IEEE Transactions on Information Theory最新文献

{"title":"Universal Slepian-Wolf Coding for Individual Sequences","authors":"Neri Merhav","doi":"10.1109/TIT.2024.3496539","DOIUrl":"https://doi.org/10.1109/TIT.2024.3496539","url":null,"abstract":"We establish a coding theorem and a matching converse theorem for separate encodings and joint decoding of individual sequences using finite-state machines. The achievable rate region is characterized in terms of the Lempel-Ziv (LZ) complexities, the conditional LZ complexities and the joint LZ complexity of the two source sequences. An important feature that is needed to this end, which may be interesting on its own right, is a certain asymptotic form of a chain rule for LZ complexities, which we establish in this work. The main emphasis in the achievability scheme is on the universal decoder and its properties. We then show that the achievable rate region is universally attainable by a modified version of Draper’s universal incremental Slepian-Wolf (SW) coding scheme, provided that there exists a low-rate reliable feedback link.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"783-796"},"PeriodicalIF":2.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890304","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":"When Does the Extended Code of an MDS Code Remain MDS?","authors":"Yansheng Wu;Cunsheng Ding;Tingfang Chen","doi":"10.1109/TIT.2024.3494813","DOIUrl":"https://doi.org/10.1109/TIT.2024.3494813","url":null,"abstract":"For a given linear code \u0000<inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula>\u0000 of length n over \u0000<inline-formula> <tex-math>${mathrm {GF}}(q)$ </tex-math></inline-formula>\u0000 and a nonzero vector u in \u0000<inline-formula> <tex-math>${mathrm {GF}}(q)^{n}$ </tex-math></inline-formula>\u0000, Sun, Ding and Chen defined an extended linear code \u0000<inline-formula> <tex-math>$overline {mathcal {C}}({mathbf {u}})$ </tex-math></inline-formula>\u0000 of \u0000<inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula>\u0000, which is a generalisation of the classical extended code \u0000<inline-formula> <tex-math>$overline {mathcal {C}}(-{mathbf {1}})$ </tex-math></inline-formula>\u0000 of \u0000<inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula>\u0000 and called the second kind of an extended code of \u0000<inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula>\u0000 (see Finite Fields Appl., vol. 96, 102401, 2024 and Discrete Math., vol. 347, no. 9, 114080, 2024). They developed some general theory of the extended codes \u0000<inline-formula> <tex-math>$overline {mathcal {C}}({mathbf {u}})$ </tex-math></inline-formula>\u0000 and studied the extended codes \u0000<inline-formula> <tex-math>$overline {mathcal {C}}({mathbf {u}})$ </tex-math></inline-formula>\u0000 of several families of linear codes, including cyclic codes, projective two-weight codes, nonbinary Hamming codes, and a family of reversible MDS cyclic codes. The objective of this paper is to investigate the extended codes \u0000<inline-formula> <tex-math>$overline {mathcal {C}}({mathbf {u}})$ </tex-math></inline-formula>\u0000 of MDS codes \u0000<inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula>\u0000 over finite fields. The main result of this paper is that the extended code \u0000<inline-formula> <tex-math>$overline {mathcal {C}}({mathbf {u}})$ </tex-math></inline-formula>\u0000 of an MDS \u0000<inline-formula> <tex-math>$[n,k]$ </tex-math></inline-formula>\u0000 code \u0000<inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula>\u0000 remains MDS if and only if the covering radius \u0000<inline-formula> <tex-math>$rho (mathcal {C}^{bot })=k$ </tex-math></inline-formula>\u0000 and the vector u is a deep hole of the dual code \u0000<inline-formula> <tex-math>${mathcal {C}}^{perp } $ </tex-math></inline-formula>\u0000. As applications of this main result, an equivalent statement of MDS Conjecture is presented, the extended codes of the GRS codes and extended GRS codes are investigated, and the covering radii and some deep holes of several families of MDS codes are also determined.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"263-272"},"PeriodicalIF":2.2,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890235","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":"Almost Two-Valued Periodic Golay Sequence Pairs Derived From the Legendre Symbol","authors":"Andrzej K. Brodzik","doi":"10.1109/TIT.2024.3491422","DOIUrl":"https://doi.org/10.1109/TIT.2024.3491422","url":null,"abstract":"We describe a new family of unimodular almost two-valued periodic Golay sequence pairs of length p, where p is an odd prime. The sequences are obtained from the Legendre symbol by replacing the letters \u0000<inline-formula> <tex-math>$0, 1, -1$ </tex-math></inline-formula>\u0000 with the letters \u0000<inline-formula> <tex-math>$1, A, Bin Bbb {C}$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$|A|=|B|=1$ </tex-math></inline-formula>\u0000, where B additionally satisfies an appropriate constraint. The family is infinite in that each value of A yields at least one Golay pair or an ideal sequence. In special cases the family includes: 1) sequences with \u0000<inline-formula> <tex-math>$A=1$ </tex-math></inline-formula>\u0000, or \u0000<inline-formula> <tex-math>$B=pm bar {A}$ </tex-math></inline-formula>\u0000, or \u0000<inline-formula> <tex-math>$B=pm ibar {A}$ </tex-math></inline-formula>\u0000, or where both A and B are Gaussian rationals, or roots of unity; and 2), sequences whose autocorrelation sidelobes approach zero as p approaches infinity. These results extend the results of Björck on two-valued/almost two-valued ideal sequences derived from cyclic p-roots and the results of Golomb on two-valued ideal sequences derived from Hadamard-Paley difference sets. Related, but in some ways more constrained results on two-valued Golay sequence pairs derived from difference set families were recently published by Li et al.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"737-751"},"PeriodicalIF":2.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890146","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 Linear Programming Bound for Sum-Rank Metric Codes","authors":"Aida Abiad;Alexander L. Gavrilyuk;Antonina P. Khramova;Ilia Ponomarenko","doi":"10.1109/TIT.2024.3488902","DOIUrl":"https://doi.org/10.1109/TIT.2024.3488902","url":null,"abstract":"We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all previously known bounds.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"317-329"},"PeriodicalIF":2.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890175","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":"Analysis of the Sparse Super Resolution Limit Using the Cramér-Rao Lower Bound","authors":"Mathias Hockmann","doi":"10.1109/TIT.2024.3488573","DOIUrl":"https://doi.org/10.1109/TIT.2024.3488573","url":null,"abstract":"Already since the work by Abbe and Rayleigh the difficulty of super resolution where one wants to recover a collection of point sources from low-resolved microscopy measurements is thought to be dependent on whether the distance between the sources is below or above a certain resolution or diffraction limit. Even though there has been a number of approaches to define this limit more rigorously, there is still a gap between the situation where the task is known to be hard and scenarios where the task is provably simpler. For instance, an interesting approach for the univariate case using the size of the Cramér-Rao lower bound was introduced in a recent work by Ferreira Da Costa and Mitra. In this paper, we prove their conjecture on the transition point between good and worse tractability of super resolution and extend it to higher dimensions. Specifically, the bivariate statistical analysis allows to link the findings by the Cramér-Rao lower bound to the classical Rayleigh limit.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"390-395"},"PeriodicalIF":2.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890147","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":"Reliable Computation by Large-Alphabet Formulas in the Presence of Noise","authors":"Andrew K. Tan;Matthew H. Ho;Isaac L. Chuang","doi":"10.1109/TIT.2024.3486278","DOIUrl":"https://doi.org/10.1109/TIT.2024.3486278","url":null,"abstract":"We present two new positive results for reliable computation using formulas over physical alphabets of size \u0000<inline-formula> <tex-math>$q gt 2$ </tex-math></inline-formula>\u0000. First, we show that for logical alphabets of size \u0000<inline-formula> <tex-math>$ell = q$ </tex-math></inline-formula>\u0000 the threshold for denoising using gates subject to q-ary symmetric noise with error probability \u0000<inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>\u0000 is strictly larger than that for Boolean computation, and we show that reliable computation is possible as long as signals remain distinguishable, i.e. \u0000<inline-formula> <tex-math>$epsilon lt (q - 1) / q$ </tex-math></inline-formula>\u0000, in the limit of large fan-in \u0000<inline-formula> <tex-math>$k rightarrow infty $ </tex-math></inline-formula>\u0000. We also determine the point at which generalized majority gates with bounded fan-in fail, and show in particular that reliable computation is possible for \u0000<inline-formula> <tex-math>$epsilon lt (q - 1) / (q (q + 1))$ </tex-math></inline-formula>\u0000 in the case of q prime and fan-in \u0000<inline-formula> <tex-math>$k = 3$ </tex-math></inline-formula>\u0000. Secondly, we provide an example where \u0000<inline-formula> <tex-math>$ell lt q$ </tex-math></inline-formula>\u0000, showing that reliable Boolean computation, \u0000<inline-formula> <tex-math>$ell = 2$ </tex-math></inline-formula>\u0000, can be performed using 2-input ternary, \u0000<inline-formula> <tex-math>$q = 3$ </tex-math></inline-formula>\u0000, logic gates subject to symmetric ternary noise of strength \u0000<inline-formula> <tex-math>$varepsilon lt 1/6$ </tex-math></inline-formula>\u0000 by using the additional alphabet element for error signaling.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9152-9164"},"PeriodicalIF":2.2,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713880","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":"Moment Analysis of Age-Dependent Gossip Networks","authors":"Han Xu;Yinfei Xu;Tiecheng Song","doi":"10.1109/TIT.2024.3488860","DOIUrl":"https://doi.org/10.1109/TIT.2024.3488860","url":null,"abstract":"We study a class of gossip networks where a source delivers fresh status updates through networks consisting of a set of gossiping nodes. Contrary to previous works, the source delivers updates subject to an age-dependent point process where the rates are related to the age process at each node. Moreover, our work divides the age-dependent gossip networks into two types, i.e., type-A and type-B, where the former allows only one node sampling from source and the latter allows all. We first prove the necessary Markovity and ergodicity of both age-dependent gossip networks and proceed with deriving the general form of unique stationary distributions. With these premises established, closed-form expressions of the stationary age moments for type-A networks with arbitrary topologies are derived with the help of SHSs, with three specified results given for the line, ring and fully-connected networks. Meanwhile, we prove that no closed-form expressions of stationary age moments can be obtained in type-B networks. An approximated model for arbitrary-connected type-B networks is proposed, where we formulate the stationary moment equations for the approximated SHSs under the guarantee of Lagrange stability. Then, we provide a moment closure method to solve two symmetric cases, i.e., fully-connected and ring networks, approximately and verify the effectiveness of our algorithm by comparing to the simulations.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"1-22"},"PeriodicalIF":2.2,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890193","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":"Permutation-Invariant Quantum Codes With Transversal Generalized Phase Gates","authors":"Eric Kubischta;Ian Teixeira","doi":"10.1109/TIT.2024.3487964","DOIUrl":"https://doi.org/10.1109/TIT.2024.3487964","url":null,"abstract":"With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin codes that correspond to permutation-invariant multiqubit codes that can implement generalized phase gates transversally. Of particular note, we construct permutation-invariant quantum codes that implement a transversal T gate using fewer qubits and with a better minimum distance than is possible with the best known stabilizer codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"485-498"},"PeriodicalIF":2.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890148","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 Constructions of Optical Priority Queues Under a Priority-Based Routing Policy","authors":"Jay Cheng;Hsin-Hung Chou;Ling-Chieh Chang;Shin-Shiang Huang;Hsueh-Wen Tseng;Cheng-Hao Yang","doi":"10.1109/TIT.2024.3486073","DOIUrl":"https://doi.org/10.1109/TIT.2024.3486073","url":null,"abstract":"In this paper, we consider Switched-Delay-Lines (SDL) constructions of optical priority queues by using optical (bufferless) crossbar switches and optical fiber delay lines. In a priority queue, each packet is associated with a priority upon its arrival, the highest-priority packet is sent out from the queue whenever there is a departure request, and the lowest-priority packet is dropped from the queue whenever there is a buffer overflow. Given any system for SDL constructions of optical priority queues, the main research problem is twofold: (i) the design of the routing policy performed by the optical crossbar switches; (ii) the choice of the delays of the optical fiber delay lines. Sarwate and Anantharam are the first to propose a feedback system consisting of an optical \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$(M+2)times (M+2)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 crossbar switch and M optical fiber delay lines (see \u0000&lt;xref&gt;Figure 1&lt;/xref&gt;\u0000 in \u0000&lt;xref&gt;Section I&lt;/xref&gt;\u0000) for SDL constructions of optical priority queues, and they have shown that the largest buffer size that can possibly be achieved by using such a feedback system is \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$2^{M}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000. However, whether this theoretical buffer size \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$2^{M}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 can be achieved or not remains an open research problem. Currently, the best result in the literature was obtained by Cheng et al. and the achieved buffer size is \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$2^{O(sqrt {alpha M})}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000, where \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$alpha $ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 is a constant that depends on the parameters used in their constructions. In this paper, we consider a discrete-time setting and use a feedback system consisting of an optical crossbar switch and multiple groups of optical first-in first-out (FIFO) multiplexers with delay one (FM1’s) for SDL constructions of optical priority queues under a \u0000&lt;italic&gt;priority&lt;/i&gt;\u0000-based routing policy (see \u0000&lt;xref&gt;Figure 2&lt;/xref&gt;\u0000 in \u0000&lt;xref&gt;Section I&lt;/xref&gt;\u0000). Our contributions are as follows: (i) We extend and generalize an important class of constructions that contains the optimal constructions in the work of Cheng et al. As a result, we achieve larger buffer sizes and less construction complexities/costs than those by Cheng et al. (ii) We obtain a closed-form expression for the maximum buffer size that is achieved by the optimal construction for the scenario that each group of FM1’s has the same number of FM1’s. (iii) Our constructions possess a salient feature, namely, fault-tolerant capability, that can tolerate the malfunctioning of some FM1’s by using the generalized results obtained in this paper. (iv) We show that our constructions can be implemented by using an optical \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$(M+2)times (M+2)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 crossbar switch and \u0000&lt;italic&gt;M&lt;/i&gt;\u0000 optical fiber delay lines, and achieve a buffer size \u0000&lt;inline-formula&gt; &lt;tex-math","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"698-736"},"PeriodicalIF":2.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890142","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":"Capacity Results for the Wiretapped Oblivious Transfer","authors":"Tianyou Pei;Wei Kang;Nan Liu","doi":"10.1109/TIT.2024.3487218","DOIUrl":"https://doi.org/10.1109/TIT.2024.3487218","url":null,"abstract":"In this paper, we study the problem of the 1-of-2 string oblivious transfer (OT) between Alice and Bob in the presence of a passive eavesdropper Eve. The eavesdropper Eve is not allowed to get any information about the private data of Alice or Bob. When Alice and Bob are honest-but-curious users, we propose a protocol that satisfies 1-private (neither Alice nor Bob colludes with Eve) OT requirements for the binary erasure symmetric broadcast channel, in which the channel provides dependent erasure patterns to Bob and Eve. We find that when the erasure probabilities of the channel are within a certain range, the derived lower and upper bounds on the wiretapped OT capacity meet. Our results generalize and improve upon the results on 1-private wiretapped OT capacity by Mishra et al. Finally, we propose a protocol for a larger class of wiretapped channels and derive a lower bound on the wiretapped OT capacity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9102-9122"},"PeriodicalIF":2.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713882","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}