IEEE Transactions on Information Theory最新文献

{"title":"The Capacity of a Finite Field Matrix Channel","authors":"Simon R. Blackburn;Jessica Claridge","doi":"10.1109/TIT.2025.3536077","DOIUrl":"https://doi.org/10.1109/TIT.2025.3536077","url":null,"abstract":"The Additive-Multiplicative Matrix Channel (AMMC) was introduced by Silva, Kschischang and Kötter in 2010 to model data transmission using random linear network coding. The input and output of the channel are <inline-formula> <tex-math>$ntimes m$ </tex-math></inline-formula> matrices over a finite field <inline-formula> <tex-math>$mathbb {F}_{q}$ </tex-math></inline-formula>. When the matrix X is input, the channel outputs <inline-formula> <tex-math>$Y=A(X+W)$ </tex-math></inline-formula> where A is a uniformly chosen <inline-formula> <tex-math>$ntimes n$ </tex-math></inline-formula> invertible matrix over <inline-formula> <tex-math>$mathbb {F}_{q}$ </tex-math></inline-formula> and where W is a uniformly chosen <inline-formula> <tex-math>$ntimes m$ </tex-math></inline-formula> matrix over <inline-formula> <tex-math>$mathbb {F}_{q}$ </tex-math></inline-formula> of rank t. Silva et al. considered the case when <inline-formula> <tex-math>$2nleq m$ </tex-math></inline-formula>. They determined the asymptotic capacity of the AMMC when t, n and m are fixed and <inline-formula> <tex-math>$qrightarrow infty $ </tex-math></inline-formula>. They also determined the leading term of the capacity when q is fixed, and t, n and m grow linearly. We generalise these results, showing that the condition <inline-formula> <tex-math>$2ngeq m$ </tex-math></inline-formula> can be removed. (Our formula for the capacity falls into two cases, one of which generalises the <inline-formula> <tex-math>$2ngeq m$ </tex-math></inline-formula> case.) We also improve the error term in the case when q is fixed.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2482-2493"},"PeriodicalIF":2.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676133","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":"Algebraic Geometry Codes for Secure Distributed Matrix Multiplication","authors":"Okko Makkonen;Elif Saçıkara;Camilla Hollanti","doi":"10.1109/TIT.2025.3535091","DOIUrl":"https://doi.org/10.1109/TIT.2025.3535091","url":null,"abstract":"In this paper, we propose a novel construction for secure distributed matrix multiplication (SDMM) based on algebraic geometry (AG) codes, which we call the PoleGap SDMM scheme. The proposed construction is inspired by the Gap Additive Secure Polynomial (GASP) code, where so-called gaps in a certain polynomial are utilized to achieve higher communication rates. Our construction considers the gaps in a Weierstrass semigroup of a rational place in an algebraic function field to achieve a similar increase in the rate. This construction shows that there is potential in utilizing AG codes and their subcodes in SDMM since we demonstrate a better performance compared to state-of-the-art schemes in some parameter regimes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2373-2382"},"PeriodicalIF":2.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10858081","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676082","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":"On Minimal Pseudocodewords of Binary Hamming Codes","authors":"Haiyang Liu;Xiaopeng Jiao;Lianrong Ma","doi":"10.1109/TIT.2025.3535947","DOIUrl":"https://doi.org/10.1109/TIT.2025.3535947","url":null,"abstract":"Pseudocodewords, and in particular minimal pseudocodewords, play an important role in understanding the performance of linear programming (LP) decoding. In this paper, we investigate minimal pseudocodewords of binary Hamming codes described by full-rank parity-check matrices. We first provide some general results on minimal pseudocodewords with support size 3 of a binary parity-check matrix. We also prove a lower bound on the minimum binary symmetric channel (BSC) pseudoweight of a binary parity-check matrix. Then we prove that a full-rank parity-check matrix of a binary Hamming code has minimal pseudocodewords of certain types whose support sizes are larger than 3. Interestingly enough, the BSC pseudoweight of all these minimal pseudocodewords is 2. Using this fact as well as the above-mentioned lower bound, we further prove that a full-rank parity-check matrix of a binary Hamming code has minimum BSC pseudoweight 2. Moreover, the additive white Gaussian noise channel (AWGNC) pseudoweight of all these minimal pseudocodewords is 3. Based on numerical observations, we conjecture that a full-rank parity-check matrix of a binary Hamming code has minimum AWGNC pseudoweight 3. Finally, we provide more properties of a subset of minimal pseudocodewords of a full-rank parity-check matrix of a binary Hamming code.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2360-2372"},"PeriodicalIF":2.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676135","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 Short-Term Forecast for Locally Stationary Functional Time Series","authors":"Yan Cui;Zhou Zhou","doi":"10.1109/TIT.2025.3536463","DOIUrl":"https://doi.org/10.1109/TIT.2025.3536463","url":null,"abstract":"Accurate curve forecasting is of vital importance for policy planning, decision making and resource allocation in many engineering and industrial applications. In this paper we establish a theoretical foundation for the optimal short-term linear prediction of non-stationary functional or curve time series with smoothly time-varying data generating mechanisms. The core of this work is to establish a unified functional auto-regressive approximation result for a general class of locally stationary functional time series. A double sieve expansion method is proposed and theoretically verified for the asymptotic optimal forecasting. A telecommunication traffic data set is used to illustrate the usefulness of the proposed theory and methodology.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2872-2887"},"PeriodicalIF":2.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667676","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":"Sphere Packing Proper Colorings of an Expander Graph","authors":"Honglin Zhu","doi":"10.1109/TIT.2025.3535747","DOIUrl":"https://doi.org/10.1109/TIT.2025.3535747","url":null,"abstract":"We introduce graphical error-correcting codes, a new notion of error-correcting codes on <inline-formula> <tex-math>$[q]^{n}$ </tex-math></inline-formula> where a code is a set of proper q-colorings of some fixed n-vertex graph G. We then say that a set of M proper q-colorings of G form a <inline-formula> <tex-math>$(G, M, d)$ </tex-math></inline-formula> code if any pair of colorings in the set have Hamming distance at least d. This directly generalizes typical <inline-formula> <tex-math>$(n, M, d)$ </tex-math></inline-formula> codes of q-ary strings of length n since we can take G as the empty graph on n vertices. We investigate how one-sided spectral expansion relates to the largest possible set of error-correcting colorings on a graph. For fixed <inline-formula> <tex-math>$(delta, lambda) in [{0, 1}] times [-1, 1]$ </tex-math></inline-formula> and positive integer d, let <inline-formula> <tex-math>$f_{delta, lambda, d}(n)$ </tex-math></inline-formula> denote the maximum M such that there exists some d-regular graph G on at most n vertices with normalized second eigenvalue at most <inline-formula> <tex-math>$lambda $ </tex-math></inline-formula> that has a <inline-formula> <tex-math>$(G, M, d)$ </tex-math></inline-formula> code. We study the growth of f as n goes to infinity. We partially characterize the regimes of <inline-formula> <tex-math>$(delta, lambda)$ </tex-math></inline-formula> where f grows exponentially or is bounded by a constant, respectively. We also prove several sharp phase transitions between these regimes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2539-2549"},"PeriodicalIF":2.2,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676089","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":"Self-Dual Cyclic Codes With Square-Root-Like Lower Bounds on Their Minimum Distances","authors":"Hao Chen;Cunsheng Ding","doi":"10.1109/TIT.2025.3535533","DOIUrl":"https://doi.org/10.1109/TIT.2025.3535533","url":null,"abstract":"Binary self-dual cyclic codes have been studied since the classical work of Sloane and Thompson published in IEEE Trans. Inf. Theory, vol. 29, 1983. Twenty five years later, an infinite family of binary self-dual cyclic codes with lengths <inline-formula> <tex-math>$n_{i}$ </tex-math></inline-formula> and minimum distances <inline-formula> <tex-math>$d_{i} geq frac {1}{2} sqrt {n_{i}+2}$ </tex-math></inline-formula> was presented in a paper of IEEE Trans. Inf. Theory, vol. 55, 2009. However, no infinite family of Euclidean self-dual binary cyclic codes whose minimum distances have the square-root lower bound and no infinite family of Euclidean self-dual nonbinary cyclic codes whose minimum distances have a lower bound better than the square-root lower bound are known in the literature. In this paper, an infinite family of Euclidean self-dual cyclic codes over the fields <inline-formula> <tex-math>${mathrm { F}}_{2^{s}}$ </tex-math></inline-formula> with a square-root-like lower bound is constructed. An infinite subfamily of this family consists of self-dual binary cyclic codes with the square-root lower bound. Another infinite subfamily of this family consists of self-dual cyclic codes over the fields <inline-formula> <tex-math>${mathrm { F}}_{2^{s}}$ </tex-math></inline-formula> with a lower bound better than the square-root bound for <inline-formula> <tex-math>$s geq 2$ </tex-math></inline-formula>. Consequently, two breakthroughs in coding theory are made in this paper. An infinite family of self-dual binary cyclic codes with a square-root-like lower bound is also presented in this paper. An infinite family of Hermitian self-dual cyclic codes over the fields <inline-formula> <tex-math>${mathrm { F}}_{2^{2s}}$ </tex-math></inline-formula> with a square-root-like lower bound and an infinite family of Euclidean self-dual linear codes over <inline-formula> <tex-math>${mathrm { F}}_{q}$ </tex-math></inline-formula> with <inline-formula> <tex-math>$q equiv 1 pmod {4}$ </tex-math></inline-formula> with a square-root-like lower bound are also constructed in this paper.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2389-2396"},"PeriodicalIF":2.2,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676038","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":"Error Exponents for Entanglement Transformations From Degenerations","authors":"Dávid Bugár;Péter Vrana","doi":"10.1109/TIT.2025.3534327","DOIUrl":"https://doi.org/10.1109/TIT.2025.3534327","url":null,"abstract":"This paper explores the trade-off relation between the rate and the strong converse exponent for asymptotic LOCC transformations between pure multipartite states. Any single-copy probabilistic transformation between a pair of states implies that an asymptotic transformation at rate 1 is possible with an exponentially decreasing success probability. However, it is possible that an asymptotic transformation is feasible with nonzero probability, but there is no transformation between any finite number of copies with the same rate, even probabilistically. In such cases it is not known if the optimal success probability decreases exponentially or faster. A fundamental tool for showing the feasibility of an asymptotic transformation is degeneration. Any degeneration gives rise to a sequence of stochastic LOCC transformations from copies of the initial state plus a sublinear number of GHZ states to the same number of copies of the target state. These protocols involve parameters that can be freely chosen, but the choice affects the success probability. In this paper, we characterize an asymptotically optimal choice of the parameters and derive a single-letter expression for the error exponent of the resulting protocol. In particular, this implies an exponential lower bound on the success probability when the stochastic transformation arises from a degeneration.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1874-1895"},"PeriodicalIF":2.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465639","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":"Quantum and Classical Communication Complexity of Permutation-Invariant Functions","authors":"Ziyi Guan;Yunqi Huang;Penghui Yao;Zekun Ye","doi":"10.1109/TIT.2025.3534920","DOIUrl":"https://doi.org/10.1109/TIT.2025.3534920","url":null,"abstract":"This paper gives a nearly tight characterization of the quantum communication complexity of permutation-invariant Boolean functions. With such a characterization, we show that the quantum and randomized communication complexity of permutation-invariant Boolean functions are quadratically equivalent (up to a polylogarithmic factor of the input size). Our results extend a recent line of research regarding query complexity to communication complexity, showing symmetry prevents exponential quantum speedups. Furthermore, we show that the Log-rank Conjecture holds for any non-trivial total permutation-invariant Boolean function. Moreover, we establish a relationship between the quantum/classical communication complexity and the approximate rank of permutation-invariant Boolean functions. This implies the correctness of the Log-approximate-rank Conjecture for permutation-invariant Boolean functions in both randomized and quantum settings (up to a polylogarithmic factor of the input size).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2782-2799"},"PeriodicalIF":2.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667308","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":"Bounds and Constructions of Quantum Locally Recoverable Codes From Quantum CSS Codes","authors":"Gaojun Luo;Bocong Chen;Martianus Frederic Ezerman;San Ling","doi":"10.1109/TIT.2025.3533494","DOIUrl":"https://doi.org/10.1109/TIT.2025.3533494","url":null,"abstract":"Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential application in quantum data storage. In this paper, we use classical LRCs to investigate quantum LRCs. We prove that the parameters of quantum LRCs are bounded by their classical counterparts. We deduce bounds on the parameters of quantum LRCs from bounds on the parameters of the classical ones. We establish a characterization of optimal pure quantum LRCs based on classical codes with specific properties. Using well-crafted classical LRCs as ingredients in the construction of quantum CSS codes, we offer the first construction of several families of optimal pure quantum LRCs.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1794-1802"},"PeriodicalIF":2.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465589","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":"Covert Communication via Action-Dependent States","authors":"Hassan ZivariFard;Xiaodong Wang","doi":"10.1109/TIT.2025.3534067","DOIUrl":"https://doi.org/10.1109/TIT.2025.3534067","url":null,"abstract":"This paper studies covert communication over channels with Action-Dependent State Information (ADSI) when the state is available either non-causally or causally at the transmitter. Covert communication refers to reliable communication between a transmitter and a receiver while ensuring a low probability of detection by an adversary, which we refer to as “warden”. It is well known that in a point-to-point Discrete Memoryless Channel (DMC), it is possible to communicate on the order of <inline-formula> <tex-math>$sqrt {N}$ </tex-math></inline-formula> bits reliably and covertly over N channel uses while the transmitter and the receiver are required to share a secret key on the order of <inline-formula> <tex-math>$sqrt {N}$ </tex-math></inline-formula> bits. This paper studies achieving reliable and covert communication of positive rate, i.e., reliable and covert communication on the order of N bits in N channel uses, over a channel with ADSI while the transmitter has non-causal or causal access to the ADSI, and the transmitter and the receiver share a secret key of negligible rate. We derive achievable rates for both the non-causal and causal scenarios by using block-Markov encoding and secret key generation from the ADSI, which subsumes the best achievable rates for channels with random states. We also derive upper bounds, for both non-causal and causal scenarios, that meet our achievable rates for some special cases. As an application of our problem setup, we study covert communication over channels with rewrite options, which are closely related to recording covert information on memory, and show that a positive covert rate can be achieved in such channels. As a special case of our problem, we study the Additive White Gaussian Noise (AWGN) channels and provide lower and upper bounds on the covert capacity that meet when the transmitter and the receiver share a secret key of sufficient rate and when the warden’s channel is noisier than the legitimate receiver channel. As another application of our problem setup, we show that cooperation can lead to a positive covert rate in Gaussian channels. A few other examples are also worked out in detail.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"3100-3128"},"PeriodicalIF":2.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667352","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}