{"title":"Robust, Secure, and Private Cache-Aided Scalar Linear Function Retrieval From Distributed System With Blind and Adversarial Servers","authors":"Qifa Yan;Zhengchun Zhou;Xiaohu Tang","doi":"10.1109/TIT.2024.3455557","DOIUrl":"10.1109/TIT.2024.3455557","url":null,"abstract":"In this work, a distributed server system composed of multiple servers that holds some coded files and multiple users that are interested in retrieving the linear functions of the files is investigated, where the servers are robust, blind and adversarial in the sense that any J servers can together recover all files, while any I colluding servers cannot obtain any information about the files, and at most A servers maliciously provides erroneous information. In addition, the file library must be secure from a wiretapper who obtains all the signals, and the demands of any subset of users must kept private from the other users and servers, even if they collude. A coding scheme is proposed by incorporating the ideas of Shamir’s secret sharing and key superposition into the framework of Placement Delivery Array (PDA), originally proposed to characterize the single-server coded caching system without any security or privacy constraints. It is shown that PDAs associated to Maddah-Ali and Niesen’s coded caching scheme results in an achievable memory-storage-communication region, such that the storage size and communication load were optimal to within a multiplicative gap, except for the small memory regime when the number of files was smaller than the number of users.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"8237-8250"},"PeriodicalIF":2.2,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194917","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}
Pablo Pascual Cobo;Kuan Hsieh;Ramji Venkataramanan
{"title":"Bayes-Optimal Estimation in Generalized Linear Models via Spatial Coupling","authors":"Pablo Pascual Cobo;Kuan Hsieh;Ramji Venkataramanan","doi":"10.1109/TIT.2024.3455228","DOIUrl":"10.1109/TIT.2024.3455228","url":null,"abstract":"We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has precisely characterized the asymptotic minimum mean-squared error (MMSE) for GLMs with i.i.d. Gaussian sensing matrices. However, in many models there is a significant gap between the MMSE and the performance of the best known feasible estimators. We address this issue by considering GLMs defined via spatially coupled sensing matrices. We propose an efficient approximate message passing (AMP) algorithm for estimation and prove that with a simple choice of spatially coupled design, the MSE of a carefully tuned AMP estimator approaches the asymptotic MMSE as the dimensions of the signal and the observation grow proportionally. To prove the result, we first rigorously characterize the asymptotic performance of AMP for a GLM with a generic spatially coupled design. This characterization is in terms of a deterministic recursion (‘state evolution’) that depends on the parameters defining the spatial coupling. Then, using a simple spatially coupled design and a judicious choice of functions for the AMP algorithm, we analyze the fixed points of the resulting state evolution and show that it achieves the asymptotic MMSE. Numerical results for phase retrieval and rectified linear regression show that spatially coupled designs can yield substantially lower MSE than i.i.d. Gaussian designs at finite dimensions when used with AMP algorithms.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"8343-8363"},"PeriodicalIF":2.2,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194907","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 the Long-Term Behavior of k-Tuples Frequencies in Mutation Systems","authors":"Ohad Elishco","doi":"10.1109/TIT.2024.3456597","DOIUrl":"10.1109/TIT.2024.3456597","url":null,"abstract":"In response to the evolving landscape of data storage, researchers have increasingly explored non-traditional platforms, with DNA-based storage emerging as a cutting-edge solution. Our work is motivated by the potential of in-vivo DNA storage, known for its capacity to store vast amounts of information efficiently and confidentially within an organism’s native DNA. While promising, in-vivo DNA storage faces challenges, including susceptibility to errors introduced by mutations. One way to understand the long-term effect of such mutations on the stored information is to investigate the frequency of k-tuples after multiple mutations. Drawing inspiration from related works, we generalize results from the study of duplication systems, particularly focusing on the frequency (or proportion) of k-tuples. We provide a general method for the analysis of mutation systems through the construction of a specialized matrix, dubbed substitution matrix, and the identification of its eigenvectors. Specifically, we derive an expression for the expected frequency of k-tuples. In the context of duplication errors, we leverage existing results on the almost sure convergence of the frequency of k-tuples. This allows us to equate the expected frequency of k-tuples to the limiting frequency of k-tuples. In addition, we demonstrate the convergence in probability of the frequency of k-tuples under certain assumptions.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8524-8545"},"PeriodicalIF":2.2,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194920","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":"Two Infinite Families of Quaternary Codes","authors":"Yansheng Wu;Bowen Li;Weibei Fan;Fu Xiao","doi":"10.1109/TIT.2024.3454959","DOIUrl":"10.1109/TIT.2024.3454959","url":null,"abstract":"Recently, Hyun et al. have utilized simplicial complexes to construct several infinite families of binary minimal and optimal linear codes. Building upon their work, we draw inspiration and extend their research by constructing codes over the ring \u0000<inline-formula> <tex-math>$mathbb {Z}_{4}$ </tex-math></inline-formula>\u0000 with the aid of simplicial complexes. In this paper, we present two infinite families of quaternary codes, one of which is linear while the other is nonlinear. We analyze the Lee weight distributions of the resulting quaternary codes and compare them with the existing database of \u0000<inline-formula> <tex-math>$mathbb {Z}_{4}$ </tex-math></inline-formula>\u0000 codes. Our findings reveal the discovery of several new quaternary codes. Furthermore, we also provide two classes of binary codes that can be obtained from these quaternary codes using the Gray map.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8723-8733"},"PeriodicalIF":2.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194909","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":"Sparse Signal Reconstruction: Sequential Convex Relaxation, Restricted Null Space Property, and Error Bounds","authors":"Shujun Bi;Lan Zhou;Shaohua Pan","doi":"10.1109/TIT.2024.3454694","DOIUrl":"10.1109/TIT.2024.3454694","url":null,"abstract":"For (nearly) sparse signal reconstruction problems, we propose an inexact sequential convex relaxation algorithm (iSCRA-TL1) by constructing the working index set iteratively with a simple and adaptive strategy, and solving inexactly a sequence of truncated \u0000<inline-formula> <tex-math>$ell _{1}$ </tex-math></inline-formula>\u0000-norm minimization subproblems. A toy example is provided to demonstrate that the exact version of iSCRA-TL1 can successfully reconstruct the true sparse signal, but almost all the present sequential convex relaxation algorithms starting from an optimal solution of the \u0000<inline-formula> <tex-math>$ell _{1}$ </tex-math></inline-formula>\u0000-norm minimization fail to recover it. To provide theoretical guarantees for iSCRA-TL1, we introduce two new types of null space properties, restricted null space property (RNSP) and sequential restricted null space property (SRNSP), and prove that they are both weaker than the common stable NSP, while their robust versions are not stronger than the existing robust NSP. Then, we justify that under a suitable (robust) SRNSP, iSCRA-TL1 can identify the support of the true r-sparse signal or the index set of the first r largest (in modulus) entries of the true nearly r-sparse signal via at most r truncated \u0000<inline-formula> <tex-math>$ell _{1}$ </tex-math></inline-formula>\u0000-norm minimization, and the error bound of its final output from the true (nearly) r-sparse signal is also quantified. To the best of our knowledge, this is the first sequential convex relaxation algorithm to recover the support of the true (nearly) sparse signal under a weaker NSP condition within a specific number of steps, provided that the classical \u0000<inline-formula> <tex-math>$ell _{1}$ </tex-math></inline-formula>\u0000-norm minimization problem lacks the good robustness.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"8378-8398"},"PeriodicalIF":2.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194911","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":"Stabiliser codes over fields of even order","authors":"Simeon Ball, Edgar Moreno, Robin Simoens","doi":"10.1109/tit.2024.3454480","DOIUrl":"https://doi.org/10.1109/tit.2024.3454480","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"54 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194941","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":"Rate-Limited Quantum-to-Classical Optimal Transport in Finite and Continuous-Variable Quantum Systems","authors":"Hafez M. Garmaroudi;S. Sandeep Pradhan;Jun Chen","doi":"10.1109/TIT.2024.3454239","DOIUrl":"10.1109/TIT.2024.3454239","url":null,"abstract":"We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding for both finite-dimensional and continuous-variable quantum-to-classical systems with limited classical common randomness. The main coding theorem provides a single-letter characterization of the achievable rate region of a lossy quantum measurement source coding for an exact construction of the destination distribution (or the equivalent quantum state) while maintaining a threshold of distortion from the source state according to a generally defined distortion observable. The constraint on the output space fixes the output distribution to an IID predefined probability mass function. Therefore, this problem can also be viewed as information-constrained optimal transport which finds the optimal cost of transporting the source quantum state to the destination classical distribution via a quantum measurement with limited communication rate and common randomness. We develop a coding framework for continuous-variable quantum systems by employing a clipping projection and a dequantization block and using our finite-dimensional coding theorem. Moreover, for the Gaussian quantum systems, we derive an analytical solution for rate-limited Wasserstein distance of order 2, along with a Gaussian optimality theorem, showing that Gaussian measurement optimizes the rate in a system with Gaussian quantum source and Gaussian destination distribution. The results further show that in contrast to the classical Wasserstein distance of Gaussian distributions, which corresponds to an infinite transmission rate, in the Quantum Gaussian measurement system, the optimal transport is achieved with a finite transmission rate due to the inherent noise of the quantum measurement imposed by Heisenberg’s uncertainty principle.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7892-7922"},"PeriodicalIF":2.2,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194910","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":"Tail-Erasure-Correcting Codes","authors":"Boaz Moav;Ryan Gabrys;Eitan Yaakobi","doi":"10.1109/TIT.2024.3453935","DOIUrl":"10.1109/TIT.2024.3453935","url":null,"abstract":"The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as a collection of two-dimensional arrays. Motivated by error patterns observed in recent prototype architectures, our study focuses on correcting erasures in the last few symbols of each row, and also correcting arbitrary deletions across rows. We present code constructions and explicit encoders and decoders that are shown to be nearly optimal in many scenarios. We show that the new coding schemes are capable of effectively mitigating these errors, making these emerging storage platforms potentially promising solutions.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8595-8613"},"PeriodicalIF":2.2,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194947","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}
Francesco Anna Mele;Giacomo De Palma;Marco Fanizza;Vittorio Giovannetti;Ludovico Lami
{"title":"Optical Fibers With Memory Effects and Their Quantum Communication Capacities","authors":"Francesco Anna Mele;Giacomo De Palma;Marco Fanizza;Vittorio Giovannetti;Ludovico Lami","doi":"10.1109/TIT.2024.3450501","DOIUrl":"10.1109/TIT.2024.3450501","url":null,"abstract":"If the transmissivity of an optical fibre falls below a critical value, its use as a reliable quantum channel is known to be drastically compromised. However, if the memoryless assumption does not hold — e.g. when input signals are separated by a sufficiently short time interval — the validity of this limitation is put into question. In this work we introduce a model of optical fibre that can describe memory effects for long transmission lines. We then solve its quantum capacity, two-way quantum capacity, and secret-key capacity exactly. By doing so, we show that — due to the memory cross-talk between the transmitted signals — reliable quantum communication is attainable even for highly noisy regimes where it was previously considered impossible.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8844-8869"},"PeriodicalIF":2.2,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194913","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":"Reconstruction From Noisy Substrings","authors":"Hengjia Wei;Moshe Schwartz;Gennian Ge","doi":"10.1109/TIT.2024.3454119","DOIUrl":"10.1109/TIT.2024.3454119","url":null,"abstract":"This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This coded reconstruction problem has applications in DNA storage. We consider both single-strand reconstruction codes and multi-strand reconstruction codes, where the message is encoded into a single strand or a set of multiple strands, respectively. Various parameter regimes are studied. New codes are constructed, some of whose rates asymptotically attain the upper bounds.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7757-7776"},"PeriodicalIF":2.2,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194912","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}