Pub Date : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834837
Aviv Adler, Jennifer Tang, Yury Polyanskiy
A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to 1. In some cases it is required to represent such a vector with only b bits per entry. A natural choice is to partition the interval [0,1] into 2b uniform bins and quantize entries to each bin independently. We show that a minor modification of this procedure – applying an entrywise non-linear function (compander) f(x) prior to quantization – yields an extremely effective quantization method. For example, for b = 8(16) and 105-sized alphabets, the quality of representation improves from a loss (under KL divergence) of 0.5(0.1) bits/entry to 10−4(10−9) bits/entry. Compared to floating point representations, our compander method improves the loss from 10−1(10−6) to 10−4(10−9) bits/entry. These numbers hold for both real-world data (word frequencies in books and DNA k-mer counts) and for synthetic randomly generated distributions. Theoretically, we set up a minimax optimality criterion and show that the compander $f(x) propto operatorname{ArcSinh} (sqrt {(1/2)(Klog K)x} )$ achieves near-optimal performance, attaining a KL-quantization loss of ≍ 2−2b log2 K for a K-letter alphabet and b →∞. Interestingly, a similar minimax criterion for the quadratic loss on the hypercube shows optimality of the standard uniform quantizer. This suggests that the ArcSinh quantizer is as fundamental for KL-distortion as the uniform quantizer for quadratic distortion.
{"title":"Efficient Representation of Large-Alphabet Probability Distributions via Arcsinh-Compander","authors":"Aviv Adler, Jennifer Tang, Yury Polyanskiy","doi":"10.1109/ISIT50566.2022.9834837","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834837","url":null,"abstract":"A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to 1. In some cases it is required to represent such a vector with only b bits per entry. A natural choice is to partition the interval [0,1] into 2b uniform bins and quantize entries to each bin independently. We show that a minor modification of this procedure – applying an entrywise non-linear function (compander) f(x) prior to quantization – yields an extremely effective quantization method. For example, for b = 8(16) and 105-sized alphabets, the quality of representation improves from a loss (under KL divergence) of 0.5(0.1) bits/entry to 10−4(10−9) bits/entry. Compared to floating point representations, our compander method improves the loss from 10−1(10−6) to 10−4(10−9) bits/entry. These numbers hold for both real-world data (word frequencies in books and DNA k-mer counts) and for synthetic randomly generated distributions. Theoretically, we set up a minimax optimality criterion and show that the compander $f(x) propto operatorname{ArcSinh} (sqrt {(1/2)(Klog K)x} )$ achieves near-optimal performance, attaining a KL-quantization loss of ≍ 2−2b log2 K for a K-letter alphabet and b →∞. Interestingly, a similar minimax criterion for the quadratic loss on the hypercube shows optimality of the standard uniform quantizer. This suggests that the ArcSinh quantizer is as fundamental for KL-distortion as the uniform quantizer for quadratic distortion.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126414677","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834562
F. Sha, Ruizhi Zhang
Community detection is a fundamental problem in network analysis and has important applications in sensor networks and social networks. In many cases, the community structure of the network may change at some unknown time and thus it is desirable to come up with efficient monitoring procedures that can detect the change as quickly as possible. In this work, we use the Erdős-Rényi model and the bisection stochastic block model (SBM) to model the pre-change and post-change distributions of the network, respectively. That is, initially, we assume there is no community in the network. However, at some unknown time, a change occurs, and two communities are formed in the network. We then propose an efficient monitoring procedure by using the number of k-cycles in the graph. The asymptotic detection properties of our proposed procedure are derived when all parameters are known. A generalized likelihood ratio (GLR) type detection procedure and an adaptive CUSUM type detection procedure are constructed to address the problem when parameters are unknown.
{"title":"Quickest Detection of the Change of Community via Stochastic Block Models","authors":"F. Sha, Ruizhi Zhang","doi":"10.1109/ISIT50566.2022.9834562","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834562","url":null,"abstract":"Community detection is a fundamental problem in network analysis and has important applications in sensor networks and social networks. In many cases, the community structure of the network may change at some unknown time and thus it is desirable to come up with efficient monitoring procedures that can detect the change as quickly as possible. In this work, we use the Erdős-Rényi model and the bisection stochastic block model (SBM) to model the pre-change and post-change distributions of the network, respectively. That is, initially, we assume there is no community in the network. However, at some unknown time, a change occurs, and two communities are formed in the network. We then propose an efficient monitoring procedure by using the number of k-cycles in the graph. The asymptotic detection properties of our proposed procedure are derived when all parameters are known. A generalized likelihood ratio (GLR) type detection procedure and an adaptive CUSUM type detection procedure are constructed to address the problem when parameters are unknown.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126801451","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 : 2022-06-26DOI: 10.48550/arXiv.2206.13752
Min Qiu, Jinhong Yuan
We propose a new family of spatially coupled product codes, called sub-block rearranged staircase (SR-staircase) codes. Each SR-staircase code block is constructed by encoding rearranged preceding code blocks and new information blocks, where the rearrangement involves sub-blocks decomposition and transposition. The proposed codes can be constructed to have each code block size of 1/q to that of the conventional staircase codes while having the same rate and component codes, for any positive integer q. In this regard, we can use strong algebraic component codes to construct SR-staircase codes with a similar or the same code block size and rate as staircase codes with weak component codes. Moreover, both waterfall and error floor performance can be further improved by using a large coupling width. The superior performance of the proposed codes is demonstrated through density evolution and error floor analysis as well as simulation.
{"title":"Sub-Block Rearranged Staircase Codes for Optical Transport Networks","authors":"Min Qiu, Jinhong Yuan","doi":"10.48550/arXiv.2206.13752","DOIUrl":"https://doi.org/10.48550/arXiv.2206.13752","url":null,"abstract":"We propose a new family of spatially coupled product codes, called sub-block rearranged staircase (SR-staircase) codes. Each SR-staircase code block is constructed by encoding rearranged preceding code blocks and new information blocks, where the rearrangement involves sub-blocks decomposition and transposition. The proposed codes can be constructed to have each code block size of 1/q to that of the conventional staircase codes while having the same rate and component codes, for any positive integer q. In this regard, we can use strong algebraic component codes to construct SR-staircase codes with a similar or the same code block size and rate as staircase codes with weak component codes. Moreover, both waterfall and error floor performance can be further improved by using a large coupling width. The superior performance of the proposed codes is demonstrated through density evolution and error floor analysis as well as simulation.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114244695","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834355
K. Ma, Yinfei Xu, Shuo Shao
We consider a general point-to-point fading multiple-input multiple-output (MIMO) Gaussian channel. The channel suffers block fading and with finite channel states, among which there is no degraded order on state information due to multi-antenna deployment. To guarantee reliable transmissions under arbitrary unpredictable fading states, we generalize the layered broadcast approach in the channel by inducing a rate splitting scheme. It assigns a specific sub-message layer for every possible state set and splits the transmission rate by allocating power to each layer. Under this scheme, a generalized broadcast approach is designed to be suitable for multi-antenna transmission. The maximum average rate under total power constraint can be characterized by an optimization problem. Numerical examples are provided to show the optimality of our transmission scheme within degradedness among different channel state information. Meanwhile, such generalization can also provide a decent performance under the general non-degraded case.
{"title":"On Broadcast Approach to MIMO Fading Channels","authors":"K. Ma, Yinfei Xu, Shuo Shao","doi":"10.1109/ISIT50566.2022.9834355","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834355","url":null,"abstract":"We consider a general point-to-point fading multiple-input multiple-output (MIMO) Gaussian channel. The channel suffers block fading and with finite channel states, among which there is no degraded order on state information due to multi-antenna deployment. To guarantee reliable transmissions under arbitrary unpredictable fading states, we generalize the layered broadcast approach in the channel by inducing a rate splitting scheme. It assigns a specific sub-message layer for every possible state set and splits the transmission rate by allocating power to each layer. Under this scheme, a generalized broadcast approach is designed to be suitable for multi-antenna transmission. The maximum average rate under total power constraint can be characterized by an optimization problem. Numerical examples are provided to show the optimality of our transmission scheme within degradedness among different channel state information. Meanwhile, such generalization can also provide a decent performance under the general non-degraded case.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120930126","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834575
Hongna Yang, Yiwei Zhang
Fractional repetition (FR) codes are a special family of regenerating codes with the repair-by-transfer property. The constructions of FR codes are naturally related to combinatorial designs, graphs, and hypergraphs. Given the file size of an FR code, it is desirable to determine the minimum number of storage nodes needed. The problem is related to an extremal graph theory problem, which asks for the minimum number of vertices of an α-regular graph such that any subgraph with k vertices has at most δ edges. In this paper, we present a class of regular graphs for this problem to give the bounds for the minimum number of storage nodes for the FR codes.
{"title":"On an extremal problem of regular graphs related to fractional repetition codes","authors":"Hongna Yang, Yiwei Zhang","doi":"10.1109/ISIT50566.2022.9834575","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834575","url":null,"abstract":"Fractional repetition (FR) codes are a special family of regenerating codes with the repair-by-transfer property. The constructions of FR codes are naturally related to combinatorial designs, graphs, and hypergraphs. Given the file size of an FR code, it is desirable to determine the minimum number of storage nodes needed. The problem is related to an extremal graph theory problem, which asks for the minimum number of vertices of an α-regular graph such that any subgraph with k vertices has at most δ edges. In this paper, we present a class of regular graphs for this problem to give the bounds for the minimum number of storage nodes for the FR codes.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115250524","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834364
Yunfeng Cai, Guanhua Fang, P. Li
This paper considers the sensitivity of the optimization problem minf(x) with the linear constraint Ax = b, where f is a general differentiable function quantifying sparsity, Ax=b is the under-determined linear system of equations, A ∈ℝn×p. Given small noises to A and b, we are able to show the difference between the perturbed solution and optimal solution. The new perturbation bound reveals the factors that affect the sensitivity of the optimal solution of the linear system. Different objective functions f’s lead to distinct perturbation bounds, whose magnitudes determine the robustness of the optimization problem. Our results shed a fresh insight in understanding the robustness of under-determined linear system.
{"title":"Sensitivity of Under-Determined Linear System","authors":"Yunfeng Cai, Guanhua Fang, P. Li","doi":"10.1109/ISIT50566.2022.9834364","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834364","url":null,"abstract":"This paper considers the sensitivity of the optimization problem minf(x) with the linear constraint Ax = b, where f is a general differentiable function quantifying sparsity, Ax=b is the under-determined linear system of equations, A ∈ℝn×p. Given small noises to A and b, we are able to show the difference between the perturbed solution and optimal solution. The new perturbation bound reveals the factors that affect the sensitivity of the optimal solution of the linear system. Different objective functions f’s lead to distinct perturbation bounds, whose magnitudes determine the robustness of the optimization problem. Our results shed a fresh insight in understanding the robustness of under-determined linear system.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123784448","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834885
Xiaomeng Guo, Yongchao Wang
In this paper, we devise a new alternating direction method of multipliers (ADMM) decoder for non-binary low-density parity-check (LDPC) codes in Galois fields of characteristic two $left( {{mathbb{F}_{{2^q}}}} right)$. Its main content are threefold: first, the procedure of formulating the maximum likelihood (ML) decoding problem in ${mathbb{F}_{{2^q}}}$ to a linear integer problem in real space is presented; Second, after relaxing the integer problem to a continuous one, an efficient ADMM algorithm is customized to solve the latter, where all the entries of the variable vectors can be obtained in parallel; Third, we show that the proposed ADMM decoder satisfies the favorable codeword-independent property under some mild conditions and its computation complexity in each ADMM iteration is roughly $mathcal{O}left( {nq} right)$, where n is code length of the considered non-binary LDPC code. Simulation results demonstrate that its performance, such as error-correction and decoding efficiency, is very competitive in comparison with state-of-the-art non-binary LDPC decoders.
{"title":"Efficient ADMM Decoder for Non-binary LDPC Codes based on Bit Embedding Technique","authors":"Xiaomeng Guo, Yongchao Wang","doi":"10.1109/ISIT50566.2022.9834885","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834885","url":null,"abstract":"In this paper, we devise a new alternating direction method of multipliers (ADMM) decoder for non-binary low-density parity-check (LDPC) codes in Galois fields of characteristic two $left( {{mathbb{F}_{{2^q}}}} right)$. Its main content are threefold: first, the procedure of formulating the maximum likelihood (ML) decoding problem in ${mathbb{F}_{{2^q}}}$ to a linear integer problem in real space is presented; Second, after relaxing the integer problem to a continuous one, an efficient ADMM algorithm is customized to solve the latter, where all the entries of the variable vectors can be obtained in parallel; Third, we show that the proposed ADMM decoder satisfies the favorable codeword-independent property under some mild conditions and its computation complexity in each ADMM iteration is roughly $mathcal{O}left( {nq} right)$, where n is code length of the considered non-binary LDPC code. Simulation results demonstrate that its performance, such as error-correction and decoding efficiency, is very competitive in comparison with state-of-the-art non-binary LDPC decoders.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124949799","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834425
Xiang Zhang, Kai Wan, Hua Sun, Mingyue Ji, G. Caire
We consider the cache-aided multiuser private information retrieval (MuPIR) problem with a focus on the special case of two messages, two users and arbitrary number of databases where the users have distinct demands of the messages. We characterize the optimal memory-load trade-off for the considered MuPIR problem by proposing a novel achievable scheme and a tight converse. The proposed achievable scheme uses the idea of cache-aided interference alignment (CIA) developed in the literature by the same authors. The proposed converse uses a tree-like decoding structure to incorporate both the decodability and privacy requirements of the users. While the optimal characterization of the cache-aided MuPIR problem is challenging in general, this work provides insight into understanding the general structure of the cache-aided MuPIR problem.
{"title":"Fundamental Limits of Cache-aided Multiuser PIR: The Two-message Two-user Case","authors":"Xiang Zhang, Kai Wan, Hua Sun, Mingyue Ji, G. Caire","doi":"10.1109/ISIT50566.2022.9834425","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834425","url":null,"abstract":"We consider the cache-aided multiuser private information retrieval (MuPIR) problem with a focus on the special case of two messages, two users and arbitrary number of databases where the users have distinct demands of the messages. We characterize the optimal memory-load trade-off for the considered MuPIR problem by proposing a novel achievable scheme and a tight converse. The proposed achievable scheme uses the idea of cache-aided interference alignment (CIA) developed in the literature by the same authors. The proposed converse uses a tree-like decoding structure to incorporate both the decodability and privacy requirements of the users. While the optimal characterization of the cache-aided MuPIR problem is challenging in general, this work provides insight into understanding the general structure of the cache-aided MuPIR problem.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131764154","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834795
Y. M. Chee, Duc Tu Dao, Long Nguyen Tien, Hoang Ta Duy, Van Khu Vu
The de Bruijn based timing and synchronization (dBTS) system has been proposed and studied recently for some channels require reliable synchronization, such as quantum communication. To avoid a long period of no-pulse in the dBTS system, we propose to study the run length limited de Bruijn sequences which not only are run length limited sequences but also can be used to locate the location of any sub-string. Such subjects are expected to have various applications and they also present some interesting theoretical questions in combinatorics, algorithms and coding theory.In this paper, we are the first to provide an explicit formula of the maximal length of the run length limited de Bruijn sequences. Besides that, using Lyndon words, we present an efficient construction of a run length limited de Bruijn sequence with the maximal length. Furthermore, we also provide a sub-linear decoding algorithm which can locate the position of an arbitrary sub-string.
{"title":"Run Length Limited de Bruijn Sequences for Quantum Communications","authors":"Y. M. Chee, Duc Tu Dao, Long Nguyen Tien, Hoang Ta Duy, Van Khu Vu","doi":"10.1109/ISIT50566.2022.9834795","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834795","url":null,"abstract":"The de Bruijn based timing and synchronization (dBTS) system has been proposed and studied recently for some channels require reliable synchronization, such as quantum communication. To avoid a long period of no-pulse in the dBTS system, we propose to study the run length limited de Bruijn sequences which not only are run length limited sequences but also can be used to locate the location of any sub-string. Such subjects are expected to have various applications and they also present some interesting theoretical questions in combinatorics, algorithms and coding theory.In this paper, we are the first to provide an explicit formula of the maximal length of the run length limited de Bruijn sequences. Besides that, using Lyndon words, we present an efficient construction of a run length limited de Bruijn sequence with the maximal length. Furthermore, we also provide a sub-linear decoding algorithm which can locate the position of an arbitrary sub-string.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126989963","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 : 2022-06-26DOI: 10.1109/ISIT50566.2022.9834659
Shikha Patel, O. Prakash
This paper establishes the relation between skew polycyclic and skew sequential codes over a finite field. We prove with different induced vectors that right Θ-polycyclic codes are left Θ−1-polycyclic codes. Further, we characterize the condition under which a code is both left and right skew polycyclic with the same induced vectors. Moreover, an analogous study is also discussed for skew sequential codes. Further, to show the novelty of our work, many examples of "MDS (Maximum Distance Separable)" codes are provided. Finally, as an application, we construct quantum codes with good parameters from these codes.
{"title":"Quantum codes construction from skew polycyclic codes","authors":"Shikha Patel, O. Prakash","doi":"10.1109/ISIT50566.2022.9834659","DOIUrl":"https://doi.org/10.1109/ISIT50566.2022.9834659","url":null,"abstract":"This paper establishes the relation between skew polycyclic and skew sequential codes over a finite field. We prove with different induced vectors that right Θ-polycyclic codes are left Θ−1-polycyclic codes. Further, we characterize the condition under which a code is both left and right skew polycyclic with the same induced vectors. Moreover, an analogous study is also discussed for skew sequential codes. Further, to show the novelty of our work, many examples of \"MDS (Maximum Distance Separable)\" codes are provided. Finally, as an application, we construct quantum codes with good parameters from these codes.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121281597","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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