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}
Pub Date : 2023-08-30DOI: 10.1109/JSAIT.2023.3308768
Anindya Bijoy Das;Aditya Ramamoorthy;David J. Love;Christopher G. Brinton
Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum distance separable) codes into the framework; this can achieve resilience against an optimal number of stragglers. However, these codes assign dense linear combinations of submatrices to the worker nodes. When the input matrices are sparse, these approaches increase the number of non-zero entries in the encoded matrices, which in turn adversely affects the worker computation time. In this work, we develop a distributed matrix computation approach where the assigned encoded submatrices are random linear combinations of a small number of submatrices. In addition to being well suited for sparse input matrices, our approach continues to have the optimal straggler resilience in a certain range of problem parameters. Moreover, compared to recent sparse matrix computation approaches, the search for a “good” set of random coefficients to promote numerical stability in our method is much more computationally efficient. We show that our approach can efficiently utilize partial computations done by slower worker nodes in a heterogeneous system which can enhance the overall computation speed. Numerical experiments conducted through Amazon Web Services (AWS) demonstrate up to 30% reduction in per worker node computation time and $100times $ faster encoding compared to the available methods.
{"title":"Distributed Matrix Computations With Low-Weight Encodings","authors":"Anindya Bijoy Das;Aditya Ramamoorthy;David J. Love;Christopher G. Brinton","doi":"10.1109/JSAIT.2023.3308768","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3308768","url":null,"abstract":"Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum distance separable) codes into the framework; this can achieve resilience against an optimal number of stragglers. However, these codes assign dense linear combinations of submatrices to the worker nodes. When the input matrices are sparse, these approaches increase the number of non-zero entries in the encoded matrices, which in turn adversely affects the worker computation time. In this work, we develop a distributed matrix computation approach where the assigned encoded submatrices are random linear combinations of a small number of submatrices. In addition to being well suited for sparse input matrices, our approach continues to have the optimal straggler resilience in a certain range of problem parameters. Moreover, compared to recent sparse matrix computation approaches, the search for a “good” set of random coefficients to promote numerical stability in our method is much more computationally efficient. We show that our approach can efficiently utilize partial computations done by slower worker nodes in a heterogeneous system which can enhance the overall computation speed. Numerical experiments conducted through Amazon Web Services (AWS) demonstrate up to 30% reduction in per worker node computation time and \u0000<inline-formula> <tex-math>$100times $ </tex-math></inline-formula>\u0000 faster encoding compared to the available methods.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"363-378"},"PeriodicalIF":0.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50427091","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 : 2023-08-16DOI: 10.1109/JSAIT.2023.3305874
Mohammad Fereydounian;Hamed Hassani;Mohammad Vahid Jamali;Hessam Mahdavifar
Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. Moreover, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime. In this paper, we study channel coding at low capacity from two perspectives: fundamental limits at finite length and code constructions. We first specify what a low-capacity regime means. We then characterize finite-length fundamental limits of channel coding in the low-capacity regime for various types of channels, including binary erasure channels (BECs), binary symmetric channels (BSCs), and additive white Gaussian noise (AWGN) channels. From the code construction perspective, we characterize the optimal number of repetitions for transmission over binary memoryless symmetric (BMS) channels, in terms of the code blocklength and the underlying channel capacity, such that the capacity loss due to the repetition is negligible. Furthermore, it is shown that capacity-achieving polar codes naturally adopt the aforementioned optimal number of repetitions.
{"title":"Channel Coding at Low Capacity","authors":"Mohammad Fereydounian;Hamed Hassani;Mohammad Vahid Jamali;Hessam Mahdavifar","doi":"10.1109/JSAIT.2023.3305874","DOIUrl":"10.1109/JSAIT.2023.3305874","url":null,"abstract":"Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. Moreover, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime. In this paper, we study channel coding at low capacity from two perspectives: fundamental limits at finite length and code constructions. We first specify what a low-capacity regime means. We then characterize finite-length fundamental limits of channel coding in the low-capacity regime for various types of channels, including binary erasure channels (BECs), binary symmetric channels (BSCs), and additive white Gaussian noise (AWGN) channels. From the code construction perspective, we characterize the optimal number of repetitions for transmission over binary memoryless symmetric (BMS) channels, in terms of the code blocklength and the underlying channel capacity, such that the capacity loss due to the repetition is negligible. Furthermore, it is shown that capacity-achieving polar codes naturally adopt the aforementioned optimal number of repetitions.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"351-362"},"PeriodicalIF":0.0,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42302948","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 : 2023-08-10DOI: 10.1109/JSAIT.2023.3304249
Zhenyu Liu;Andrea Conti;Sanjoy K. Mitter;Moe Z. Win
Distributed filtering is crucial in many applications such as localization, radar, autonomy, and environmental monitoring. The aim of distributed filtering is to infer time-varying unknown states using data obtained via sensing and communication in a network. This paper analyzes continuous-time distributed filtering with sensing and communication constraints. In particular, the paper considers a building-block system of two nodes, where each node is tasked with inferring a time-varying unknown state. At each time, the two nodes obtain noisy observations of the unknown states via sensing and perform communication via a Gaussian feedback channel. The distributed filter of the unknown state is computed based on both the sensor observations and the received messages. We analyze the asymptotic performance of the distributed filter by deriving a necessary and sufficient condition of the sensing and communication capabilities under which the mean-square error of the distributed filter is bounded over time. Numerical results are presented to validate the derived necessary and sufficient condition.
{"title":"Continuous-Time Distributed Filtering With Sensing and Communication Constraints","authors":"Zhenyu Liu;Andrea Conti;Sanjoy K. Mitter;Moe Z. Win","doi":"10.1109/JSAIT.2023.3304249","DOIUrl":"10.1109/JSAIT.2023.3304249","url":null,"abstract":"Distributed filtering is crucial in many applications such as localization, radar, autonomy, and environmental monitoring. The aim of distributed filtering is to infer time-varying unknown states using data obtained via sensing and communication in a network. This paper analyzes continuous-time distributed filtering with sensing and communication constraints. In particular, the paper considers a building-block system of two nodes, where each node is tasked with inferring a time-varying unknown state. At each time, the two nodes obtain noisy observations of the unknown states via sensing and perform communication via a Gaussian feedback channel. The distributed filter of the unknown state is computed based on both the sensor observations and the received messages. We analyze the asymptotic performance of the distributed filter by deriving a necessary and sufficient condition of the sensing and communication capabilities under which the mean-square error of the distributed filter is bounded over time. Numerical results are presented to validate the derived necessary and sufficient condition.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"667-681"},"PeriodicalIF":0.0,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62353985","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 : 2023-08-07DOI: 10.1109/JSAIT.2023.3279333
Ron M. Roth
Let $[qrangle $ denote the integer set ${0,1, {ldots },q-1}$ and let ${{mathbb {B}}}={0,1}$ . The problem of implementing functions $[qrangle rightarrow {{mathbb {B}}}$ on content-addressable memories (CAMs) is considered. CAMs can be classified by the input alphabet and the state alphabet of their cells; for example, in binary CAMs, those alphabets are both ${{mathbb {B}}}$ , while in a ternary CAM (TCAM), both alphabets are endowed with a “don’t care” symbol. This work is motivated by recent proposals for using CAMs for fast inference on decision trees. In such learning models, the tree nodes carry out integer comparisons, such as testing equality $(x=t$ ?) or inequality $(xle t$ ?), where $xin [qrangle $ is an input to the node and $tin [qrangle $ is a node parameter. A CAM implementation of such comparisons includes mapping (i.e., encoding) $t$ into internal states of some number $n$ of cells and mapping $x$ into inputs to these cells, with the goal of minimizing $n$ . Such mappings are presented for various comparison families, as well as for the set of all functions $[qrangle rightarrow {{mathbb {B}}}$ , under several scenarios of input and state alphabets of the CAM cells. All those mappings are shown to be optimal in that they attain the smallest possible $n$ for any given $q$ .
{"title":"On the Implementation of Boolean Functions on Content-Addressable Memories","authors":"Ron M. Roth","doi":"10.1109/JSAIT.2023.3279333","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3279333","url":null,"abstract":"Let \u0000<inline-formula> <tex-math>$[qrangle $ </tex-math></inline-formula>\u0000 denote the integer set \u0000<inline-formula> <tex-math>${0,1, {ldots },q-1}$ </tex-math></inline-formula>\u0000 and let \u0000<inline-formula> <tex-math>${{mathbb {B}}}={0,1}$ </tex-math></inline-formula>\u0000. The problem of implementing functions \u0000<inline-formula> <tex-math>$[qrangle rightarrow {{mathbb {B}}}$ </tex-math></inline-formula>\u0000 on content-addressable memories (CAMs) is considered. CAMs can be classified by the input alphabet and the state alphabet of their cells; for example, in binary CAMs, those alphabets are both \u0000<inline-formula> <tex-math>${{mathbb {B}}}$ </tex-math></inline-formula>\u0000, while in a ternary CAM (TCAM), both alphabets are endowed with a “don’t care” symbol. This work is motivated by recent proposals for using CAMs for fast inference on decision trees. In such learning models, the tree nodes carry out integer comparisons, such as testing equality \u0000<inline-formula> <tex-math>$(x=t$ </tex-math></inline-formula>\u0000 ?) or inequality \u0000<inline-formula> <tex-math>$(xle t$ </tex-math></inline-formula>\u0000 ?), where \u0000<inline-formula> <tex-math>$xin [qrangle $ </tex-math></inline-formula>\u0000 is an input to the node and \u0000<inline-formula> <tex-math>$tin [qrangle $ </tex-math></inline-formula>\u0000 is a node parameter. A CAM implementation of such comparisons includes mapping (i.e., encoding) \u0000<inline-formula> <tex-math>$t$ </tex-math></inline-formula>\u0000 into internal states of some number \u0000<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\u0000 of cells and mapping \u0000<inline-formula> <tex-math>$x$ </tex-math></inline-formula>\u0000 into inputs to these cells, with the goal of minimizing \u0000<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\u0000. Such mappings are presented for various comparison families, as well as for the set of all functions \u0000<inline-formula> <tex-math>$[qrangle rightarrow {{mathbb {B}}}$ </tex-math></inline-formula>\u0000, under several scenarios of input and state alphabets of the CAM cells. All those mappings are shown to be optimal in that they attain the smallest possible \u0000<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\u0000 for any given \u0000<inline-formula> <tex-math>$q$ </tex-math></inline-formula>\u0000.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"379-392"},"PeriodicalIF":0.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354870","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 : 2023-08-01DOI: 10.1109/JSAIT.2023.3300831
Yotam Gershon;Yuval Cassuto
We propose a new compression scheme for genomic data given as sequence fragments called reads. The scheme uses a reference genome at the decoder side only, freeing the encoder from the burdens of storing references and performing computationally costly alignment operations. The main ingredient of the scheme is a multi-layer code construction, delivering to the decoder sufficient information to align the reads, correct their differences from the reference, validate their reconstruction, and correct reconstruction errors. The core of the method is the well-known concept of distributed source coding with decoder side information, fortified by a generalized-concatenation code construction enabling efficient embedding of all the information needed for reliable reconstruction. We first present the scheme for the case of substitution errors only between the reads and the reference, and then extend it to support reads with a single deletion and multiple substitutions. A central tool in this extension is a new distance metric that is shown analytically to improve alignment performance over existing distance metrics.
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