IEEE Transactions on Information Theory最新文献_第8页

Soft-Output Successive Cancellation List Decoding

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-05 DOI: 10.1109/TIT.2024.3512412

Peihong Yuan;Ken R. Duffy;Muriel Médard

{"title":"Soft-Output Successive Cancellation List Decoding","authors":"Peihong Yuan;Ken R. Duffy;Muriel Médard","doi":"10.1109/TIT.2024.3512412","DOIUrl":"https://doi.org/10.1109/TIT.2024.3512412","url":null,"abstract":"We introduce an algorithm for approximating the codebook probability that is compatible with all successive cancellation (SC)-based decoding algorithms, including SC list (SCL) decoding. This approximation is based on an auxiliary distribution that mimics the dynamics of decoding algorithms with an SC decoding schedule. Based on this codebook probability and SCL decoding, we introduce soft-output SCL (SO-SCL) to generate both blockwise and bitwise soft-output (SO). Using that blockwise SO, we first establish that, in terms of both block error rate (BLER) and undetected error rate (UER), SO-SCL decoding of dynamic Reed-Muller (RM) codes significantly outperforms the CRC-concatenated polar codes from 5G New Radio under SCL decoding. Moreover, using SO-SCL, the decoding misdetection rate (MDR) can be constrained to not exceed any predefined value, making it suitable for practical systems. Proposed bitwise SO can be readily generated from blockwise SO via a weighted sum of beliefs that includes a term where SO is weighted by the codebook probability, resulting in a soft-input soft-output (SISO) decoder. Simulation results for SO-SCL iterative decoding of product codes and generalized LDPC (GLDPC) codes, along with information-theoretical analysis, demonstrate significant superiority over existing list-max and list-sum approximations.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1007-1017"},"PeriodicalIF":2.2,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106960","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}

引用次数: 0

A Deterministic Construction of a Large Distance Code From the Wozencraft Ensemble

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-04 DOI: 10.1109/TIT.2024.3510698

Venkatesan Guruswami;Shilun Li

引用次数: 0

Computation of the Schläfli Function

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-04 DOI: 10.1109/TIT.2024.3511134

Andrey A. Shoom

{"title":"Computation of the Schläfli Function","authors":"Andrey A. Shoom","doi":"10.1109/TIT.2024.3511134","DOIUrl":"https://doi.org/10.1109/TIT.2024.3511134","url":null,"abstract":"The Schläfli function <inline-formula> <tex-math>$f_{n}(x)$ </tex-math></inline-formula> allows to compute volume of a regular <inline-formula> <tex-math>$(n-1)$ </tex-math></inline-formula>-dimensional spherical simplex of the dihedral angle <inline-formula> <tex-math>$2alpha =$ </tex-math></inline-formula> arcsec(x) and it has many applications. For example, it defines conjectured upper bounds on the sphere packing problem and the kissing number problem, and a lower bound on the mean-squared error in the quantizing problem. The function is defined recursively via a first-order non-linear differential relation, that makes it difficult to compute, especially for large values of n. Here we present a method for an accurate numerical computation of the Schläfli function <inline-formula> <tex-math>$f_{n}(x)$ </tex-math></inline-formula> for <inline-formula> <tex-math>$ngeq 4$ </tex-math></inline-formula> in the frequently used in applications interval <inline-formula> <tex-math>$xin [n-1,n+1]$ </tex-math></inline-formula>. The computation is based on the Chebyshev approximation of the function <inline-formula> <tex-math>$q_{n}(x)$ </tex-math></inline-formula>, which is related to the Schläfli function via a simple factor of an algebraic expression and regular in the interval. We also present the computation algorithm based on the method.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1481-1486"},"PeriodicalIF":2.2,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361451","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}

引用次数: 0

List-Decoding of AG Codes Without Genus Penalty

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-04 DOI: 10.1109/TIT.2024.3510874

Peter Beelen;Maria Montanucci

{"title":"List-Decoding of AG Codes Without Genus Penalty","authors":"Peter Beelen;Maria Montanucci","doi":"10.1109/TIT.2024.3510874","DOIUrl":"https://doi.org/10.1109/TIT.2024.3510874","url":null,"abstract":"In this paper we consider algebraic geometry (AG) codes: a class of codes constructed from algebraic codes (equivalently, using function fields) by Goppa. These codes can be list-decoded using the famous Guruswami-Sudan (GS) list-decoder, but the genus g of the used function field gives rise to negative term in the decoding radius, which we call the genus penalty. In this article, we present a GS-like list-decoding algorithm for arbitrary AG codes, which we call the inseparable GS list-decoder. Apart from the multiplicity parameter s and designed list size <inline-formula> <tex-math>$ell $ </tex-math></inline-formula>, common for the GS list-decoder, we introduce an inseparability exponent e. Choosing this exponent to be positive gives rise to a list-decoder for which the genus penalty is reduced with a factor <inline-formula> <tex-math>$1/p^{e}$ </tex-math></inline-formula> compared to the usual GS list-decoder. Here p is the characteristic. Our list-decoder can be executed in <inline-formula> <tex-math>$tilde {mathcal {O}} (sell ^{omega }mu ^{omega -1}p^{e}(n+g))$ </tex-math></inline-formula> field operations, where n is the code length and <inline-formula> <tex-math>$tilde {mathcal {O}} $ </tex-math></inline-formula> means that logarithmic factors are ignored.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"871-880"},"PeriodicalIF":2.2,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106996","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}

引用次数: 0

Decoding Algorithms of Twisted GRS Codes and Twisted Goppa Codes

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-02 DOI: 10.1109/TIT.2024.3509895

Huan Sun;Qin Yue;Xue Jia;Chengju Li

引用次数: 0

Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-02 DOI: 10.1109/TIT.2024.3509476

Zhuohang He;Junjie Ma;Xiaojun Yuan

{"title":"Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis","authors":"Zhuohang He;Junjie Ma;Xiaojun Yuan","doi":"10.1109/TIT.2024.3509476","DOIUrl":"https://doi.org/10.1109/TIT.2024.3509476","url":null,"abstract":"Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix <inline-formula> <tex-math>$boldsymbol {L}$ </tex-math></inline-formula> and a sparse matrix <inline-formula> <tex-math>$boldsymbol {S}$ </tex-math></inline-formula> from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. Our numerical results validate the theoretical results, demonstrating that the proposed asymptotic framework accurately characterize the dynamical behavior of the ITMP algorithm, and the phase transition curve specified by the sufficient condition agrees well with numerical simulations.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1323-1361"},"PeriodicalIF":2.2,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361306","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}

引用次数: 0

Rate-Distortion Theory for Mixed States

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-02 DOI: 10.1109/TIT.2024.3509825

Zahra Baghali Khanian;Kohdai Kuroiwa;Debbie Leung

引用次数: 0

A Universal List Decoding Algorithm With Application to Decoding of Polar Codes

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-02 DOI: 10.1109/TIT.2024.3509673

Xiangping Zheng;Xiao Ma

{"title":"A Universal List Decoding Algorithm With Application to Decoding of Polar Codes","authors":"Xiangping Zheng;Xiao Ma","doi":"10.1109/TIT.2024.3509673","DOIUrl":"https://doi.org/10.1109/TIT.2024.3509673","url":null,"abstract":"This paper is concerned with a guessing codeword decoding (GCD) of linear block codes, which is optimal and typically requires a fewer number of searches than the naive exhaustive search decoding (ESD). Compared with the guessing random additive noise decoding (GRAND), which is only efficient for high-rate codes, the GCD is efficient for not only high-rate codes but also low-rate codes. We prove that the GCD typically requires a fewer number of queries than the GRAND. Compared with the conventional ordered statistics decoding (OSD), the GCD does not require the online Gaussian elimination (GE). In addition to limiting the maximum number of searches, we suggest limiting the radius of searches in terms of soft weights or tolerated performance loss to further reduce the decoding complexity, resulting in the so-called truncated GCD. The performance gap between the truncated GCD and the optimal decoding can be upper bounded approximately by the saddlepoint approach or other numerical approaches. The derived upper bound captures the relationship between the performance and the decoding parameters, enabling us to balance the performance and the complexity by optimizing the decoding parameters of the truncated GCD. We also introduce a parallel implementation of the (truncated) GCD algorithm to reduce decoding latency without compromising performance. Another contribution of this paper is the application of the GCD to the polar codes. We propose a multiple-bit-wise decoding algorithm over a pruned tree for the polar codes, referred to as the successive-cancellation list (SCL) decoding algorithm by GCD. First, we present a strategy for pruning the conventional polar decoding tree based on the complexity analysis rather than the specific bit patterns. Then we apply the GCD algorithm in parallel aided by the early stopping criteria to the leaves of the pruned tree. Simulation results show that, without any performance loss as justified by analysis, the proposed decoding algorithm can significantly reduce the decoding latency of the polar codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"975-995"},"PeriodicalIF":2.2,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106958","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}

引用次数: 0

Optimal Signals and Detectors Based on Correlation and Energy 基于相关性和能量的最优信号和检测器

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-28 DOI: 10.1109/TIT.2024.3508537

Yossi Marciano;Neri Merhav

{"title":"Optimal Signals and Detectors Based on Correlation and Energy","authors":"Yossi Marciano;Neri Merhav","doi":"10.1109/TIT.2024.3508537","DOIUrl":"https://doi.org/10.1109/TIT.2024.3508537","url":null,"abstract":"In continuation of an earlier study, we explore a Neymann-Pearson hypothesis testing scenario where, under the null hypothesis (\u0000<inline-formula> <tex-math>${mathcal { H}}_{0}$ </tex-math></inline-formula>\u0000), the received signal is a white noise process \u0000<inline-formula> <tex-math>$N_{t}$ </tex-math></inline-formula>\u0000, which is not Gaussian in general, and under the alternative hypothesis (\u0000<inline-formula> <tex-math>${mathcal { H}}_{1}$ </tex-math></inline-formula>\u0000), the received signal comprises a deterministic transmitted signal \u0000<inline-formula> <tex-math>$s_{t}$ </tex-math></inline-formula>\u0000 corrupted by additive white noise, the sum of \u0000<inline-formula> <tex-math>$N_{t}$ </tex-math></inline-formula>\u0000 and another noise process originating from the transmitter, denoted as \u0000<inline-formula> <tex-math>$Z_{t}$ </tex-math></inline-formula>\u0000, which is not necessarily Gaussian either. Our approach focuses on detectors that are based on the correlation and energy of the received signal, which are motivated by implementation simplicity. We optimize the detector parameters to achieve the best trade-off between missed-detection and false-alarm error exponents. First, we optimize the detectors for a given signal, resulting in a non-linear relation between the signal and correlator weights to be optimized. Subsequently, we optimize the transmitted signal and the detector parameters jointly, revealing that the optimal signal is a balanced ternary signal and the correlator has at most three different coefficients, thus facilitating a computationally feasible solution.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"833-846"},"PeriodicalIF":2.2,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890327","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}

引用次数: 0

A Time-Causal and Time-Recursive Analogue of the Gabor Transform

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-27 DOI: 10.1109/TIT.2024.3507879

Tony Lindeberg

{"title":"A Time-Causal and Time-Recursive Analogue of the Gabor Transform","authors":"Tony Lindeberg","doi":"10.1109/TIT.2024.3507879","DOIUrl":"https://doi.org/10.1109/TIT.2024.3507879","url":null,"abstract":"This paper presents a time-causal analogue of the Gabor filter, as well as a both time-causal and time-recursive analogue of the Gabor transform, where the proposed time-causal representations obey both temporal scale covariance and a cascade property over temporal scales. The motivation behind these constructions is to enable theoretically well-founded time-frequency analysis over multiple temporal scales for real-time situations, or for physical or biological modelling situations, when the future cannot be accessed, and the non-causal access to the future in Gabor filtering is therefore not viable for a time-frequency analysis of the system. We develop a principled axiomatically determined theory for formulating these time-causal time-frequency representations, obtained by replacing the Gaussian kernel in the Gabor filtering with a time-causal kernel, referred to as the time-causal limit kernel, and which guarantees simplification properties from finer to coarser levels of scales in a time-causal situation, similar as the Gaussian kernel can be shown to guarantee over a non-causal temporal domain. We do also develop an axiomatically determined theory for implementing a discrete analogue of the proposed time-causal frequency analysis method on discrete data, based on first-order recursive filters coupled in cascade, with provable variation-diminishing properties that strongly suppress the influence from local perturbations and noise, and with specially chosen time constants to achieve self-similarity over scales and temporal scale covariance. In these ways, the proposed time-frequency representations guarantee well-founded treatment over multiple temporal scales, in situations when the characteristic scales in the signals, or physical or biological phenomena, to be analyzed may vary substantially, and additionally all steps in the time-frequency analysis have to be fully time-causal.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1450-1480"},"PeriodicalIF":2.2,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10770264","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361307","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}

引用次数: 0