IEEE Transactions on Information Theory最新文献

{"title":"Streaming Codes for Three-Node Relay Networks With Burst Erasures","authors":"Vinayak Ramkumar;Myna Vajha;M. Nikhil Krishnan","doi":"10.1109/TIT.2024.3504538","DOIUrl":"https://doi.org/10.1109/TIT.2024.3504538","url":null,"abstract":"We study burst erasure correcting streaming codes for three-node relay networks, where there is a source-relay link and a relay-destination link. These codes guarantee that all message packets are recovered within a delay of \u0000<inline-formula> <tex-math>$tau $ </tex-math></inline-formula>\u0000 time slots, given that a single burst erasure of length at most b packets occurs in both links. Leveraging previously known techniques in the streaming code literature, we first provide a simple upper bound on the rate of burst erasure correcting streaming codes for three-node relay networks. Our main result is a coding scheme that achieves rates arbitrarily close to the rate upper bound, as message size increases.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"348-359"},"PeriodicalIF":2.2,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890297","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":"On Optimal Finite-Length Block Codes of Size Four for Binary Symmetric Channels","authors":"Yanyan Dong;Shenghao Yang","doi":"10.1109/TIT.2024.3504823","DOIUrl":"https://doi.org/10.1109/TIT.2024.3504823","url":null,"abstract":"An \u0000<inline-formula> <tex-math>$(n,M)$ </tex-math></inline-formula>\u0000 code refers to a binary code with blocklength n and codebook size M. Such codes are studied in the context of memoryless binary symmetric channels (BSCs) with maximum likelihood (ML) decoding. Previous research has characterized some optimal codes among the linear \u0000<inline-formula> <tex-math>$(n,4)$ </tex-math></inline-formula>\u0000 codes for any \u0000<inline-formula> <tex-math>$n geq 2$ </tex-math></inline-formula>\u0000. However, it was unknown whether these optimal codes among linear codes were better than all nonlinear codes. In this paper, we first demonstrate that for any \u0000<inline-formula> <tex-math>$n geq 2$ </tex-math></inline-formula>\u0000, there exists an optimal code among all \u0000<inline-formula> <tex-math>$(n,4)$ </tex-math></inline-formula>\u0000 codes that is either linear or belongs to a subset of nonlinear codes called Class-I codes. We identify all the optimal codes among the linear \u0000<inline-formula> <tex-math>$(n,4)$ </tex-math></inline-formula>\u0000 codes for each blocklength \u0000<inline-formula> <tex-math>$n geq 2$ </tex-math></inline-formula>\u0000 and discover some that were not previously reported in the literature. For any n from 2 to 8, all the optimal \u0000<inline-formula> <tex-math>$(n,4)$ </tex-math></inline-formula>\u0000 codes are identified. Except for \u0000<inline-formula> <tex-math>$n=3$ </tex-math></inline-formula>\u0000, all the optimal \u0000<inline-formula> <tex-math>$(n,4)$ </tex-math></inline-formula>\u0000 codes are equivalent to linear codes. There exist optimal \u0000<inline-formula> <tex-math>$(3,4)$ </tex-math></inline-formula>\u0000 codes that are not equivalent to linear codes. Furthermore, we introduce a subset of nonlinear codes called Class-II codes and show that for any \u0000<inline-formula> <tex-math>$n gt 3$ </tex-math></inline-formula>\u0000, the set composed of linear, Class-I, and Class-II codes and their equivalent codes contains all the optimal \u0000<inline-formula> <tex-math>$(n,4)$ </tex-math></inline-formula>\u0000 codes. Both Class-I and Class-II codes are close to linear codes in the sense that they involve only one type of column that is not included in linear codes. We derive a sufficient condition such that all the optimal \u0000<inline-formula> <tex-math>$(n,4)$ </tex-math></inline-formula>\u0000 codes are equivalent to linear codes, which can be evaluated by computer with a computation cost \u0000<inline-formula> <tex-math>$O(n^{6})$ </tex-math></inline-formula>\u0000.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"138-166"},"PeriodicalIF":2.2,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890176","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":"Optimal Codes in the Class of 2-Bit Delay Decodable Codes","authors":"Kengo Hashimoto;Ken-Ichi Iwata","doi":"10.1109/TIT.2024.3503717","DOIUrl":"https://doi.org/10.1109/TIT.2024.3503717","url":null,"abstract":"For an integer \u0000<inline-formula> <tex-math>$k geq 0$ </tex-math></inline-formula>\u0000, k-bit delay decodable code-tuples are source codes that use a finite number of code tables and allow a decoding delay of at most k bits. It is known that the class of k-bit delay decodable code-tuples can achieve a better average codeword length than Huffman codes for \u0000<inline-formula> <tex-math>$k geq 2$ </tex-math></inline-formula>\u0000. However, it is generally challenging to find an optimal k-bit delay decodable code-tuple (i.e., a k-bit delay decodable code-tuple achieving the optimal average codeword length among all k-bit delay decodable code-tuples) because the class of k-bit delay decodable code-tuples is a comprehensive and flexible class containing a variety of source code consisting of any finite number of code tables. AIFV (almost instantaneous fixed-to-variable length) codes are 2-bit delay decodable code-tuples consisting of two code tables satisfying certain constraints. This paper proves that the class of AIFV codes always contains an optimal 2-bit delay decodable code-tuple for any given source distribution. Thus, we can find an optimal 2-bit delay decodable code-tuple in the class of 2-bit delay decodable code-tuples by considering only the class of AIFV codes, which is a very restricted subclass compared to the whole class of 2-bit delay decodable code-tuples.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"797-832"},"PeriodicalIF":2.2,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890232","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":"Tradeoff Constructions for Quantum Locally Testable Codes","authors":"Adam Wills;Ting-Chun Lin;Min-Hsiu Hsieh","doi":"10.1109/TIT.2024.3503500","DOIUrl":"https://doi.org/10.1109/TIT.2024.3503500","url":null,"abstract":"In this work, we continue the search for quantum locally testable codes (qLTCs) of new parameters by presenting three constructions that can make new qLTCs from old. The first analyses the soundness of a quantum code under Hastings’ weight reduction construction for qLDPC codes to give a weight reduction procedure for qLTCs. Secondly, we describe a novel ‘soundness amplification’ procedure for qLTCs which can increase the soundness of any qLTC to a constant while preserving its distance and dimension, with an impact only felt on its locality. Finally, we apply the AEL distance amplification construction to the case of qLTCs for the first time which can turn a high-distance qLTC into one with linear distance, at the expense of other parameters. These constructions can be used on as-yet undiscovered qLTCs to obtain new parameters, but we also find a number of present applications to prove the existence of codes in previously unknown parameter regimes. In particular, applications of these operations to the hypersphere product code and the hemicubic code yield many previously unknown parameters. In addition, applications of all three results are described to an upcoming work.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"426-458"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10759074","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890197","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}

{"title":"Tight Lower Bound on the Error Exponent of Classical-Quantum Channels","authors":"Joseph M. Renes","doi":"10.1109/TIT.2024.3500578","DOIUrl":"https://doi.org/10.1109/TIT.2024.3500578","url":null,"abstract":"A fundamental quantity of interest in Shannon theory, classical or quantum, is the error exponent of a given channel W and rate R: the constant \u0000<inline-formula> <tex-math>$E(W,R)$ </tex-math></inline-formula>\u0000 which governs the exponential decay of decoding error when using ever larger optimal codes of fixed rate R to communicate over ever more (memoryless) instances of a given channel W. Nearly matching lower and upper bounds are well-known for classical channels. Here I show a lower bound on the error exponent of communication over arbitrary classical-quantum (CQ) channels which matches Dalai’s sphere-packing upper bound for rates above a critical value, exactly analogous to the case of classical channels. This proves a conjecture made by Holevo in his investigation of the problem. Unlike the classical case, however, the argument does not proceed via a refined analysis of a suitable decoder, but instead by leveraging a bound by Hayashi on the error exponent of the cryptographic task of privacy amplification. This bound is then related to the coding problem via tight entropic uncertainty relations and Gallager’s method of constructing capacity-achieving parity-check codes for arbitrary channels. Along the way, I find a lower bound on the error exponent of the task of compression of classical information relative to quantum side information that matches the sphere-packing upper bound of Cheng et al. In turn, the polynomial prefactors to the sphere-packing bound found by Cheng et al. may be translated to the privacy amplification problem, sharpening a recent result by Li, Yao, and Hayashi, at least for linear randomness extractors.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"530-538"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890174","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 Matrix Exponential Generalization of the Laplace Transform of Poisson Shot Noise","authors":"Nicholas R. Olson;Jeffrey G. Andrews","doi":"10.1109/TIT.2024.3502295","DOIUrl":"https://doi.org/10.1109/TIT.2024.3502295","url":null,"abstract":"We consider a generalization of the Laplace transform of Poisson shot noise defined as an integral transform with respect to a matrix exponential. We denote this as the matrix Laplace transform and establish that it is in general a matrix function extension of the scalar Laplace transform. We show that the matrix Laplace transform of Poisson shot noise admits an expression analogous to that implied by Campbell’s theorem. We demonstrate the utility of this generalization of Campbell’s theorem in two important applications: the characterization of a Poisson shot noise process and the derivation of the complementary CDF (CCDF) and meta-distribution of signal-to-interference-and-noise (SINR) models in Poisson networks. In the former application, we demonstrate how the higher order moments of Poisson shot noise may be obtained directly from the elements of its matrix Laplace transform. We further show how the CCDF of this object may be bounded using a summation of the first row of its matrix Laplace transform. For the latter application, we show how the CCDF of SINR models with phase-type distributed desired signal power may be obtained via an expectation of the matrix Laplace transform of the interference and noise, analogous to the canonical case of SINR models with Rayleigh fading. Additionally, when the power of the desired signal is exponentially distributed, we establish that the meta-distribution may be obtained in terms of the limit of a sequence expressed in terms of the matrix Laplace transform of a related Poisson shot noise process.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"396-412"},"PeriodicalIF":2.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890196","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 New Algebraic Approach for String Reconstruction From Substring Compositions","authors":"Utkarsh Gupta;Hessam Mahdavifar","doi":"10.1109/TIT.2024.3493762","DOIUrl":"https://doi.org/10.1109/TIT.2024.3493762","url":null,"abstract":"In this paper, we propose a new algorithm for the problem of string reconstruction from its substring composition multiset. Motivated by applications in polymer-based data storage for recovering strings from tandem mass-spectrometry sequencing, the proposed algorithm leverages the equivalent polynomial formulation of the problem which facilitates efficient parallel implementation. The computational complexity of the proposed reconstruction algorithm is upper bounded by \u0000<inline-formula> <tex-math>$6.5n^{2}$ </tex-math></inline-formula>\u0000 finite field operations, where the field size is upper bounded by \u0000<inline-formula> <tex-math>$10n$ </tex-math></inline-formula>\u0000, implying that the computational complexity is upper bounded by \u0000<inline-formula> <tex-math>$6.5n^{2}(3.22+log {n})$ </tex-math></inline-formula>\u0000 binary operations. Furthermore, it allows parallelization leading to \u0000<inline-formula> <tex-math>$O(n log n)$ </tex-math></inline-formula>\u0000 reconstruction latency. We characterize sufficient conditions for a length n binary string that guarantee the string’s reconstruction time complexity to be bounded polynomially. Moreover, the sufficient conditions on binary strings that guarantee reconstruction in polynomial time are more general than the conditions for the algorithm by Acharya et al. This is used to construct new codebooks of reconstruction codes that have efficient encoding procedures, and are larger, by at least a linear factor in size, compared to the previously best known construction by Pattabiraman et al., (2023).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"125-137"},"PeriodicalIF":2.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890192","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":"Repairing Schemes for Tamo-Barg Codes","authors":"Han Cai;Ying Miao;Moshe Schwartz;Xiaohu Tang","doi":"10.1109/TIT.2024.3498033","DOIUrl":"https://doi.org/10.1109/TIT.2024.3498033","url":null,"abstract":"In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.n this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"227-243"},"PeriodicalIF":2.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890302","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":"Secure Groupcast: Extra-Entropic Structure and Linear Feasibility","authors":"Hua Sun","doi":"10.1109/TIT.2024.3497920","DOIUrl":"https://doi.org/10.1109/TIT.2024.3497920","url":null,"abstract":"In the secure groupcast problem, a transmitter wants to securely groupcast a message with the maximum rate to the first N of K receivers by broadcasting with the minimum bandwidth, where the K receivers are each equipped with a key variable from a known joint distribution. Examples are provided to prove that different instances of secure groupcast that have the same entropic structure, i.e., the same entropy for all subsets of the key variables, can have different maximum groupcast rates and different minimum broadcast bandwidth. Thus, extra-entropic structure matters for secure groupcast. Next, the maximum groupcast rate is explored when the key variables are generic linear combinations of a basis set of independent key symbols, i.e., the keys lie in generic subspaces. The maximum groupcast rate is characterized when the dimension of each key subspace is either small or large, i.e., the extreme regimes. For the intermediate regime, various interference alignment schemes originated from wireless interference networks, such as eigenvector based and asymptotic schemes, are shown to be useful.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"683-697"},"PeriodicalIF":2.2,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890144","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":"Symplectic Self-Orthogonal Quasi-Cyclic Codes","authors":"Chaofeng Guan;Ruihu Li;Jingjie Lv;Zhi Ma","doi":"10.1109/TIT.2024.3497008","DOIUrl":"https://doi.org/10.1109/TIT.2024.3497008","url":null,"abstract":"In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of 1-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct many new binary symplectic self-orthogonal QC codes with excellent parameters, leading to 117 record-breaking quantum error-correction codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"114-124"},"PeriodicalIF":2.2,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890306","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}