M. Borges-Quintana, M. Borges-Trenard, Irene Marquez Corbella, E. Martínez-Moro
{"title":"An algebraic view to gradient descent decoding","authors":"M. Borges-Quintana, M. Borges-Trenard, Irene Marquez Corbella, E. Martínez-Moro","doi":"10.1109/CIG.2010.5592830","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592830","url":null,"abstract":"There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper [15] mentions that both algorithms have the same philosophy but in fact they are rather different. The purpose of this communication is to show that both algorithms can be seen as two ways of understanding the reduction process algebraic monoid structure related to the code. The main tool used for showing this is the Gröbner representation of the monoid associated to the linear code.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128105317","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}
{"title":"Bit-interleaved coded modulation with shaping","authors":"A. G. Fàbregas, Alfonso Martinez","doi":"10.1109/CIG.2010.5592692","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592692","url":null,"abstract":"The performance of bit-interleaved coded modulation (BICM) with shaping (i.e., non-equiprobable bit probabilities) is studied. For the AWGN channel, the rates achievable with BICM and shaping are practically identical to those of coded modulation or multilevel coding, virtually closing the gap that made BICM suboptimal in terms of information rates.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127205394","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}
{"title":"Properties of optimal prefix-free machines as instantaneous codes","authors":"K. Tadaki","doi":"10.1109/CIG.2010.5592776","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592776","url":null,"abstract":"The optimal prefix-free machine U is a universal decoding algorithm used to define the notion of program-size complexity H(s) for a finite binary string s. Since the set of all halting inputs for U is chosen to form a prefix-free set, the optimal prefix-free machine can be regarded as an instantaneous code for noiseless source coding scheme. In this paper, we investigate the properties of optimal prefix-free machines as instantaneous codes. In particular, we investigate the properties of the set U−1(s) of codewords associated with a symbol s. Namely, we investigate the number of codewords in U−1(s) and the distribution of codewords in U−1(s) for each symbol s, using the toolkit of algorithmic information theory.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131187149","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}
{"title":"Characterization of graph-cover pseudocodewords of codes over F3","authors":"Vitaly Skachek","doi":"10.1109/CIG.2010.5592884","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592884","url":null,"abstract":"Linear-programming pseudocodewords play a pivotal role in our understanding of the linear-programming decoding algorithms. These pseudocodewords are known to be equivalent to the graph-cover pseudocodewords. The latter pseudocodewords, when viewed as points in the multidimensional Euclidean space, lie inside a fundamental cone. This fundamental cone depends on the choice of a parity-check matrix of a code, rather than on the choice of the code itself. The cone does not depend on the channel, over which the code is employed. The knowledge of the boundaries of the fundamental cone could help in studying various properties of the pseudocodewords, such as their minimum pseudoweight, pseudoredundancy of the codes, etc. For the binary codes, the full characterization of the fundamental cone was derived by Koetter et al. However, if the underlying alphabet is large, such characterization becomes more involved. In this work, a characterization of the fundamental cone for codes over F3 is discussed.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129056608","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}
{"title":"Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes","authors":"R. Mori, Toshiyuki TANAKA","doi":"10.1109/CIG.2010.5592755","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592755","url":null,"abstract":"Polar codes, introduced by Arıkan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error probability of non-binary polar codes constructed on the basis of Reed-Solomon matrices by numerical simulations. It is confirmed that 4-ary polar codes have significantly better performance than binary polar codes on binary-input AWGN channel. We also discuss an interpretation of polar codes in terms of algebraic geometry codes, and further show that polar codes using Hermitian codes have asymptotically good performance.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"421 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131985746","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}
{"title":"Quantum channel capacities","authors":"Graeme Smith","doi":"10.1109/CIG.2010.5592851","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592851","url":null,"abstract":"A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each of these settings there is a capacity that quantifies a channel's potential for communication. In this short review, I summarize what is known about the various capacities of a quantum channel, including a discussion of the relevant additivity questions. I also give some indication of potentially interesting directions for future research.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128829919","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}
{"title":"A multi-hop multi-source Algebraic Watchdog","authors":"Minji Kim, M. Médard, J. Barros","doi":"10.1109/CIG.2010.5592893","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592893","url":null,"abstract":"In our previous work (‘An Algebraic Watchdog for Wireless Network Coding’), we proposed a new scheme in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages; thus, provide a secure global self-checking network. As the first building block of such a system, we focused on a two-hop network, and presented a graphical model to understand the inference process by which nodes police their downstream neighbors and to compute the probabilities of misdetection and false detection. In this paper, we extend the Algebraic Watchdog to a more general network setting, and propose a protocol in which we can establish trust in coded systems in a distributed manner. We develop a graphical model to detect the presence of an adversarial node downstream within a general two-hop network. The structure of the graphical model (a trellis) lends itself to well-known algorithms, such as Viterbi algorithm, that can compute the probabilities of misdetection and false detection. Using this as a building block, we generalize our scheme to multi-hop networks. We show analytically that as long as the min-cut is not dominated by the Byzantine adversaries, upstream nodes can monitor downstream neighbors and allow reliable communication with certain probability. Finally, we present preliminary simulation results that support our analysis.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127506582","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}
{"title":"Unimodular lattices for the Gaussian Wiretap Channel","authors":"J. Belfiore, P. Solé","doi":"10.1109/CIG.2010.5592923","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592923","url":null,"abstract":"In [1] the authors introduced a lattice invariant called “Secrecy Gain” which measures the confusion experienced by a passive eavesdropper on the Gaussian Wiretap Channel. We study, here, the behavior of this invariant for unimodular lattices by using tools from Modular Forms and show that, for some families of unimodular lattices, indexed by the dimension, the secrecy gain exponentially goes to infinity with the dimension.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131307370","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}
David G. M. Mitchell, R. Smarandache, M. Lentmaier, D. Costello
{"title":"Quasi-cyclic asymptotically regular LDPC codes","authors":"David G. M. Mitchell, R. Smarandache, M. Lentmaier, D. Costello","doi":"10.1109/CIG.2010.5592641","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592641","url":null,"abstract":"Families of asymptotically regular LDPC block code ensembles can be formed by terminating (J, K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles with varying code rates, minimum distance that grows linearly with block length, and capacity approaching iterative decoding thresholds, despite the fact that the terminated ensembles are almost regular. In this paper, we investigate the properties of the quasi-cyclic (QC) members of such an ensemble. We show that an upper bound on the minimum Hamming distance of members of the QC sub-ensemble can be improved by careful choice of the component protographs used in the code construction. Further, we show that the upper bound on the minimum distance can be improved by using arrays of circulants in a graph cover of the protograph.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131236774","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}
{"title":"The Euclidean algorithm for Generalized Minimum Distance decoding of Reed-Solomon codes","authors":"Sabine Kampf, M. Bossert","doi":"10.1109/CIG.2010.5592677","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592677","url":null,"abstract":"This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps performed in Generalized Minimum Distance decoding are similar to those of the extended Euclidean algorithm. The resulting algorithm has a complexity of O(n2).","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115737217","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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