{"title":"Using Rank-Metric Codes for Error Correction in Random Network Coding","authors":"Danilo Silva, F. Kschischang","doi":"10.1109/ISIT.2007.4557322","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557322","url":null,"abstract":"It is shown that the error correction problem in random network coding is closely related to a generalized decoding problem for rank-metric codes. This result enables many of the rich tools devised for the rank metric to be naturally applied to random network coding. The generalized decoding problem introduced in this paper allows partial information about the error to be supplied. This partial information can be either in the form of erasures (knowledge of an error location but not its value) or deviations (knowledge of an error value but not its location). For Gabidulin codes, an efficient decoding algorithm is proposed that can correct e errors, mu erasures and v deviations, provided 2isin + mu + v les d - 1, where d is the minimum distance of the code.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130517339","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":"EXIT Chart Analysis of Binary Message-Passing Decoders","authors":"G. Lechner, T. Pedersen, G. Kramer","doi":"10.1109/ISIT.2007.4557334","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557334","url":null,"abstract":"Binary message-passing decoders for LDPC codes are analyzed using EXIT charts. For the analysis, the variable node decoder performs all computations in the L-value domain. For the special case of a hard decision channel, this leads to the well-know Gallager B algorithm, while the analysis can be extended to channels with larger output alphabets. By increasing the output alphabet from hard decisions to four symbols, a gain of more than 1.0 dB is achieved using optimized codes. For this code optimization, the mixing property of EXIT functions has to be modified to the case of binary message-passing decoders.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130528951","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":"Construction of Linear Network Codes that Achieve a Refined Singleton Bound","authors":"Shenghao Yang, C. Ngai, R. Yeung","doi":"10.1109/ISIT.2007.4557139","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557139","url":null,"abstract":"In this paper, we present a refined version of the Singleton bound for network error correction, and propose an algorithm for constructing network codes that achieve this bound.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127870975","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}
K. Momihara, Meinard Müller, Junya Satoh, Masakazu Jimbo
{"title":"Bounds and Constructions for Optimal Constant Weight Conflict-Avoiding Codes","authors":"K. Momihara, Meinard Müller, Junya Satoh, Masakazu Jimbo","doi":"10.1109/ISIT.2007.4557248","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557248","url":null,"abstract":"A conflict-avoiding code (CAC) C of length n with weight k is a family of binary sequences of length n and weight k satisfying Sigma<sub>0</sub> <sub>les</sub> <sub>t</sub> <sub>les</sub> <sub>n-1</sub> x<sub>it</sub> x<sub>j</sub>, <sub>t+s</sub> les lambda for any distinct codewords x<sub>j</sub> = (x<sub>i0</sub>,x<sub>i1</sub>,hellip,x<sub>i,</sub> <sub>n-1</sub>) and x<sub>j</sub> = (x<sub>j0</sub>, x<sub>j1</sub>,hellip, x<sub>j,</sub> <sub>n-1</sub>) in C and for any integer s, where the subscripts are taken modulo n. A CAC with maximal code size for given n and k is said to be optimal. A CAC has been studied for sending messages correctly through a multiple-access channel. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, the case lambda = 1 is treated, and various direct and recursive constructions of optimal CACs for weight k = 4 and 5 are obtained by providing constructions of CACs for general weight k. In particular, the maximum code size of CACs satisfying certain sufficient conditions is determined through number theoretical and combinatorial approaches.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129224128","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":"Code Decomposition: Theory and Applications","authors":"N. Kashyap","doi":"10.1109/ISIT.2007.4557271","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557271","url":null,"abstract":"In this paper, we give an overview of Seymour's matroid decomposition theory in the context of binary linear codes, and discuss some of its implications for linear programming (LP) decoding of a binary linear code. As shown by Feldman et al. maximum-likelihood (ML) decoding over a discrete memoryless channel can be formulated as an LP problem. Using this formulation, we translate matroid-theoretic results of Grotschel and Truemper from the combinatorial optimization literature as examples of non-trivial families of codes for which ML decoding can be implemented in time polynomial in the length of the code. However, we also show that such families of codes are not good in a coding-theoretic sense - either their dimension or their minimum distance must grow sub-linearly with codelength.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125363776","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":"ID-based Ring Proxy Signatures","authors":"Baodian Wei, Fangguo Zhang, Xiaofeng Chen","doi":"10.1109/ISIT.2007.4557359","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557359","url":null,"abstract":"In this paper, by combining the functionalities of proxy signatures and ring signatures, we propose a new concept, named ring proxy signature, which is a proxy signature generated by an anonymous member from a set of potential signers. We construct two ID-based ring proxy signature schemes. The security analysis is provided as well.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126836781","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":"Channel coding with strictly casual colored side-information at transmitter","authors":"V. Prabhakaran, David Tse, K. Ramchandran","doi":"10.1109/ISIT.2007.4557254","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557254","url":null,"abstract":"In this paper we study channels where a side-information sequence is available strictly causally at the transmitter, i.e., the channel input at time k may depend on the side-information sequence up to and including time k - 1. This is in contrast to Shannon's channel coding with causal side-information at the transmitter where the channel input at time k may depend on the side-information sequence up to and including time k. We consider side-information sequences with memory and study the Gaussian and modulo-additive channels.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121303100","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":"Network Coding in Wireless Networks with Random Access","authors":"D. Traskov, D. Lun, R. Koetter, M. Médard","doi":"10.1109/ISIT.2007.4557185","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557185","url":null,"abstract":"We consider the problem of applying network coding in wireless networks with random medium access. To optimize the network coding subgraph and the transmission attempt probabilities jointly is a tractable problem only for rather small networks. Therefore, we suggest a suboptimal, yet practical and decentralized algorithm to combine network coding with random access. We illustrate the performance gains of our approach with simulations.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126268553","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}
Sarah H. Sellke, Chih-Chun Wang, N. Shroff, S. Bagchi
{"title":"Capacity Bounds on Timing Channels with Bounded Service Times","authors":"Sarah H. Sellke, Chih-Chun Wang, N. Shroff, S. Bagchi","doi":"10.1109/ISIT.2007.4557351","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557351","url":null,"abstract":"It is well known that queues with exponentially distributed service times have the smallest Shannon capacity among all single-server queues with the same service rate. In this paper, we study the capacity of timing channels in which the service time distributions have bounded support, i.e., Bounded Service Timing Channels (BSTC). We derive an upper bound and two lower bounds on the capacity of such timing channels. The tightness of these bounds is investigated analytically as well as via simulations. We find that the uniform BSTC serves a role for BSTCs that is similar to what the exponential service timing channel does for the case of timing channels with unbounded service time distributions. That is, when the length of the support interval is small, the uniform BSTC has the smallest capacity among all BSTCs.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"86 22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126290681","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":"Resilient network codes in the presence of eavesdropping Byzantine adversaries","authors":"S. Jaggi, M. Langberg","doi":"10.1109/ISIT.2007.4557281","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557281","url":null,"abstract":"Network coding can substantially improve network throughput and performance. However, these codes have a major drawback if the network contains hidden malicious nodes that can eavesdrop on transmissions and inject fake information. In this scenario, even a small amount of information injected by a single malicious hidden node could mix with and contaminate much of the information inside the network, causing a decoding error. We improve on previous work by providing a polynomial- time, rate-optimal distributed network code design that functions even in the presence of a Byzantine adversary with substantial eavesdropping capabilities. As long as the sum of the adversary's jamming rate Zo and his eavesdropping rate ZI is less than the network capacity C, (Zo + ZI < C), our codes attain the optimal rate of C - Zo. The network codes we design are information-theoretically secure and assume no knowledge of network topology. Prior to transmission, no honest node knows the location or strength of the adversary. In our code design, interior nodes are oblivious to the presence of adversaries and implement a classical low- complexity distributed network code design; only the source and destination need to be changed. Finally, our codes work for both wired and wireless networks.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126799046","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}