Pub Date : 2023-10-06DOI: 10.1109/JSAIT.2023.3322620
Md Kamran Chowdhury Shisher;Bo Ji;I-Hong Hou;Yin Sun
In this paper, we consider a remote inference system, where a neural network is used to infer a time-varying target (e.g., robot movement), based on features (e.g., video clips) that are progressively received from a sensing node (e.g., a camera). Each feature is a temporal sequence of sensory data. The inference error is determined by (i) the timeliness and (ii) the sequence length of the feature, where we use Age of Information (AoI) as a metric for timeliness. While a longer feature can typically provide better inference performance, it often requires more channel resources for sending the feature. To minimize the time-averaged inference error, we study a learning and communication co-design problem that jointly optimizes feature length selection and transmission scheduling. When there is a single sensor-predictor pair and a single channel, we develop low-complexity optimal co-designs for both the cases of time-invariant and time-variant feature length. When there are multiple sensor-predictor pairs and multiple channels, the co-design problem becomes a restless multi-arm multi-action bandit problem that is PSPACE-hard. For this setting, we design a low-complexity algorithm to solve the problem. Trace-driven evaluations demonstrate the potential of these co-designs to reduce inference error by up to 10000 times.
{"title":"Learning and Communications Co-Design for Remote Inference Systems: Feature Length Selection and Transmission Scheduling","authors":"Md Kamran Chowdhury Shisher;Bo Ji;I-Hong Hou;Yin Sun","doi":"10.1109/JSAIT.2023.3322620","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3322620","url":null,"abstract":"In this paper, we consider a remote inference system, where a neural network is used to infer a time-varying target (e.g., robot movement), based on features (e.g., video clips) that are progressively received from a sensing node (e.g., a camera). Each feature is a temporal sequence of sensory data. The inference error is determined by (i) the timeliness and (ii) the sequence length of the feature, where we use Age of Information (AoI) as a metric for timeliness. While a longer feature can typically provide better inference performance, it often requires more channel resources for sending the feature. To minimize the time-averaged inference error, we study a learning and communication co-design problem that jointly optimizes feature length selection and transmission scheduling. When there is a single sensor-predictor pair and a single channel, we develop low-complexity optimal co-designs for both the cases of time-invariant and time-variant feature length. When there are multiple sensor-predictor pairs and multiple channels, the co-design problem becomes a restless multi-arm multi-action bandit problem that is PSPACE-hard. For this setting, we design a low-complexity algorithm to solve the problem. Trace-driven evaluations demonstrate the potential of these co-designs to reduce inference error by up to 10000 times.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"524-538"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1109/JSAIT.2023.3320068
Shailja Agrawal;K. V. Sushena Sree;Prasad Krishnan;Abhinav Vaishya;Srikar Kale
We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache ) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. One of the chief drawbacks of many of these existing constructions is the large subpacketization level, which denotes the number of times a file should be split for the schemes to provide coding gain. In this work, using a new binary matrix model, we present several novel constructions for coded caching based on the various types of combinatorial designs and their $q$ -analogs, which are also called subspace designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement, they provide a rate that is either constant or decreasing, and moreover require competitively small levels of subpacketization, which is an extremely important feature in practical applications of coded caching. We also apply our constructions to the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. Using our binary matrix framework, we present a new simple generic coded data shuffling scheme. Employing our designs-based constructions in conjunction with this new shuffling scheme, we obtain new coded computing schemes which have low file complexity, with marginally higher communication load compared to the optimal scheme for equivalent parameters. We show that our schemes can neatly extend to the scenario with full and partial stragglers also.
{"title":"Cache-Aided Communication Schemes via Combinatorial Designs and Their q-Analogs","authors":"Shailja Agrawal;K. V. Sushena Sree;Prasad Krishnan;Abhinav Vaishya;Srikar Kale","doi":"10.1109/JSAIT.2023.3320068","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3320068","url":null,"abstract":"We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called \u0000<italic>cache</i>\u0000) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. One of the chief drawbacks of many of these existing constructions is the large subpacketization level, which denotes the number of times a file should be split for the schemes to provide coding gain. In this work, using a new binary matrix model, we present several novel constructions for coded caching based on the various types of combinatorial designs and their \u0000<inline-formula> <tex-math>$q$ </tex-math></inline-formula>\u0000-analogs, which are also called subspace designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement, they provide a rate that is either constant or decreasing, and moreover require competitively small levels of subpacketization, which is an extremely important feature in practical applications of coded caching. We also apply our constructions to the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. Using our binary matrix framework, we present a new simple generic coded data shuffling scheme. Employing our designs-based constructions in conjunction with this new shuffling scheme, we obtain new coded computing schemes which have low file complexity, with marginally higher communication load compared to the optimal scheme for equivalent parameters. We show that our schemes can neatly extend to the scenario with full and partial stragglers also.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"551-568"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-22DOI: 10.1109/JSAIT.2023.3317941
Xuan Guang;Raymond W. Yeung
We consider linear network erro correction (LNEC) coding when errors may occur on the edges of a communication network of which the topology is known. In this paper, we first present a framework of additive adversarial network for LNEC coding, and then prove the equivalence of two well-known LNEC coding approaches, which can be unified under this framework. Furthermore, by developing a graph-theoretic approach, we obtain a significantly enhanced characterization of the error correction capability of LNEC codes in terms of the minimum distances at the sink nodes. Specifically, in order to ensure that an LNEC code can correct up to $r$ errors at a sink node $t$ , it suffices to ensure that this code can correct every error vector in a reduced set of error vectors; and on the other hand, this LNEC code in fact can correct every error vector in an enlarged set of error vectors. In general, the size of this reduced set is considerably smaller than the number of error vectors with Hamming weight not larger than $r$ , and the size of this enlarged set is considerably larger than the same number. This result has the important implication that the computational complexities for decoding and for code construction can be significantly reduced.
{"title":"A Revisit of Linear Network Error Correction Coding","authors":"Xuan Guang;Raymond W. Yeung","doi":"10.1109/JSAIT.2023.3317941","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3317941","url":null,"abstract":"We consider linear network erro correction (LNEC) coding when errors may occur on the edges of a communication network of which the topology is known. In this paper, we first present a framework of additive adversarial network for LNEC coding, and then prove the equivalence of two well-known LNEC coding approaches, which can be unified under this framework. Furthermore, by developing a graph-theoretic approach, we obtain a significantly enhanced characterization of the error correction capability of LNEC codes in terms of the minimum distances at the sink nodes. Specifically, in order to ensure that an LNEC code can correct up to \u0000<inline-formula> <tex-math>$r$ </tex-math></inline-formula>\u0000 errors at a sink node \u0000<inline-formula> <tex-math>$t$ </tex-math></inline-formula>\u0000, it suffices to ensure that this code can correct every error vector in a reduced set of error vectors; and on the other hand, this LNEC code in fact can correct every error vector in an enlarged set of error vectors. In general, the size of this reduced set is considerably smaller than the number of error vectors with Hamming weight not larger than \u0000<inline-formula> <tex-math>$r$ </tex-math></inline-formula>\u0000, and the size of this enlarged set is considerably larger than the same number. This result has the important implication that the computational complexities for decoding and for code construction can be significantly reduced.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"514-523"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-19DOI: 10.1109/JSAIT.2023.3317094
Coleman DeLude;Rakshith S. Srinivasa;Santhosh Karnik;Christopher Hood;Mark A. Davenport;Justin Romberg
In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the problem of spectral line estimation, where our goal is simply to estimate the active frequencies from a weighted mixture of pure sinusoids. There exists a plethora of modern and classical methods that effectively solve this problem. However, for a wide variety of applications the underlying sources are not narrowband and can have an appreciable amount of bandwidth. In this work, we extend classical greedy algorithms for sparse recovery (e.g., orthogonal matching pursuit) to localize broadband sources. We leverage models for samples of broadband signals based on a union of Slepian subspaces, which are more aptly suited for dealing with spectral leakage and dynamic range disparities. We show that by using these models, our adapted algorithms can successfully localize broadband sources under a variety of adverse operating scenarios. Furthermore, we show that our algorithms outperform complementary methods that use more standard Fourier models. We also show that we can perform estimation from compressed measurements with little loss in fidelity as long as the number of measurements are on the order of the signal’s implicit degrees of freedom. We conclude with an in-depth application of these ideas to the problem of localization in multi-sensor arrays.
{"title":"Iterative Broadband Source Localization","authors":"Coleman DeLude;Rakshith S. Srinivasa;Santhosh Karnik;Christopher Hood;Mark A. Davenport;Justin Romberg","doi":"10.1109/JSAIT.2023.3317094","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3317094","url":null,"abstract":"In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the problem of spectral line estimation, where our goal is simply to estimate the active frequencies from a weighted mixture of pure sinusoids. There exists a plethora of modern and classical methods that effectively solve this problem. However, for a wide variety of applications the underlying sources are not narrowband and can have an appreciable amount of bandwidth. In this work, we extend classical greedy algorithms for sparse recovery (e.g., orthogonal matching pursuit) to localize broadband sources. We leverage models for samples of broadband signals based on a union of Slepian subspaces, which are more aptly suited for dealing with spectral leakage and dynamic range disparities. We show that by using these models, our adapted algorithms can successfully localize broadband sources under a variety of adverse operating scenarios. Furthermore, we show that our algorithms outperform complementary methods that use more standard Fourier models. We also show that we can perform estimation from compressed measurements with little loss in fidelity as long as the number of measurements are on the order of the signal’s implicit degrees of freedom. We conclude with an in-depth application of these ideas to the problem of localization in multi-sensor arrays.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"453-469"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-14DOI: 10.1109/JSAIT.2023.3315585
Anthony Gómez-Fonseca;Roxana Smarandache;David G. M. Mitchell
In this paper, we present an efficient strategy to enumerate the number of $k$ -cycles, $gleq k < 2g$ , in the Tanner graph of a quasi-cyclic low-density parity-check (QC-LDPC) code with girth $g$ using its polynomial parity-check matrix $H$ . This strategy works for both $(d_{v},d_{c})$ -regular and irregular QC-LDPC codes. In this approach, we note that the $m$ th power of the polynomial adjacency matrix can be used to describe walks of length $m$ in the protograph and can therefore be sufficiently described by the matrices $B_{m}(H) triangleq (HH^{mathsf {T}})^{lfloor {m/2}rfloor }H^{(mmod 2)}$ , where $mgeq 0$ . We provide formulas for the number of $k$ -cycles, $mathcal {N}_{k}$ , by just taking into account repetitions in some multisets constructed from the matrices $B_{m}(H)$ . This approach is shown to have low complexity. For example, in the case of QC-LDPC codes based on the $3times n_{v}$ fully-connected protograph, the complexity of determining $mathcal {N}_{k}$ , for $k=4,6,8,10$ and 12, is $O(n_{v}^{2}log (N))$ , $O(n_{v}^{2}log (n_{v})log (N))$ , $O(n_{v}^{4}log ^{4}(n_{v})log (N))$ , $O(n_{v}^{4}log (n_{v})log (N))$ and $O(n_{v}^{6}log ^{6}(n_{v})log (N))$ , respectively. The complexity, depending logarithmically on the lifting factor $N$ , gives our approach, to the best of our knowledge, a significant advantage over previous works on the cycle distribution of QC-LDPC codes.
{"title":"An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes","authors":"Anthony Gómez-Fonseca;Roxana Smarandache;David G. M. Mitchell","doi":"10.1109/JSAIT.2023.3315585","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3315585","url":null,"abstract":"In this paper, we present an efficient strategy to enumerate the number of \u0000<inline-formula> <tex-math>$k$ </tex-math></inline-formula>\u0000-cycles, \u0000<inline-formula> <tex-math>$gleq k < 2g$ </tex-math></inline-formula>\u0000, in the Tanner graph of a quasi-cyclic low-density parity-check (QC-LDPC) code with girth \u0000<inline-formula> <tex-math>$g$ </tex-math></inline-formula>\u0000 using its polynomial parity-check matrix \u0000<inline-formula> <tex-math>$H$ </tex-math></inline-formula>\u0000. This strategy works for both \u0000<inline-formula> <tex-math>$(d_{v},d_{c})$ </tex-math></inline-formula>\u0000-regular and irregular QC-LDPC codes. In this approach, we note that the \u0000<inline-formula> <tex-math>$m$ </tex-math></inline-formula>\u0000th power of the polynomial adjacency matrix can be used to describe walks of length \u0000<inline-formula> <tex-math>$m$ </tex-math></inline-formula>\u0000 in the protograph and can therefore be sufficiently described by the matrices \u0000<inline-formula> <tex-math>$B_{m}(H) triangleq (HH^{mathsf {T}})^{lfloor {m/2}rfloor }H^{(mmod 2)}$ </tex-math></inline-formula>\u0000, where \u0000<inline-formula> <tex-math>$mgeq 0$ </tex-math></inline-formula>\u0000. We provide formulas for the number of \u0000<inline-formula> <tex-math>$k$ </tex-math></inline-formula>\u0000-cycles, \u0000<inline-formula> <tex-math>$mathcal {N}_{k}$ </tex-math></inline-formula>\u0000, by just taking into account repetitions in some multisets constructed from the matrices \u0000<inline-formula> <tex-math>$B_{m}(H)$ </tex-math></inline-formula>\u0000. This approach is shown to have low complexity. For example, in the case of QC-LDPC codes based on the \u0000<inline-formula> <tex-math>$3times n_{v}$ </tex-math></inline-formula>\u0000 fully-connected protograph, the complexity of determining \u0000<inline-formula> <tex-math>$mathcal {N}_{k}$ </tex-math></inline-formula>\u0000, for \u0000<inline-formula> <tex-math>$k=4,6,8,10$ </tex-math></inline-formula>\u0000 and 12, is \u0000<inline-formula> <tex-math>$O(n_{v}^{2}log (N))$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$O(n_{v}^{2}log (n_{v})log (N))$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$O(n_{v}^{4}log ^{4}(n_{v})log (N))$ </tex-math></inline-formula>\u0000, \u0000<inline-formula> <tex-math>$O(n_{v}^{4}log (n_{v})log (N))$ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$O(n_{v}^{6}log ^{6}(n_{v})log (N))$ </tex-math></inline-formula>\u0000, respectively. The complexity, depending logarithmically on the lifting factor \u0000<inline-formula> <tex-math>$N$ </tex-math></inline-formula>\u0000, gives our approach, to the best of our knowledge, a significant advantage over previous works on the cycle distribution of QC-LDPC codes.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"499-513"},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a soft decoding scheme based on the binary representations transferred from the parity-check matrices (PCMs) for Reed-Solomon (RS) codes. Referring to the modified binary PCM that has a systematic part and a high-density part corresponding to the least reliable variable nodes (LRVNs) and the most reliable variable nodes (MRVNs), respectively, an informed dynamic scheduling method, called Nested-Polling Residual Belief Propagation (NP-RBP), is applied to the corresponding Tanner graph. As with the popular adaptive BP (ABP) decoding approach, adaptation in a binary PCM based on the reliability of variable nodes is also conducted in the proposed NP-RBP decoding. The NP-RBP enables the LRVNs to receive significant updates and limits the correlation accumulation from the short cycles in the MRVNs. In order to enhance the error-rate performance for long codes, a bit-flipping (BF) technique is conducted in order to correct a selection of the errors in the MRVNs such that the propagation of these errors in the subsequent NP-RBP process can be avoided. The resultant decoder is termed NP-RBP-BF. For short codes such as the (31, 25) and (63, 55) RS codes, NP-RBP is able to provide an error-rate performance close to the maximum-likelihood (ML) bound. A more significant improvement can be observed for long codes. For instance, when the proposed NP-RBP-BF decoding is applied to the (255, 239) RS code, it can provide a gain of about 0.4 dB compared to the ABP decoding and the performance gap to the ML bound can be narrowed to about 0.25 dB at a frame error rate of $2times 10^{-3}$ .
{"title":"A Graph-Based Soft-Decision Decoding Scheme for Reed-Solomon Codes","authors":"Huang-Chang Lee;Jyun-Han Wu;Chung-Hsuan Wang;Yeong-Luh Ueng","doi":"10.1109/JSAIT.2023.3315453","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3315453","url":null,"abstract":"This paper presents a soft decoding scheme based on the binary representations transferred from the parity-check matrices (PCMs) for Reed-Solomon (RS) codes. Referring to the modified binary PCM that has a systematic part and a high-density part corresponding to the least reliable variable nodes (LRVNs) and the most reliable variable nodes (MRVNs), respectively, an informed dynamic scheduling method, called Nested-Polling Residual Belief Propagation (NP-RBP), is applied to the corresponding Tanner graph. As with the popular adaptive BP (ABP) decoding approach, adaptation in a binary PCM based on the reliability of variable nodes is also conducted in the proposed NP-RBP decoding. The NP-RBP enables the LRVNs to receive significant updates and limits the correlation accumulation from the short cycles in the MRVNs. In order to enhance the error-rate performance for long codes, a bit-flipping (BF) technique is conducted in order to correct a selection of the errors in the MRVNs such that the propagation of these errors in the subsequent NP-RBP process can be avoided. The resultant decoder is termed NP-RBP-BF. For short codes such as the (31, 25) and (63, 55) RS codes, NP-RBP is able to provide an error-rate performance close to the maximum-likelihood (ML) bound. A more significant improvement can be observed for long codes. For instance, when the proposed NP-RBP-BF decoding is applied to the (255, 239) RS code, it can provide a gain of about 0.4 dB compared to the ABP decoding and the performance gap to the ML bound can be narrowed to about 0.25 dB at a frame error rate of \u0000<inline-formula> <tex-math>$2times 10^{-3}$ </tex-math></inline-formula>\u0000.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"420-433"},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50426629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-13DOI: 10.1109/JSAIT.2023.3315148
Debarnab Mitra;Lev Tauz;Lara Dolecek
Data availability (DA) attack is a well-known problem in certain blockchains where users accept an invalid block with unavailable portions. Previous works have used LDPC and 2-D Reed Solomon (2D-RS) codes with Merkle trees to mitigate DA attacks. These codes perform well across various metrics such as DA detection probability and communication cost. However, these codes are difficult to apply to blockchains with large blocks due to large decoding complexity and coding fraud proof size (2D-RS codes), and intractable code guarantees for large code lengths (LDPC codes). In this paper, we focus on large block size applications and address the above challenges by proposing the novel Graph Coded Merkle Tree (GCMT): a Merkle tree encoded using polar encoding graphs. We provide a specialized polar encoding graph design algorithm called Sampling Efficient Freezing and an algorithm to prune the polar encoding graph. We demonstrate that the GCMT built using the above techniques results in a better DA detection probability and communication cost compared to LDPC codes, has a lower coding fraud proof size compared to LDPC and 2D-RS codes, provides tractable code guarantees at large code lengths (similar to 2D-RS codes), and has comparable decoding complexity to 2D-RS and LDPC codes.
{"title":"Graph Coded Merkle Tree: Mitigating Data Availability Attacks in Blockchain Systems Using Informed Design of Polar Factor Graphs","authors":"Debarnab Mitra;Lev Tauz;Lara Dolecek","doi":"10.1109/JSAIT.2023.3315148","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3315148","url":null,"abstract":"Data availability (DA) attack is a well-known problem in certain blockchains where users accept an invalid block with unavailable portions. Previous works have used LDPC and 2-D Reed Solomon (2D-RS) codes with Merkle trees to mitigate DA attacks. These codes perform well across various metrics such as DA detection probability and communication cost. However, these codes are difficult to apply to blockchains with large blocks due to large decoding complexity and coding fraud proof size (2D-RS codes), and intractable code guarantees for large code lengths (LDPC codes). In this paper, we focus on large block size applications and address the above challenges by proposing the novel Graph Coded Merkle Tree (GCMT): a Merkle tree encoded using polar encoding graphs. We provide a specialized polar encoding graph design algorithm called Sampling Efficient Freezing and an algorithm to prune the polar encoding graph. We demonstrate that the GCMT built using the above techniques results in a better DA detection probability and communication cost compared to LDPC codes, has a lower coding fraud proof size compared to LDPC and 2D-RS codes, provides tractable code guarantees at large code lengths (similar to 2D-RS codes), and has comparable decoding complexity to 2D-RS and LDPC codes.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"434-452"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50426630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-11DOI: 10.1109/JSAIT.2023.3312678
Mohammad Rowshan;Jinhong Yuan
The minimum Hamming distance of a linear block code is the smallest number of bit changes required to transform one valid codeword into another. The code’s minimum distance determines the code’s error-correcting capabilities. Furthermore, The number of minimum weight codewords, a.k.a. error coefficient, gives a good comparative measure for the block error rate (BLER) of linear block codes with identical minimum distance, in particular at a high SNR regime under maximum likelihood (ML) decoding. A code with a smaller error coefficient would give a lower BLER. Unlike polar codes, a closed-form expression for the enumeration of the error coefficient of polarization-adjusted convolutional (PAC) codes is yet unknown. As PAC codes are convolutionally pre-transformed polar codes, we study the impact of pre-transformation on polar codes in terms of minimum Hamming distance and error coefficient by partitioning the codewords into cosets. We show that the minimum distance of PAC codes does not decrease; however, the pre-transformation may reduce the error coefficient depending on the choice of convolutional polynomial. We recognize the properties of the cosets where pre-transformation is ineffective in decreasing the error coefficient, giving a lower bound for the error coefficient. Then, we propose a low-complexity enumeration method that determines the number of minimum weight codewords of PAC codes relying on the error coefficient of polar codes. That is, given the error coefficient ${mathcal {A}}_{w_{min}}$ of polar codes, we determine the reduction $X$ in the error coefficient due to convolutional pre-transformation in PAC coding and subtract it from the error coefficient of polar codes, ${mathcal {A}}_{w_{min}}-X$ . Furthermore, we numerically analyze the tightness of the lower bound and the impact of the choice of the convolutional polynomial on the error coefficient based on the sub-patterns in the polynomial’s coefficients. Eventually, we show how we can further reduce the error coefficient in the cosets.
{"title":"On the Minimum Weight Codewords of PAC Codes: The Impact of Pre-Transformation","authors":"Mohammad Rowshan;Jinhong Yuan","doi":"10.1109/JSAIT.2023.3312678","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3312678","url":null,"abstract":"The minimum Hamming distance of a linear block code is the smallest number of bit changes required to transform one valid codeword into another. The code’s minimum distance determines the code’s error-correcting capabilities. Furthermore, The number of minimum weight codewords, a.k.a. error coefficient, gives a good comparative measure for the block error rate (BLER) of linear block codes with identical minimum distance, in particular at a high SNR regime under maximum likelihood (ML) decoding. A code with a smaller error coefficient would give a lower BLER. Unlike polar codes, a closed-form expression for the enumeration of the error coefficient of polarization-adjusted convolutional (PAC) codes is yet unknown. As PAC codes are convolutionally pre-transformed polar codes, we study the impact of pre-transformation on polar codes in terms of minimum Hamming distance and error coefficient by partitioning the codewords into cosets. We show that the minimum distance of PAC codes does not decrease; however, the pre-transformation may reduce the error coefficient depending on the choice of convolutional polynomial. We recognize the properties of the cosets where pre-transformation is ineffective in decreasing the error coefficient, giving a lower bound for the error coefficient. Then, we propose a low-complexity enumeration method that determines the number of minimum weight codewords of PAC codes relying on the error coefficient of polar codes. That is, given the error coefficient \u0000<inline-formula> <tex-math>${mathcal {A}}_{w_{min}}$ </tex-math></inline-formula>\u0000 of polar codes, we determine the reduction \u0000<inline-formula> <tex-math>$X$ </tex-math></inline-formula>\u0000 in the error coefficient due to convolutional pre-transformation in PAC coding and subtract it from the error coefficient of polar codes, \u0000<inline-formula> <tex-math>${mathcal {A}}_{w_{min}}-X$ </tex-math></inline-formula>\u0000. Furthermore, we numerically analyze the tightness of the lower bound and the impact of the choice of the convolutional polynomial on the error coefficient based on the sub-patterns in the polynomial’s coefficients. Eventually, we show how we can further reduce the error coefficient in the cosets.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"487-498"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50426700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-08DOI: 10.1109/JSAIT.2023.3312233
Neophytos Charalambides;Mert Pilanci;Alfred O. Hero
Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients; similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding. We modify this method so that the coordinator does not access the local data at any point; while the clients access the aggregated matrix in order to complete their tasks. The network we consider is not centrally administrated, and the communications which take place are secure against potential eavesdroppers.
{"title":"Securely Aggregated Coded Matrix Inversion","authors":"Neophytos Charalambides;Mert Pilanci;Alfred O. Hero","doi":"10.1109/JSAIT.2023.3312233","DOIUrl":"10.1109/JSAIT.2023.3312233","url":null,"abstract":"Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients; similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding. We modify this method so that the coordinator does not access the local data at any point; while the clients access the aggregated matrix in order to complete their tasks. The network we consider is not centrally administrated, and the communications which take place are secure against potential eavesdroppers.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"405-419"},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46029173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-04DOI: 10.1109/JSAIT.2023.3310931
Burak Bartan;Mert Pilanci
We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching and polar codes in the context of coded computation. We propose a sequential decoding algorithm designed to handle real valued data while maintaining low computational complexity for recovery. Additionally, we provide an anytime estimator that can generate provably accurate estimates even when the set of available node outputs is not decodable. We demonstrate the potential applications of this framework in various contexts, such as large-scale matrix multiplication and black-box optimization. We present the implementation of these methods on a serverless cloud computing system and provide numerical results to demonstrate their scalability in practice, including ImageNet scale computations.
{"title":"Randomized Polar Codes for Anytime Distributed Machine Learning","authors":"Burak Bartan;Mert Pilanci","doi":"10.1109/JSAIT.2023.3310931","DOIUrl":"10.1109/JSAIT.2023.3310931","url":null,"abstract":"We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching and polar codes in the context of coded computation. We propose a sequential decoding algorithm designed to handle real valued data while maintaining low computational complexity for recovery. Additionally, we provide an anytime estimator that can generate provably accurate estimates even when the set of available node outputs is not decodable. We demonstrate the potential applications of this framework in various contexts, such as large-scale matrix multiplication and black-box optimization. We present the implementation of these methods on a serverless cloud computing system and provide numerical results to demonstrate their scalability in practice, including ImageNet scale computations.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"393-404"},"PeriodicalIF":0.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43691019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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