Pub Date : 2004-10-20DOI: 10.1109/ISIT.2004.1365313
Vidya Kumar, O. Milenkovic, B. Vasic
It is well known that random-like low-density parity-check (LDPC) codes over the extension fields GF(2/sup m/) of GF(2), for m>1, tend to outperform their binary counterparts of comparable length and rate. At the same time, structured LDPC codes offer the advantage of reduced implementation and storage complexity, so that it is of interest to investigate mathematical design methods for codes on graphs over fields of large order. We propose a new class of combinatorially developed codes obtained by properly combining Reed-Solomon (RS) type parity-check matrices and sparse parity-check matrices based on permutation matrices. The proposed codes have large girth and minimum distance. In order to further reduce the decoding complexity of the proposed scheme, we introduce a new decoding algorithm based on matrix representations of the underlying field, which trades performance for complexity. The particular field representation described in this abstract is based on a power basis generated by a companion matrix of a primitive polynomial of the field GF(2/sup m/). It is observed that the choice of the primitive polynomial influences the cycle distribution of the code graph.
{"title":"Structured LDPC codes over GF(2/sup m/) and companion matrix based decoding","authors":"Vidya Kumar, O. Milenkovic, B. Vasic","doi":"10.1109/ISIT.2004.1365313","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365313","url":null,"abstract":"It is well known that random-like low-density parity-check (LDPC) codes over the extension fields GF(2/sup m/) of GF(2), for m>1, tend to outperform their binary counterparts of comparable length and rate. At the same time, structured LDPC codes offer the advantage of reduced implementation and storage complexity, so that it is of interest to investigate mathematical design methods for codes on graphs over fields of large order. We propose a new class of combinatorially developed codes obtained by properly combining Reed-Solomon (RS) type parity-check matrices and sparse parity-check matrices based on permutation matrices. The proposed codes have large girth and minimum distance. In order to further reduce the decoding complexity of the proposed scheme, we introduce a new decoding algorithm based on matrix representations of the underlying field, which trades performance for complexity. The particular field representation described in this abstract is based on a power basis generated by a companion matrix of a primitive polynomial of the field GF(2/sup m/). It is observed that the choice of the primitive polynomial influences the cycle distribution of the code graph.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134007650","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365386
Dongning Guo, S. Shamai, S. Verdú
Consider arbitrarily distributed input signals observed in additive Gaussian noise. A new fundamental relationship is found between the input-output mutual information and the minimum mean-square error (MMSE) of an estimate of the input given the output: The derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE. This identity holds for both scalar and vector signals, as well as for discrete- and continuous-time noncausal MMSE estimation (smoothing). A consequence of the result is a new relationship in continuous-time nonlinear filtering: Regardless of the input statistics, the causal MMSE achieved at snr is equal to the expected value of the noncausal MMSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and snr
{"title":"Mutual information and MMSE in gaussian channels","authors":"Dongning Guo, S. Shamai, S. Verdú","doi":"10.1109/ISIT.2004.1365386","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365386","url":null,"abstract":"Consider arbitrarily distributed input signals observed in additive Gaussian noise. A new fundamental relationship is found between the input-output mutual information and the minimum mean-square error (MMSE) of an estimate of the input given the output: The derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE. This identity holds for both scalar and vector signals, as well as for discrete- and continuous-time noncausal MMSE estimation (smoothing). A consequence of the result is a new relationship in continuous-time nonlinear filtering: Regardless of the input statistics, the causal MMSE achieved at snr is equal to the expected value of the noncausal MMSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and snr","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121662173","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365440
Yingbin Liang, V. Veeravalli
The capacity of two broadcast systems with relay links is studied in this paper. Both of these systems are extensions of two users degraded broadcast channels, which achieves a rate region of channels and includes the capacity region of original broadcast channel. We then consider another system, the dumb relay broadcast channel, where an additional relay node is introduced into the two users degraded broadcast channel that assists both user. This relay node does not have its own information from the source, and hence is referred to as dumb relay node. From the results an achievable rate region for this channel is derived and is shown to include that for the cooperative broadcast channel.
{"title":"The impact of relaying on the capacity of broadcast channels","authors":"Yingbin Liang, V. Veeravalli","doi":"10.1109/ISIT.2004.1365440","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365440","url":null,"abstract":"The capacity of two broadcast systems with relay links is studied in this paper. Both of these systems are extensions of two users degraded broadcast channels, which achieves a rate region of channels and includes the capacity region of original broadcast channel. We then consider another system, the dumb relay broadcast channel, where an additional relay node is introduced into the two users degraded broadcast channel that assists both user. This relay node does not have its own information from the source, and hence is referred to as dumb relay node. From the results an achievable rate region for this channel is derived and is shown to include that for the cooperative broadcast channel.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122021355","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365061
A. Orlitsky, N. Santhanam, Junan Zhang
Standard redundancy measures the excess number of bits needed to compress sequences of a given length. Instead, we consider relative redundancy that measures the excess number of bits for sequences of a given minimum description length. Low relative redundancy implies that number of bits needed to compress any sequence is essentially the lowest possible. We show that low relative redundancy implies low standard redundancy, that while block relative redundancy resembles block standard redundancy, sequential relative redundancy is twice its counterpart, and that common algorithms achieving standard redundancy have unbounded relative redundancy.
{"title":"Relative redundancy: a more stringent performance guarantee for universal compression","authors":"A. Orlitsky, N. Santhanam, Junan Zhang","doi":"10.1109/ISIT.2004.1365061","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365061","url":null,"abstract":"Standard redundancy measures the excess number of bits needed to compress sequences of a given length. Instead, we consider relative redundancy that measures the excess number of bits for sequences of a given minimum description length. Low relative redundancy implies that number of bits needed to compress any sequence is essentially the lowest possible. We show that low relative redundancy implies low standard redundancy, that while block relative redundancy resembles block standard redundancy, sequential relative redundancy is twice its counterpart, and that common algorithms achieving standard redundancy have unbounded relative redundancy.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130370588","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365227
S. Aviran, P. Siegel, J. Wolf
The bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence. This approach was previously introduced and applied to (d, k) constrained codes. Results show that the maximum average rate of the bit stuffing code achieves capacity when k=d+1 or k=/spl infin/, while it is suboptimal for all other (d, k) pairs. We propose a modification to the bit stuffing algorithm. We show analytically that the proposed algorithm achieves improved average rates over bit stuffing for most (d, k) constraints.
{"title":"An improvement to the bit stuffing algorithm","authors":"S. Aviran, P. Siegel, J. Wolf","doi":"10.1109/ISIT.2004.1365227","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365227","url":null,"abstract":"The bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence. This approach was previously introduced and applied to (d, k) constrained codes. Results show that the maximum average rate of the bit stuffing code achieves capacity when k=d+1 or k=/spl infin/, while it is suboptimal for all other (d, k) pairs. We propose a modification to the bit stuffing algorithm. We show analytically that the proposed algorithm achieves improved average rates over bit stuffing for most (d, k) constraints.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129931926","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365205
A. Banerjee, Xin Guo, Hui Wang
This paper provides necessary and sufficient conditions for general loss functions under which the conditional expectation is the unique optimal predictor of a random variable. Further, using such loss functions, we give an exact characterization of the difference between the two sides of Jensen's inequality.
{"title":"Optimal Bregman prediction and Jensen's equality","authors":"A. Banerjee, Xin Guo, Hui Wang","doi":"10.1109/ISIT.2004.1365205","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365205","url":null,"abstract":"This paper provides necessary and sufficient conditions for general loss functions under which the conditional expectation is the unique optimal predictor of a random variable. Further, using such loss functions, we give an exact characterization of the difference between the two sides of Jensen's inequality.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113947988","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365108
Jialing Liu, N. Elia, S. Tatikonda
This paper proposes a capacity-achieving feedback communication scheme for finite-state Markov channels (FSMC) with channel state information (CSI). This scheme considerably reduces coding complexity, shortens coding delay, and has a doubly exponential reliability function.
{"title":"Capacity-achieving feedback scheme for Markov channels with channel state information","authors":"Jialing Liu, N. Elia, S. Tatikonda","doi":"10.1109/ISIT.2004.1365108","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365108","url":null,"abstract":"This paper proposes a capacity-achieving feedback communication scheme for finite-state Markov channels (FSMC) with channel state information (CSI). This scheme considerably reduces coding complexity, shortens coding delay, and has a doubly exponential reliability function.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121948163","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365545
Jianghong Luo, Ruoheng Liu, P. Spasojevic
This paper studies the performance of variable-rate turbo bit-interleaved coded modulation (Turbo-BICM) with random puncturing. A union-Bhattacharyya rate threshold for the variable-rate Turbo-BICM is derived. A closed form approximation of this rate threshold is determined for an AWGN channel and shown to predict the Turbo-BICM iterative decoding performance very well.
{"title":"Variable-rate turbo bit-interleaved coded modulation","authors":"Jianghong Luo, Ruoheng Liu, P. Spasojevic","doi":"10.1109/ISIT.2004.1365545","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365545","url":null,"abstract":"This paper studies the performance of variable-rate turbo bit-interleaved coded modulation (Turbo-BICM) with random puncturing. A union-Bhattacharyya rate threshold for the variable-rate Turbo-BICM is derived. A closed form approximation of this rate threshold is determined for an AWGN channel and shown to predict the Turbo-BICM iterative decoding performance very well.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123247255","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365438
Yingwei Yao, Xiaodong Cai, G. Giannakis
Relay links are expected to play a critical role in the design of wireless networks. In this paper, we investigate the energy efficiency of relay communications under two different scenarios: when the relay has unlimited and when it has limited power supply. Relative merits of these relay schemes in comparison with direct transmissions are discussed.
{"title":"On energy efficiency of relay transmissions","authors":"Yingwei Yao, Xiaodong Cai, G. Giannakis","doi":"10.1109/ISIT.2004.1365438","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365438","url":null,"abstract":"Relay links are expected to play a critical role in the design of wireless networks. In this paper, we investigate the energy efficiency of relay communications under two different scenarios: when the relay has unlimited and when it has limited power supply. Relative merits of these relay schemes in comparison with direct transmissions are discussed.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123765444","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 : 2004-10-20DOI: 10.1109/ISIT.2004.1365134
S. Tavildar, P. Viswanath
This paper considers reliable communication over a parallel (correlated) fading channel for short periods of time. We derive a code design criterion by taking a compound channel viewpoint of the outage capacity of the channel. Motivated by the criterion, we show existence of simple codes that achieve the optimal diversity-multiplexing tradeoff curve, introduced recently in (Zheng, L et al., 2003), simultaneously for every correlated parallel channel. We demonstrate a code with simple encoding and decoding for a parallel channel with two diversity branches. The codes for the parallel channel can be used on a correlated MIMO channel by using the DBLAST architecture to simultaneously achieve the diversity-multiplexing tradeoff curve for arbitrary fading channels.
{"title":"Permutation codes: achieving the diversity-multiplexing tradeoff","authors":"S. Tavildar, P. Viswanath","doi":"10.1109/ISIT.2004.1365134","DOIUrl":"https://doi.org/10.1109/ISIT.2004.1365134","url":null,"abstract":"This paper considers reliable communication over a parallel (correlated) fading channel for short periods of time. We derive a code design criterion by taking a compound channel viewpoint of the outage capacity of the channel. Motivated by the criterion, we show existence of simple codes that achieve the optimal diversity-multiplexing tradeoff curve, introduced recently in (Zheng, L et al., 2003), simultaneously for every correlated parallel channel. We demonstrate a code with simple encoding and decoding for a parallel channel with two diversity branches. The codes for the parallel channel can be used on a correlated MIMO channel by using the DBLAST architecture to simultaneously achieve the diversity-multiplexing tradeoff curve for arbitrary fading channels.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114617090","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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