Pub Date : 2005-10-31DOI: 10.1109/ISIT.2005.1523599
W. Szpankowski
One-to-one codes are "one shot" codes that assign a distinct codeword to source symbols and are not necessarily prefix codes (more generally, uniquely decodable). For example, such codes arise when there exists an "end of message" channel symbol. Interestingly, as Wyner proved in 1972, for such codes the average code length can be smaller than the source entropy. By how much? We call this difference the anti-redundancy. Various authors over the years have shown that the anti-redundancy can be as big as minus the logarithm of the source entropy. However, to the best of our knowledge precise estimates do not exist. In this note, we consider a block code of length n generated by a binary memoryless source, and prove that the average anti-redundancy is -(1/2)log2n + C + F(n) + o(1) where C is a constant and either F(n) = O if log2(1 - p)/p is irrational (where p is the probability of generating a "0") or otherwise F(ri) is a fluctuating function as the code length increases. This relatively simple finding requires a combination of quite sophisticated analytic tools such as precise evaluation of Bernoulli sums, the saddle point method, and theory of distribution of sequences modulo 1
{"title":"One-to-one code and its anti-redundancy","authors":"W. Szpankowski","doi":"10.1109/ISIT.2005.1523599","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523599","url":null,"abstract":"One-to-one codes are \"one shot\" codes that assign a distinct codeword to source symbols and are not necessarily prefix codes (more generally, uniquely decodable). For example, such codes arise when there exists an \"end of message\" channel symbol. Interestingly, as Wyner proved in 1972, for such codes the average code length can be smaller than the source entropy. By how much? We call this difference the anti-redundancy. Various authors over the years have shown that the anti-redundancy can be as big as minus the logarithm of the source entropy. However, to the best of our knowledge precise estimates do not exist. In this note, we consider a block code of length n generated by a binary memoryless source, and prove that the average anti-redundancy is -(1/2)log2n + C + F(n) + o(1) where C is a constant and either F(n) = O if log2(1 - p)/p is irrational (where p is the probability of generating a \"0\") or otherwise F(ri) is a fluctuating function as the code length increases. This relatively simple finding requires a combination of quite sophisticated analytic tools such as precise evaluation of Bernoulli sums, the saddle point method, and theory of distribution of sequences modulo 1","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130980474","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523488
A. Gilbert, J. Tropp
Sparse approximation problems abound in many scientific, mathematical, and engineering applications. These problems are defined by two competing notions: we approximate a signal vector as a linear combination of elementary atoms and we require that the approximation be both as accurate and as concise as possible. We introduce two natural and direct applications of these problems and algorithmic solutions in communications. We do so by constructing enhanced codebooks from base codebooks. We show that we can decode these enhanced codebooks in the presence of Gaussian noise. For MIMO wireless communication channels, we construct simultaneous sparse approximation problems and demonstrate that our algorithms can both decode the transmitted signals and estimate the channel parameters
{"title":"Applications of sparse approximation in communications","authors":"A. Gilbert, J. Tropp","doi":"10.1109/ISIT.2005.1523488","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523488","url":null,"abstract":"Sparse approximation problems abound in many scientific, mathematical, and engineering applications. These problems are defined by two competing notions: we approximate a signal vector as a linear combination of elementary atoms and we require that the approximation be both as accurate and as concise as possible. We introduce two natural and direct applications of these problems and algorithmic solutions in communications. We do so by constructing enhanced codebooks from base codebooks. We show that we can decode these enhanced codebooks in the presence of Gaussian noise. For MIMO wireless communication channels, we construct simultaneous sparse approximation problems and demonstrate that our algorithms can both decode the transmitted signals and estimate the channel parameters","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132850650","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523382
Jiwoong Jang, Jong-Seon No, Habong Chung, Xiaohu Tang
In this paper, for integers e and n such that e|n and 2e - 1 is a prime, we propose a method of constructing binary low correlation zone (LCZ) sequences of period 2n - 1 by using the extended form sequence with the same period. These new LCZ sequences use Legendre sequences as their column sequences
{"title":"Binary sequence sets with low correlation zone","authors":"Jiwoong Jang, Jong-Seon No, Habong Chung, Xiaohu Tang","doi":"10.1109/ISIT.2005.1523382","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523382","url":null,"abstract":"In this paper, for integers e and n such that e|n and 2e - 1 is a prime, we propose a method of constructing binary low correlation zone (LCZ) sequences of period 2n - 1 by using the extended form sequence with the same period. These new LCZ sequences use Legendre sequences as their column sequences","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133085991","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523562
J. Soriaga, P. Siegel, J. Wolf, M. Marrow
The achievable information rates for multilevel coding (MLC) systems with multistage decoding (MSD) are examined on two-dimensional binary-input intersymbol interference (ISI) channels. One MSD scheme employs trellis-based detection, while another involves zero-forcing equalization and linear noise prediction. Information rates are determined by examining the output statistics at each stage of MSD. The first scheme is shown to achieve rates very close to known information-theoretic limits. Systems with low-density parity-check codes are then optimized to approach these rates
{"title":"On achievable rates of multistage decoding on two-dimensional ISi channels","authors":"J. Soriaga, P. Siegel, J. Wolf, M. Marrow","doi":"10.1109/ISIT.2005.1523562","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523562","url":null,"abstract":"The achievable information rates for multilevel coding (MLC) systems with multistage decoding (MSD) are examined on two-dimensional binary-input intersymbol interference (ISI) channels. One MSD scheme employs trellis-based detection, while another involves zero-forcing equalization and linear noise prediction. Information rates are determined by examining the output statistics at each stage of MSD. The first scheme is shown to achieve rates very close to known information-theoretic limits. Systems with low-density parity-check codes are then optimized to approach these rates","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127650444","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523507
Hon-Fah Chong, M. Motani, H. K. Garg
This paper studies coding strategies for a three-node relay channel. We first review the basic coding strategies of Cover and El Gamal for the relay channel. Next, two new coding strategies superimposing cooperation and facilitation are developed. One of the coding strategies is shown to include the generalized strategy of Cover and El Gamal. For certain parameters of the Gaussian relay channel, the two new strategies give higher achievable rates than the generalized strategy of Cover and El Gamal
{"title":"New coding strategies for the relay channel","authors":"Hon-Fah Chong, M. Motani, H. K. Garg","doi":"10.1109/ISIT.2005.1523507","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523507","url":null,"abstract":"This paper studies coding strategies for a three-node relay channel. We first review the basic coding strategies of Cover and El Gamal for the relay channel. Next, two new coding strategies superimposing cooperation and facilitation are developed. One of the coding strategies is shown to include the generalized strategy of Cover and El Gamal. For certain parameters of the Gaussian relay channel, the two new strategies give higher achievable rates than the generalized strategy of Cover and El Gamal","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115352259","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523742
G. Lindell
In this paper we investigate some properties of the union bound for a basic MIMO system, assuming uncoded QAM transmission, uncorrelated Rayleigh fading, and maximum likelihood detection. The presented union bound results cover several choices of the number of transmitting and receiving antennas (up to 16). It is also illustrated how the pair-wise error probability approaches the Q( )-function as the number of receiving antennas increases
{"title":"Some exact union bound results for maximum likelihood detection in MIMO systems","authors":"G. Lindell","doi":"10.1109/ISIT.2005.1523742","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523742","url":null,"abstract":"In this paper we investigate some properties of the union bound for a basic MIMO system, assuming uncoded QAM transmission, uncorrelated Rayleigh fading, and maximum likelihood detection. The presented union bound results cover several choices of the number of transmitting and receiving antennas (up to 16). It is also illustrated how the pair-wise error probability approaches the Q( )-function as the number of receiving antennas increases","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124269478","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523503
T. Swart, Ian de Beer, H. C. Ferreira
We investigate the optimal Hamming distance that is achievable when mapping binary sequences to permutation sequences. This is used to determine how close to optimum some of the known mappings are. Furthermore, using simulation results we show that mappings found by exhaustive search using optimum distance as criterion perform better than previous known mappings
{"title":"On the distance optimality of permutation mappings","authors":"T. Swart, Ian de Beer, H. C. Ferreira","doi":"10.1109/ISIT.2005.1523503","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523503","url":null,"abstract":"We investigate the optimal Hamming distance that is achievable when mapping binary sequences to permutation sequences. This is used to determine how close to optimum some of the known mappings are. Furthermore, using simulation results we show that mappings found by exhaustive search using optimum distance as criterion perform better than previous known mappings","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114474077","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523309
R. Mudumbai, J. Hespanha, Upamanyu Madhow, G. Barriac
Recent work has shown that large gains in communication capacity are achievable by distributed beamforming in sensor networks. The principal challenge in realizing these gains in practice, is in synchronizing the carrier signal of individual sensors in such a way that they combine coherently at the intended receiver. In this paper, we provide a scalable mechanism for achieving phase synchronization in completely distributed fashion, based only on feedback regarding the power of the net received signal. Insight into the workings of the protocol is obtained from a simple theoretical model that provides accurate performance estimates
{"title":"Scalable feedback control for distributed beamforming in sensor networks","authors":"R. Mudumbai, J. Hespanha, Upamanyu Madhow, G. Barriac","doi":"10.1109/ISIT.2005.1523309","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523309","url":null,"abstract":"Recent work has shown that large gains in communication capacity are achievable by distributed beamforming in sensor networks. The principal challenge in realizing these gains in practice, is in synchronizing the carrier signal of individual sensors in such a way that they combine coherently at the intended receiver. In this paper, we provide a scalable mechanism for achieving phase synchronization in completely distributed fashion, based only on feedback regarding the power of the net received signal. Insight into the workings of the protocol is obtained from a simple theoretical model that provides accurate performance estimates","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116897286","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523313
J. Massey, P. Massey
Two conservation laws for mutual information in terms of directed informations between two synchronized sequences of random variables are derived, the first for the case of no conditioning and the second for the case of causal conditioning on a third synchronized sequence. As a byproduct of the derivation of the first conservation law, the directed information specifying the feedback flowing from the second sequence to the first sequence is identified, which leads to a simple proof that a previously known sufficient condition for equality of mutual and directed information is also a necessary condition
{"title":"Conservation of mutual and directed information","authors":"J. Massey, P. Massey","doi":"10.1109/ISIT.2005.1523313","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523313","url":null,"abstract":"Two conservation laws for mutual information in terms of directed informations between two synchronized sequences of random variables are derived, the first for the case of no conditioning and the second for the case of causal conditioning on a third synchronized sequence. As a byproduct of the derivation of the first conservation law, the directed information specifying the feedback flowing from the second sequence to the first sequence is identified, which leads to a simple proof that a previously known sufficient condition for equality of mutual and directed information is also a necessary condition","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116916631","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 : 2005-10-31DOI: 10.1109/ISIT.2005.1523397
V. Farias, C. Moallemi, B. Prabhakar
Many practical systems perform load balancing. The main aim of load balancing is to utilize the capacity of a system of parallel processors efficiently and to reduce the delay of processing jobs. This paper is concerned with load balancing, or process migration, when there is a penalty associated with migration. We consider the following model: jobs arrive at each of n parallel servers. An arriving job can either be processed in a unit of time, on average, at the server where it arrives, or it can migrate to another server where it creates K ges 1 independent jobs. When K = 1, migrating jobs impose no extra cost and this problem is considered extensively in the literature. We are interested in the situation K > 1. The problem is to decide whether a job should migrate or not. On the one hand migration leads to load balancing and hence reduces backlogs. However, it also leads to the creation of extra work and, hence, to a potential loss of throughput. We ask: do there exist simple migration policies that can reduce backlogs while providing the highest throughput? Somewhat surprisingly, we find that policies like "migrate to the least loaded server" are unstable: they cause a loss of throughput. However, we find that a simple variant of this rule is stable and leads to a reduction of backlogs
{"title":"Load balancing with migration penalties","authors":"V. Farias, C. Moallemi, B. Prabhakar","doi":"10.1109/ISIT.2005.1523397","DOIUrl":"https://doi.org/10.1109/ISIT.2005.1523397","url":null,"abstract":"Many practical systems perform load balancing. The main aim of load balancing is to utilize the capacity of a system of parallel processors efficiently and to reduce the delay of processing jobs. This paper is concerned with load balancing, or process migration, when there is a penalty associated with migration. We consider the following model: jobs arrive at each of n parallel servers. An arriving job can either be processed in a unit of time, on average, at the server where it arrives, or it can migrate to another server where it creates K ges 1 independent jobs. When K = 1, migrating jobs impose no extra cost and this problem is considered extensively in the literature. We are interested in the situation K > 1. The problem is to decide whether a job should migrate or not. On the one hand migration leads to load balancing and hence reduces backlogs. However, it also leads to the creation of extra work and, hence, to a potential loss of throughput. We ask: do there exist simple migration policies that can reduce backlogs while providing the highest throughput? Somewhat surprisingly, we find that policies like \"migrate to the least loaded server\" are unstable: they cause a loss of throughput. However, we find that a simple variant of this rule is stable and leads to a reduction of backlogs","PeriodicalId":166130,"journal":{"name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117235702","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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