{"title":"A renormalization group decoding algorithm for topological quantum codes","authors":"G. Duclos-Cianci, D. Poulin","doi":"10.1109/CIG.2010.5592866","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592866","url":null,"abstract":"Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we present a decoding algorithm for topological codes that is faster than previously known algorithms and applies to a wider class of topo-logical codes. Our algorithm makes use of two methods inspired from statistical physics: renormalization groups and mean-field approximations. First, the topological code is approximated by a concatenated block code that can be efficiently decoded. To improve this approximation, additional consistency conditions are imposed between the blocks, and are solved by a belief propagation algorithm.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131824236","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":"Polar coding for reliable communications over parallel channels","authors":"E. Hof, I. Sason, S. Shamai","doi":"10.1109/CIG.2010.5592728","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592728","url":null,"abstract":"A capacity-achieving polar coding scheme is introduced for reliable communications over a set of parallel communication channels. They are assumed to be arbitrarily-permuted memoryless binary-input and output-symmetric (MBIOS) channels, and they form a set of (stochastically) degraded channels. The general case where the parallel channels are not necessarily degraded is addressed in the full paper version [3], though the suggested scheme is not capacity-achieving in the general case.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"232 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128620890","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":"Approximate capacity of a class of multi-source Gaussian relay networks","authors":"Sang-Woon Jeon, Sae-Young Chung, S. Jafar","doi":"10.1109/CIG.2010.5592674","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592674","url":null,"abstract":"We study K-user M-hop Gaussian relay networks with K<inf>m</inf> nodes in the m-th layer, where M is even and K = K<inf>1</inf> = K<inf>M+1</inf>. We observe that the time-varying nature of wireless channels (fading) can be exploited to mitigate the inter-user interference. The proposed block Markov encoding and relaying scheme exploits such channel variations and works for any isotropically distributed channels including Rayleigh fading. We show a general achievable degrees of freedom (DoF) region of this class of Gaussian relay networks, which coincides with the cut-set outer bound if M/K<inf>min</inf> is an integer, where K<inf>min</inf> = min<inf>m</inf> {K<inf>m</inf>}. Therefore, we completely characterize the DoF region for the case where M/K<inf>min</inf> is an integer.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125882205","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}
A. Suresh, A. Subramanian, A. Thangaraj, M. Bloch, S. McLaughlin
{"title":"Strong secrecy for erasure wiretap channels","authors":"A. Suresh, A. Subramanian, A. Thangaraj, M. Bloch, S. McLaughlin","doi":"10.1109/CIG.2010.5592770","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592770","url":null,"abstract":"We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length n and girth ⋛ for some ⋛. We show that if the minimum left degree of the ensemble is l<inf>min</inf>, the expected probability of block error is O(1/n⌈<sup>l</sup> min<sup>k/2</sup>⌉ −k) when the erasure probability ∊ < ∊<inf>ef</inf>, where ∊<inf>ef</inf> depends on the degree distribution of the ensemble. As long as l<inf>min</inf> and k > 2, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than 1–∊<inf>ef</inf>.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115966378","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":"Outer bounds for the interference channel with a cognitive relay","authors":"S. Rini, Daniela Tuninetti, N. Devroye","doi":"10.1109/CIG.2010.5592758","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592758","url":null,"abstract":"In this paper, we first present an outer bound for a general interference channel with a cognitive relay, i.e., a relay that has non-causal knowledge of both independent messages transmitted in the interference channel. This outer bound reduces to the capacity region of the deterministic broadcast channel and of the deterministic cognitive interference channel the through nulling of certain channel inputs. It does not, however, reduce to that of certain deterministic interference channels for which capacity is known. As such, we subsequently tighten the bound for channels whose outputs satisfy an “invertibility” condition. This second outer bound now reduces to the capacity of the special class of deterministic interference channels for which capacity is known. The second outer bound is further tightened for the high-SNR deterministic approximation of the Gaussian channel by exploiting the special structure of the interference. We provide an example that suggests that this third bound is tight in at least some parameter regimes for the high-SNR deterministic approximation of the Gaussian channel. Another example shows that the third bound is capacity in the special case where there are no direct links between the non-cognitive transmitters.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127160781","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":"Universal a posteriori metrics game","authors":"E. Abbe, R. Pulikkoonattu","doi":"10.1109/CIG.2010.5592854","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592854","url":null,"abstract":"Over binary input channels, the uniform distribution is a universal prior, in the sense that it maximizes the worst case mutual information of all binary input channels and achieves at least 94.2% of the capacity. In this paper, we address a similar question. We look for the best collection of finitely many a posteriori metrics, to maximize the worst case mismatched mutual information achieved by decoding with these metrics (instead of an optimal decoder such as the Maximum Likelihood (ML) tuned to the true channel). It is shown that for binary input and output channels, two metrics suffice to actually achieve the same performance as an optimal decoder. In particular, this implies that there exist a decoder which is generalized linear and achieves at least 94.2% of the compound capacity on any compound set, without knowledge of the underlying set.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131065801","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-systematic codes for physical layer security","authors":"M. Baldi, Marco Bianchi, F. Chiaraluce","doi":"10.1109/CIG.2010.5592833","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592833","url":null,"abstract":"This paper is a first study on the usage of non-systematic codes based on scrambling matrices for physical layer security. The chance of implementing transmission security at the physical layer is known since many years, but it is now gaining an increasing interest due to its several possible applications. It has been shown that channel coding techniques can be effectively exploited for designing physical layer security schemes, in such a way that an unauthorized receiver, experiencing a channel different from that of the authorized receiver, is not able to gather any information. Recently, it has been proposed to exploit puncturing techniques in order to reduce the security gap between the authorized and unauthorized channels. In this paper, we show that the security gap can be further reduced by using non-systematic codes, able to scramble information bits within the transmitted codeword.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129982097","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":"Valiant transform of forney graphs","authors":"A. Al-Bashabsheh, Yongyi Mao","doi":"10.1109/CIG.2010.5592848","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592848","url":null,"abstract":"In his recent work, Valiant presented a powerful family of new algorithms, which he calls holographic algorithms. The mathematical foundation of holographic algorithms is what is known as Holant Theorem. Synthesizing from Valiant's work, in this paper, we introduce the notion of Valiant transform for normal graphs. Exploiting this synthesis, we establish a more general version of Holant Theorem, which allows an alternative interpretation of the duality results on normal graphs.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"446 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124276826","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":"An extension of Massey scheme for secret sharing","authors":"R. D. Cruz, P. Solé","doi":"10.1109/CIG.2010.5592719","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592719","url":null,"abstract":"We consider an extension of Massey's construction of secret sharing schemes using linear codes. We describe the access structure of the scheme and show its connection to the dual code. We use the g-fold joint weight enumerator and invariant theory to study the access structure.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126830076","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":"Lossy source compression of non-uniform binary sources using GQ-LDGM codes","authors":"L. Cappellari","doi":"10.1109/CIG.2010.5592821","DOIUrl":"https://doi.org/10.1109/CIG.2010.5592821","url":null,"abstract":"In this paper, we study the use of GF(q)-quantized LDGM codes for binary source coding. By employing quantization, it is possible to obtain binary codewords with a non-uniform distribution. The obtained statistics is hence suitable for optimal, direct quantization of non-uniform Bernoulli sources. We employ a message-passing algorithm combined with a decimation procedure in order to perform compression. The experimental results based on GF(q)-LDGM codes with regular degree distributions yield performances quite close to the theoretical rate-distortion bounds.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130653053","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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