Pub Date : 2024-09-09DOI: 10.1109/tit.2024.3456597
Ohad Elishco
{"title":"On the Long-Term Behavior of k-tuples Frequencies in Mutation Systems","authors":"Ohad Elishco","doi":"10.1109/tit.2024.3456597","DOIUrl":"https://doi.org/10.1109/tit.2024.3456597","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"160 1","pages":""},"PeriodicalIF":2.5,"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}
Pub Date : 2024-09-05DOI: 10.1109/tit.2024.3454959
Yansheng Wu, Bowen Li, Weibei Fan, Fu Xiao
{"title":"Two Infinite Families of Quaternary Codes","authors":"Yansheng Wu, Bowen Li, Weibei Fan, Fu Xiao","doi":"10.1109/tit.2024.3454959","DOIUrl":"https://doi.org/10.1109/tit.2024.3454959","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"63 1","pages":""},"PeriodicalIF":2.5,"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}
Pub Date : 2024-09-05DOI: 10.1109/TIT.2024.3454694
Shujun Bi;Lan Zhou;Shaohua Pan
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 $ell _{1}$ -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 $ell _{1}$ -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 $ell _{1}$ -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 $ell _{1}$ -norm minimization problem lacks the good robustness.
{"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}
Pub Date : 2024-09-04DOI: 10.1109/tit.2024.3454480
Simeon Ball, Edgar Moreno, Robin Simoens
{"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}
Pub Date : 2024-09-04DOI: 10.1109/TIT.2024.3454239
Hafez M. Garmaroudi;S. Sandeep Pradhan;Jun Chen
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.
{"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}
Pub Date : 2024-09-03DOI: 10.1109/tit.2024.3453935
Boaz Moav, Ryan Gabrys, Eitan Yaakobi
{"title":"Tail-Erasure-Correcting Codes","authors":"Boaz Moav, Ryan Gabrys, Eitan Yaakobi","doi":"10.1109/tit.2024.3453935","DOIUrl":"https://doi.org/10.1109/tit.2024.3453935","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"76 1","pages":""},"PeriodicalIF":2.5,"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}
Pub Date : 2024-09-03DOI: 10.1109/tit.2024.3450501
Francesco Anna Mele, Giacomo De Palma, Marco Fanizza, Vittorio Giovannetti, Ludovico Lami
{"title":"Optical fibres 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":"https://doi.org/10.1109/tit.2024.3450501","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"15 1","pages":""},"PeriodicalIF":2.5,"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}
Pub Date : 2024-09-03DOI: 10.1109/TIT.2024.3454119
Hengjia Wei;Moshe Schwartz;Gennian Ge
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.
本文研究将信息编码成序列的问题，这些序列可以从对其子串的一些噪声观测中唯一恢复。观察到的读数由连续的子串组成，具有给定的最小重叠度。这种编码重构问题可应用于 DNA 存储。我们考虑了单链重构码和多链重构码，其中信息分别被编码到单链或多链集合中。我们研究了各种参数机制。我们构建了新的编码，其中一些编码的速率渐近地达到了上限。
{"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}
Pub Date : 2024-09-03DOI: 10.1109/TIT.2024.3454059
Anxiao Jiang
A new type of analog error-correcting codes (Analog ECCs) has been proposed by Roth recently. The codes can correct errors of unlimited magnitudes even though the codeword is affected not only by such errors, but also by ubiquitous noise of limited magnitudes. The codes have the potential to accelerate the widely used vector-matrix multiplication in machine learning via their implementation in nanoscale analog circuits. Several Analog ECCs, which mainly focus on correcting or detecting a single unlimited-magnitude error, have been proposed. This paper explores the analysis and constructions of Analog ECCs in multiple ways. It presents a linear-programming based algorithm that computes the m-heights of Analog ECCs efficiently, which can be used to determine the error correction/detection capabilities of the codes. It then presents a family of Analog ECCs based on permutations, and proves that the time complexity for determining the m-heights of such codes can be further reduced substantially. The analysis forms a basis for the time-complexity tradeoff between the searching of codes and the verification of their performance. The paper then presents a number of newly discovered codes based on such a search and verification process, which achieve state-of-the-art performance.
罗思最近提出了一种新型模拟纠错码（Analog ECCs）。这种纠错码可以纠正无限大小的错误，即使码字不仅会受到这些错误的影响，还会受到无处不在的有限大小的噪声的影响。通过在纳米级模拟电路中的实施，这些编码有可能加速机器学习中广泛使用的向量矩阵乘法。目前已提出了几种模拟 ECC，主要侧重于纠正或检测单个无限幅度的错误。本文从多个方面探讨了模拟 ECC 的分析和构造。它提出了一种基于线性编程的算法，该算法能高效计算模拟 ECC 的 m 高，可用于确定编码的纠错/检测能力。然后，它提出了基于排列的模拟 ECC 系列，并证明确定此类编码 m 高的时间复杂度可进一步大幅降低。该分析为编码搜索和性能验证之间的时间复杂度权衡奠定了基础。论文随后介绍了一些基于这种搜索和验证过程的新发现的代码，它们达到了最先进的性能。
{"title":"Analog Error-Correcting Codes: Designs and Analysis","authors":"Anxiao Jiang","doi":"10.1109/TIT.2024.3454059","DOIUrl":"10.1109/TIT.2024.3454059","url":null,"abstract":"A new type of analog error-correcting codes (Analog ECCs) has been proposed by Roth recently. The codes can correct errors of unlimited magnitudes even though the codeword is affected not only by such errors, but also by ubiquitous noise of limited magnitudes. The codes have the potential to accelerate the widely used vector-matrix multiplication in machine learning via their implementation in nanoscale analog circuits. Several Analog ECCs, which mainly focus on correcting or detecting a single unlimited-magnitude error, have been proposed. This paper explores the analysis and constructions of Analog ECCs in multiple ways. It presents a linear-programming based algorithm that computes the m-heights of Analog ECCs efficiently, which can be used to determine the error correction/detection capabilities of the codes. It then presents a family of Analog ECCs based on permutations, and proves that the time complexity for determining the m-heights of such codes can be further reduced substantially. The analysis forms a basis for the time-complexity tradeoff between the searching of codes and the verification of their performance. The paper then presents a number of newly discovered codes based on such a search and verification process, which achieve state-of-the-art performance.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7740-7756"},"PeriodicalIF":2.2,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194914","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}
Pub Date : 2024-09-02DOI: 10.1109/TIT.2024.3452976
Touraj Soleymani;John S. Baras;Deniz Gündüz
We study networked control of a dynamical process over a lossy channel with a hybrid automatic repeat request protocol that connects a sensor to an actuator. The dynamical process is modeled by a Gauss-Markov process, and the lossy channel by a packet-erasure channel with ideal feedback. We suppose that data is communicated in the format of packets with negligible quantization error. In such a networked control system, whenever a packet loss occurs, there exists a tradeoff between transmitting new sensory information with a lower success probability and retransmitting previously failed sensory information with a higher success probability. In essence, an inherent tradeoff between freshness and reliability. To address this tradeoff, we consider a linear-quadratic-regulator performance index, which penalizes state deviations and control efforts over a finite horizon, and jointly design optimal encoding and decoding policies for the encoder and the decoder, which are collocated with the sensor and the actuator, respectively. Our emphasis here lies specifically on designing switching and control policies, rather than error-correcting codes. We show that the optimal encoding policy is a threshold switching policy and the optimal decoding policy is a certainty-equivalent control policy. In addition, we determine the equations that the encoder and the decoder need to solve in order to implement the optimal policies. More specifically, we show that the encoder must solve the Kalman filtering equations, a mismatch linear equation, and a Bellman optimality equation, while the decoder must solve a linear filtering equation and an algebraic Riccati equation.
{"title":"Transmit or Retransmit: A Tradeoff in Networked Control of Dynamical Processes Over Lossy Channels With Ideal Feedback","authors":"Touraj Soleymani;John S. Baras;Deniz Gündüz","doi":"10.1109/TIT.2024.3452976","DOIUrl":"10.1109/TIT.2024.3452976","url":null,"abstract":"We study networked control of a dynamical process over a lossy channel with a hybrid automatic repeat request protocol that connects a sensor to an actuator. The dynamical process is modeled by a Gauss-Markov process, and the lossy channel by a packet-erasure channel with ideal feedback. We suppose that data is communicated in the format of packets with negligible quantization error. In such a networked control system, whenever a packet loss occurs, there exists a tradeoff between transmitting new sensory information with a lower success probability and retransmitting previously failed sensory information with a higher success probability. In essence, an inherent tradeoff between freshness and reliability. To address this tradeoff, we consider a linear-quadratic-regulator performance index, which penalizes state deviations and control efforts over a finite horizon, and jointly design optimal encoding and decoding policies for the encoder and the decoder, which are collocated with the sensor and the actuator, respectively. Our emphasis here lies specifically on designing switching and control policies, rather than error-correcting codes. We show that the optimal encoding policy is a threshold switching policy and the optimal decoding policy is a certainty-equivalent control policy. In addition, we determine the equations that the encoder and the decoder need to solve in order to implement the optimal policies. More specifically, we show that the encoder must solve the Kalman filtering equations, a mismatch linear equation, and a Bellman optimality equation, while the decoder must solve a linear filtering equation and an algebraic Riccati equation.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7853-7866"},"PeriodicalIF":2.2,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194916","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}
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