IEEE Transactions on Information Theory最新文献

{"title":"Two Generic Constructions of MDS Array Codes With Optimal Repair Bandwidth From Two Special Sets","authors":"Hongwei Zhu;Jingjie Lv;Shu-Tao Xia;Hanxu Hou","doi":"10.1109/TIT.2025.3545109","DOIUrl":"https://doi.org/10.1109/TIT.2025.3545109","url":null,"abstract":"The maximum distance separable (MDS) codes are the optimal codes to achieve Singleton bound, providing maximum error tolerance under a given number of parity nodes. Ye and Barg leveraged permutation matrices and Reed-Solomon type codes to devise 7 explicit constructions for constructing MDS array codes with optimal repair property (as known as MSR codes) or even optimal access property. Drawing inspiration from these explicit constructions, we provide two generic constructions for constructing MSR codes from high-rate MDS codes or MDS array codes. In this paper, we introduce the concepts of s-pairwise MDS codes sets and s-pairwise MDS array codes sets. Two generic constructions (<xref>Generic Constructions I</xref> and <xref>II</xref>) for constructing the MSR code using the <italic>s</i>-pairwise MDS codes sets or the <italic>s</i>-pairwise MDS array codes sets are given. Constructions 1 to 3 proposed by Ye and Barg can be regarded as some special cases of <xref>Generic Construction I</xref>, and Constructions 1 to 3 proposed by Li et al., can be regarded as some special cases of <xref>Generic Construction II</xref>. It is worth mentioning that <xref>Generic Construction II</xref> can be applied to any finite field, including the binary field. We also demonstrate how to obtain the <italic>s</i>-pairwise MDS code sets and the <italic>s</i>-pairwise MDS array code sets from a high-rate MDS code or MDS array code over <inline-formula> <tex-math>$mathbb {F}_{q}$ </tex-math></inline-formula>. We obtain a novel class of MSR codes by utilizing the MDS array codes provided by Lv et al., as component codes according to <xref>Generic Construction II</xref>. As a byproduct of Constructions 4 to 7, we obtain a new class of MSR codes with optimal access property. Using two types of sets <inline-formula> <tex-math>$Gamma _{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$Gamma _{2}$ </tex-math></inline-formula> with the property that matrices commute, we present several new constructions for MSR codes with the optimal access property over any finite field. In this paper, compared with the constructions over binary field proposed by Li et al., the sub-packetization of our constructions applicable to the binary field is significantly reduced.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3582-3601"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870978","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":"Combinatorial Alphabet-Dependent Bounds for Insdel Codes","authors":"Xiangliang Kong;Itzhak Tamo;Hengjia Wei","doi":"10.1109/TIT.2025.3545061","DOIUrl":"https://doi.org/10.1109/TIT.2025.3545061","url":null,"abstract":"Error-correcting codes resilient to synchronization errors such as insertions and deletions are known as insdel codes. In this paper, we present several new combinatorial upper and lower bounds on the maximum size of <italic>q</i>-ary insdel codes. Our main upper bound is a sphere-packing bound obtained by solving a linear programming (LP) problem. It improves upon previous results for cases when the distance <italic>d</i> or the alphabet size <italic>q</i> is large. Our first lower bound is derived from a connection between insdel codes and matchings in special hypergraphs. This lower bound, together with our upper bound, shows that for fixed block length <italic>n</i> and edit distance <italic>d</i>, when <italic>q</i> is sufficiently large, the maximum size of insdel codes is <inline-formula> <tex-math>$ frac {q^{n-frac {d}{2}+1}}{binom {n}{frac {d}{2}-1}}(1 pm o(1))$ </tex-math></inline-formula>. The second lower bound refines Alon et al.’s recent logarithmic improvement on Levenshtein’s GV-type bound and extends its applicability to large <italic>q</i> and <italic>d</i>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3544-3559"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875159","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":"Key-Cast Over Networks","authors":"Michael Langberg;Michelle Effros","doi":"10.1109/TIT.2025.3544444","DOIUrl":"https://doi.org/10.1109/TIT.2025.3544444","url":null,"abstract":"For a multi-source multi-terminal noiseless network, the multicast <italic>key-dissemination</i> problem, here called the <italic>key-cast</i> problem, involves the task of multicasting a (secret) key <italic>K</i> from the network sources to its terminals. Unlike traditional communication, where messages must be delivered from source to destination(s) unchanged, key-cast is more flexible since key-cast need not require source reconstruction at destination nodes. Instead, the distributed key can be a mixture of sources from which the sources themselves may be unrecoverable. Key-cast (also known as secret key agreement) in memoryless networks has seen significant studies over the past decades. This work initiates the study of key-cast in noiseless networks, i.e., network coding, and addresses the similarities and differences between traditional forms of communication that require source reconstruction and the less constrained form of communication in the key-cast task. The study varies according to three criteria. The setting can be secure, in which case the shared key is not revealed to an eavesdropper (whose capabilities we constrain), or non-secure, in which case the key need not be hidden. The setting can have one or multiple source nodes capable of generating independent randomness to be used in the key generation process. And the setting can have one or multiple terminal sets, where the latter case is referred to as multiple key-cast. In multiple key-cast, one requires that terminals in each terminal set decode a different shared key. In the given settings, this work derives combinatorial conditions for key-cast and multiple key-cast and designs corresponding communication schemes. In addition, the study compares the key-cast rate with and without the restriction of source reconstruction that is needed in traditional forms of communication. Key-cast achieves a strict advantage in rate when source reconstruction is relaxed.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3409-3423"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873125","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":"The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models","authors":"Tolga Ergen;Mert Pilanci","doi":"10.1109/TIT.2025.3545564","DOIUrl":"https://doi.org/10.1109/TIT.2025.3545564","url":null,"abstract":"Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce successful models and do not have a clear theoretical foundation. In this study, we examine the use of convex optimization theory and sparse recovery models to refine the training process of neural networks and provide a better interpretation of their optimal weights. We focus on training two-layer neural networks with piecewise linear activations and demonstrate that they can be formulated as a finite-dimensional convex program. These programs include a regularization term that promotes sparsity, which constitutes a variant of group Lasso. We first utilize semi-infinite programming theory to prove strong duality for finite width neural networks and then we express these architectures equivalently as high dimensional convex sparse recovery models. Remarkably, the worst-case complexity to solve the convex program is polynomial in the number of samples and number of neurons when the rank of the data matrix is bounded, which is the case in convolutional networks. To extend our method to training data of arbitrary rank, we develop a novel polynomial-time approximation scheme based on zonotope subsampling that comes with a guaranteed approximation ratio. We also show that all the stationary points of the nonconvex training objective can be characterized as the global optimum of a subsampled convex program. Our convex models can be trained using standard convex solvers without resorting to heuristics or extensive hyper-parameter tuning unlike non-convex methods. Due to the convexity, optimizer hyperparameters such as initialization, batch sizes, and step size schedules have no effect on the final model. Through extensive numerical experiments, we show that convex models can outperform traditional non-convex methods and are not sensitive to optimizer hyperparameters. The code for our experiments is available at <uri>https://github.com/pilancilab/convex_nn</uri>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3854-3870"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871118","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":"The Duality Upper Bound for Finite-State Channels With Feedback","authors":"Bashar Huleihel;Oron Sabag;Ziv Aharoni;Haim H. Permuter","doi":"10.1109/TIT.2025.3545688","DOIUrl":"https://doi.org/10.1109/TIT.2025.3545688","url":null,"abstract":"This paper investigates the capacity of finite-state channels (FSCs) with feedback. We derive an upper bound on the feedback capacity of FSCs by extending the duality upper bound method from mutual information to the case of directed information. The upper bound is expressed as a multi-letter expression that depends on a test distribution on the sequence of channel outputs. For any FSC, we show that if the test distribution is structured on a <italic>Q</i>-graph, the upper bound can be formulated as a Markov decision process (MDP) whose state being a belief on the channel state. In the case of FSCs and states that are either unifilar or have a finite memory, the MDP state simplifies to take values in a finite set. Consequently, the MDP consists of a finite number of states, actions, and disturbances. This finite nature of the MDP is of significant importance, as it ensures that dynamic programming algorithms can solve the associated Bellman equation to establish analytical upper bounds, even for channels with large alphabets. We demonstrate the simplicity of computing bounds by establishing the capacity of a broad family of Noisy Output is the State (NOST) channels as a simple closed-form analytical expression. Furthermore, we introduce novel, nearly optimal analytical upper bounds on the capacity of the Noisy Ising channel.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3255-3270"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875158","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":"Bounding the Graph Capacity With Quantum Mechanics and Finite Automata","authors":"Alexander Meiburg","doi":"10.1109/TIT.2025.3544970","DOIUrl":"https://doi.org/10.1109/TIT.2025.3544970","url":null,"abstract":"The zero-error capacity of a channel (or “Shannon capacity of a graph”) quantifies how much information can be transmitted with no risk of error. In contrast to the Shannon capacity of a <italic>channel</i>, the zero-error capacity has not even been shown to be computable: we have no convergent upper bounds. In this work, we present a new quantity, the zero-error <italic>unitary</i> capacity, and show that it can be succinctly represented as the tensor product value of a quantum game. By studying the structure of finite automata, we show that the unitary capacity is within a controllable factor of the zero-error capacity. This allows new upper bounds through the sum-of-squares hierarchy, which converges to the commuting operator value of the game. Under the conjecture that the commuting operator and tensor product value of this game are equal, this would yield an algorithm for computing the zero-error capacity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3305-3316"},"PeriodicalIF":2.2,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875073","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":"Determining the Covering Radius of All Generalized Zetterberg Codes in Odd Characteristic","authors":"Minjia Shi;Shitao Li;Tor Helleseth;Ferruh Özbudak","doi":"10.1109/TIT.2025.3544025","DOIUrl":"https://doi.org/10.1109/TIT.2025.3544025","url":null,"abstract":"For an integer <inline-formula> <tex-math>$sge 1$ </tex-math></inline-formula>, let <inline-formula> <tex-math>${mathcal {C}}_{s}(q_{0})$ </tex-math></inline-formula> be the generalized Zetterberg code of length <inline-formula> <tex-math>$q_{0}^{s}+1$ </tex-math></inline-formula> over the finite field <inline-formula> <tex-math>${mathbb {F}}_{q_{0}}$ </tex-math></inline-formula> of odd characteristic. Recently, Shi et al. determined the covering radius of <inline-formula> <tex-math>${mathcal {C}}_{s}(q_{0})$ </tex-math></inline-formula> for <inline-formula> <tex-math>$q_{0}^{s} cancel {equiv }7 pmod {8}$ </tex-math></inline-formula>, and left the remaining case as an open problem. In this paper, we develop a general technique involving arithmetic of finite fields and algebraic curves over finite fields to determine the covering radius of all generalized Zetterberg codes for <inline-formula> <tex-math>$q_{0}^{s} equiv 7 pmod {8}$ </tex-math></inline-formula>, which therefore solves this open problem. We also introduce the concept of twisted half generalized Zetterberg codes of length <inline-formula> <tex-math>$frac {q_{0}^{s}+1}{2}$ </tex-math></inline-formula>, and show the same results hold for them. As a result, we obtain some quasi-perfect codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3602-3613"},"PeriodicalIF":2.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870977","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":"Higher-Order Staircase Codes","authors":"Mohannad Shehadeh;Frank R. Kschischang;Alvin Y. Sukmadji;William Kingsford","doi":"10.1109/TIT.2025.3544168","DOIUrl":"https://doi.org/10.1109/TIT.2025.3544168","url":null,"abstract":"We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term “higher-order staircase codes” arises from the marriage of two distinct combinatorial objects: difference triangle sets and finite-geometric nets, which have typically been applied separately to code design. We demonstrate one possible realization of these codes, obtaining powerful, high-rate, low-error-floor, and low-complexity coding schemes based on simple iterative syndrome-domain decoding of coupled Hamming component codes. We anticipate that the proposed codes could improve performance–complexity–latency tradeoffs in high-throughput communications applications, most notably fiber-optic, in which classical staircase codes and zipper codes have been applied. We consider the construction of difference triangle sets having minimum scope and sum-of-lengths, which lead to memory-optimal realizations of higher-order staircase codes. These results also enable memory reductions for early families of convolutional codes constructed from difference triangle sets.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2517-2538"},"PeriodicalIF":2.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676090","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":"IEEE Transactions on Information Theory Publication Information","authors":"","doi":"10.1109/TIT.2025.3539816","DOIUrl":"https://doi.org/10.1109/TIT.2025.3539816","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"C2-C2"},"PeriodicalIF":2.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10896911","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465591","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":"Wide-Gap Frequency Hopping Sequences With No-Hit-Zone: Bounds and Their Optimal Constructions","authors":"Xingyu Zheng;Cuiling Fan;Zhengchun Zhou;Sihem Mesnager;Yang Yang","doi":"10.1109/TIT.2025.3544225","DOIUrl":"https://doi.org/10.1109/TIT.2025.3544225","url":null,"abstract":"Frequency hopping sequences (FHSs) play a crucial role in frequency hopping (FH) communication systems due to their strong anti-interference ability, low interception probability, high confidentiality and strong concealment. The objective of this paper is to construct FHSs for quasi-synchronous frequency-hopping multiple access (FHMA) communication systems that simultaneously achieve optimal no-hit zone (NHZ) length and optimal gap. To accomplish this, the paper first derives tighter upper bounds for the gap size in both periodic and aperiodic scenarios under the assumption that all frequencies within the designated frequency slot set are fully utilized. Subsequently, this paper proposes a class of wide-gap frequency hopping sequences (WGFHSs) and a class of multi-timeslot wide-gap frequency hopping sequences (MTWGFHSs), both of which simultaneously exhibit optimal NHZ length and optimal gap.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3989-3998"},"PeriodicalIF":2.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870963","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}