansions with explicit constants are obtained for the optimal rate, using tools from large deviations and Gaussian approximation. When the source distribution is unknown, a universal achievability result is obtained with an explicit “price for universality” term. This is based on a fine combinatorial estimate on the number of sequences with small empirical entropy, which might be of independent interest. Examples are shown indicating that, in the small excess-rate-probability regime, the approximation to the fundamental limit of the compression rate suggested by these bounds is significantly more accurate than the approximations provided by either normal approximation or error exponents. The new bounds reinforce the crucial operational conclusion that, in applications where the blocklength is relatively short and where stringent guarantees are required on the excess-rate probability, the best achievable rate is no longer close to the entropy. Rather, it is an appropriate, more <italic>pragmatic rate, determined via the inverse error exponent function and the blocklength.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4587-4601"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512043","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}

引用次数: 0

Minimax Optimal Sample Complexity for Iterated CVaR Reinforcement Learning With a Generative Model 基于生成模型的迭代CVaR强化学习的最小最大最优样本复杂度

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-13 DOI: 10.1109/TIT.2026.3692816

Zilong Deng;Alvaro Velasquez;Shaofeng Zou

{"title":"Minimax Optimal Sample Complexity for Iterated CVaR Reinforcement Learning With a Generative Model","authors":"Zilong Deng;Alvaro Velasquez;Shaofeng Zou","doi":"10.1109/TIT.2026.3692816","DOIUrl":"https://doi.org/10.1109/TIT.2026.3692816","url":null,"abstract":"Standard Reinforcement Learning (RL) algorithms are typically designed to maximize the expected accumulative reward, which may be inadequate in scenarios where risk sensitivity is critical. In this work, the problem of risk-sensitive RL with Iterated Conditional Value at Risk is studied, where the objective is to optimize outcomes under a specified risk level <inline-formula> <tex-math>$tau $ </tex-math></inline-formula> at each step. This work provides the first minimax optimal sample complexity analysis for this problem with a generative model. Specifically, the sample complexity is firstly characterized as a function of the number of states <inline-formula> <tex-math>$S$ </tex-math></inline-formula>, actions <inline-formula> <tex-math>$A$ </tex-math></inline-formula>, and effective horizon <inline-formula> <tex-math>$(1-gamma)^{-1}$ </tex-math></inline-formula> (resp. horizon <inline-formula> <tex-math>$H$ </tex-math></inline-formula> in the finite-horizon setting), and is further shown to be minimax optimal via a novel minimax lower bound analysis when the risk level <inline-formula> <tex-math>$0lt tau leq 1$ </tex-math></inline-formula> is treated as a constant or the risk level is above a threshold of <inline-formula> <tex-math>$gamma $ </tex-math></inline-formula> (resp. <inline-formula> <tex-math>$1-1/H$ </tex-math></inline-formula> in the finite horizon setting). For the case when the risk level is small, the limiting case of <inline-formula> <tex-math>$tau rightarrow 0$ </tex-math></inline-formula>, termed worst-path RL, is then studied, and the minimax optimal sample complexity is also theoretically characterized.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5077-5103"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512146","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}

引用次数: 0

Doubly Minimized Petz and Sandwiched Rényi Mutual Information: Operational Interpretation From Binary Quantum State Discrimination 双最小化Petz和三明治r<s:1>互信息：二元量子态判别的运算解释

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-20 DOI: 10.1109/TIT.2026.3695315

Laura Burri

{"title":"Doubly Minimized Petz and Sandwiched Rényi Mutual Information: Operational Interpretation From Binary Quantum State Discrimination","authors":"Laura Burri","doi":"10.1109/TIT.2026.3695315","DOIUrl":"https://doi.org/10.1109/TIT.2026.3695315","url":null,"abstract":"The doubly minimized Petz Rényi mutual information of order <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula> is defined as the minimum of the Petz divergence of order <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula> of a given bipartite quantum state relative to all product states. The doubly minimized sandwiched Rényi mutual information is defined analogously, with the Petz divergence replaced by the sandwiched divergence. In this work, we study certain binary quantum state discrimination problems related to correlation detection. We show that the corresponding direct exponent is determined by the doubly minimized Petz Rényi mutual information of order <inline-formula> <tex-math>$alpha in (1/2,1)$ </tex-math></inline-formula>, and that the strong converse exponent is determined by the doubly minimized sandwiched Rényi mutual information of order <inline-formula> <tex-math>$alpha in (1,infty)$ </tex-math></inline-formula>. This provides an operational interpretation of these types of Rényi mutual information and generalizes previous results for classical probability distributions to the quantum setting. For completeness, we also study the corresponding moderate deviation regime both below and above the threshold, and determine the Stein exponent and the second-order asymptotics.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4958-4979"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11527399","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized Inverse Discrete Fourier Transform With Application to Goppa Codes 广义离散傅里叶反变换在Goppa码中的应用

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-15 DOI: 10.1109/TIT.2026.3693655

Nianqi Tang;Yunghsiang S. Han;Chao Chen;Danyang Pei

{"title":"Generalized Inverse Discrete Fourier Transform With Application to Goppa Codes","authors":"Nianqi Tang;Yunghsiang S. Han;Chao Chen;Danyang Pei","doi":"10.1109/TIT.2026.3693655","DOIUrl":"https://doi.org/10.1109/TIT.2026.3693655","url":null,"abstract":"This paper introduces the concept of the generalized inverse discrete Fourier transform over a finite field and studies its application to the decoding of codes. It also proposes an efficient algorithm for computing the generalized inverse discrete Fourier transform, called the fast generalized inverse discrete Fourier transform. Based on this fast transform, the paper shows that, for any <inline-formula> <tex-math>$(n, k)$ </tex-math></inline-formula> generalized Reed–Solomon code, if the underlying field contains an additive or multiplicative subgroup of order <inline-formula> <tex-math>$2^{mu } geq n - k$ </tex-math></inline-formula> and <inline-formula> <tex-math>$n$ </tex-math></inline-formula> is proportional to the field size, then there exists a decoding algorithm with complexity <inline-formula> <tex-math>$Obigl (nlog (n - k) + (n - k)log ^{2}(n - k)bigr)$ </tex-math></inline-formula>. The paper further discusses the additive fast generalized inverse discrete Fourier transform over binary extension fields, which leads to a fast decoding algorithm for binary Goppa codes with complexity <inline-formula> <tex-math>$Obigl (nlog r + rlog ^{2} rbigr)$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$n$ </tex-math></inline-formula> is the code length and <inline-formula> <tex-math>$r$ </tex-math></inline-formula> is the degree of the Goppa polynomial. This achieves the best known decoding complexity for binary Goppa codes to date. A complexity comparison shows that the proposed algorithm reduces the number of field operations by 88% compared to traditional methods when decoding the Goppa code with parameters <inline-formula> <tex-math>$n = 8192$ </tex-math></inline-formula> and <inline-formula> <tex-math>$r = 128$ </tex-math></inline-formula>, which is used in the McEliece cryptosystem as a candidate scheme for post-quantum cryptography.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4719-4738"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148507542","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}

引用次数: 0

Achievable Rates for the Relay Channel With Orthogonal Receiver Components 具有正交接收器组件的中继信道的可实现速率

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-13 DOI: 10.1109/TIT.2026.3693057

Abbas El Gamal;Amin Gohari;Chandra Nair

引用次数: 0

Covert Entanglement Generation and Secrecy 隐蔽纠缠的产生和保密

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-04-30 DOI: 10.1109/TIT.2026.3689208

Ohad Kimelfeld;Boulat A. Bash;Uzi Pereg

引用次数: 0

Structured Codes for Distributed Matrix Multiplication 分布式矩阵乘法的结构化代码

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-11 DOI: 10.1109/TIT.2026.3692427

Derya Malak

{"title":"Structured Codes for Distributed Matrix Multiplication","authors":"Derya Malak","doi":"10.1109/TIT.2026.3692427","DOIUrl":"https://doi.org/10.1109/TIT.2026.3692427","url":null,"abstract":"Our work addresses the well-known open problem of distributed computing of bilinear functions of two correlated sources <bold>A and <bold>B. In a setting with two nodes, with the first node having access to <bold>A and the second to <bold>B, we establish bounds on the optimal sum rate that allows a receiver to compute an important class of non-linear functions, and in particular bilinear functions, including dot products <inline-formula> <tex-math>$langle {mathbf { A}},{mathbf { B}}rangle $ </tex-math></inline-formula>, and general matrix products <inline-formula> <tex-math>${mathbf { A}}^{intercal }{mathbf { B}}$ </tex-math></inline-formula> over finite fields. The bounds are tight for large field sizes, for which case we can derive the exact fundamental performance limits for all problem dimensions and a large class of sources. Our achievability scheme involves the design of non-linear transformations of <bold>A and <bold>B, carefully calibrated to work synergistically with the structured linear encoding scheme by Körner and Marton. The subsequent converses derived here, calibrate the Han-Kobayashi approach and the strong converse of Ahlswede-Gács-Körner to yield relatively tight converses on the sum rate. We exhibit unbounded compression gains over Slepian-Wolf coding, depending on the source correlations. In the end, this work characterizes the fundamental limits of distributed computing for a crucial class of functions, while succinctly capturing the inherent computation structures and source correlations.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5160-5182"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511369","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}

引用次数: 0

Nonasymptotic Oblivious Relaying and Variable-Length Noisy Lossy Source Coding 非渐近无关中继与变长噪声有损源编码

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-04 DOI: 10.1109/TIT.2026.3690044

Yanxiao Liu;Sepehr Heidari Advary;Cheuk Ting Li

引用次数: 0

Four Classes of LCD Codes From (*)-(L, P)-Twisted Generalized Reed–Solomon Codes （*）-(L， P)-扭曲广义Reed-Solomon码的四类LCD码

IF 2.6 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-11 DOI: 10.1109/TIT.2026.3691789

Zhonghao Liang;Qunying Liao

{"title":"Four Classes of LCD Codes From (*)-(L, P)-Twisted Generalized Reed–Solomon Codes","authors":"Zhonghao Liang;Qunying Liao","doi":"10.1109/TIT.2026.3691789","DOIUrl":"https://doi.org/10.1109/TIT.2026.3691789","url":null,"abstract":"It is well known that maximum distance separable (in short, MDS) codes and linear complementary dual (in short, LCD) codes are very important in coding theory and practice. In 2023, Yue et al. constructed three classes of LCD MDS codes via a class of TGRS codes with one twists, i.e., <inline-formula> <tex-math>$(*)$ </tex-math></inline-formula>-TGRS codes. Recently, Wu et al. also constructed several classes of LCD MDS codes via a class of TGRS codes with two twists. In this paper, we unify their constructions by defining the <inline-formula> <tex-math>$(*)$ </tex-math></inline-formula>-<inline-formula> <tex-math>$(mathcal {L},mathcal {P})$ </tex-math></inline-formula>- twisted generalized Reed-Solomon (in short, <inline-formula> <tex-math>$(*)$ </tex-math></inline-formula>-<inline-formula> <tex-math>$(mathcal {L},mathcal {P})$ </tex-math></inline-formula>-TGRS) code, give the parity-check matrix of <inline-formula> <tex-math>$(*)$ </tex-math></inline-formula>-<inline-formula> <tex-math>$(mathcal {L},mathcal {P})$ </tex-math></inline-formula>-TGRS codes, and then construct four classes of LCD codes. Finally, some corresponding examples are given.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4788-4801"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512045","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}

引用次数: 0