Summary form only given: Recently Terence Tao approached Szemeredi's regularity lemma from the perspectives of probability theory and of information theory instead of graph theory and found a stronger variant of this lemma, which involves a new parameter. To pass from an entropy formulation to an expectation formulation he found the following lemma. Let Y, and X, X' be discrete random variables taking values in y and x, respectively, where y sub [-1, 1], and with X' = f(X) for a (deterministic) function f. Then we have E(|E(Y|X') - E(Y|X)|) les 2I(X nland Y|X')1/2. We show that the constant 2 can be improved to (2ln2)1/2 and that this is the best possible constant
{"title":"The final form of Tao's inequality relating conditional expectation and conditional mutual information","authors":"R. Ahlswede","doi":"10.3934/amc.2007.1.239","DOIUrl":"https://doi.org/10.3934/amc.2007.1.239","url":null,"abstract":"Summary form only given: Recently Terence Tao approached Szemeredi's regularity lemma from the perspectives of probability theory and of information theory instead of graph theory and found a stronger variant of this lemma, which involves a new parameter. To pass from an entropy formulation to an expectation formulation he found the following lemma. Let Y, and X, X' be discrete random variables taking values in y and x, respectively, where y sub [-1, 1], and with X' = f(X) for a (deterministic) function f. Then we have E(|E(Y|X') - E(Y|X)|) les 2I(X nland Y|X')1/2. We show that the constant 2 can be improved to (2ln2)1/2 and that this is the best possible constant","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115730914","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261555
O. Moreno, Reza Omrani, S. Maric
There are only a few multiple target families of Costas and sonar arrays with perfect correlation property. In this paper using the Welch Costas array and some results from design theory we construct perfect auto and cross-correlation families of sonar and extended Costas arrays
{"title":"Doubly Periodic Arrays and a New Construction of Multiple Target Sonar and Extended Costas Arrays with Perfect Correlation","authors":"O. Moreno, Reza Omrani, S. Maric","doi":"10.1109/ISIT.2006.261555","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261555","url":null,"abstract":"There are only a few multiple target families of Costas and sonar arrays with perfect correlation property. In this paper using the Welch Costas array and some results from design theory we construct perfect auto and cross-correlation families of sonar and extended Costas arrays","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123979634","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261754
O. Lévêque, Ritesh Madan, D. Shah
Starting with the seminal work of Gupta and Kumar (2000), there have been many interesting results that give information theoretic outer and inner approximations to the rate region for wireless networks. While these bounds are almost tight for geometric random networks, not much is known about their tightness for arbitrary wireless networks. In contrast, Leighton and Rao (1988) established a powerful result that uniform multi-commodity flow (UMCF) is within a factor of log n of the natural min-cut capacity for any graph (equivalent to a wireline network) of n nodes. Our motivation is to obtain a similar simple and general characterization for UMCF (shown to be equivalent to the characterization for a much wider class of traffic models) for any wireless network. In this paper, we apply and extend known results to obtain such characterization for networks with Gaussian fading channels. For channel state information (CSI) only at the receivers, we establish that UMCF is within a Delta2 log n factor of the information theoretic min-cut capacity of a wireless network, where Delta is the max-degree of a sub-graph induced by the underlying wireless network. For deterministic AWGN channels, we show that UMCF is within square root of the min-cut bound for any network
{"title":"Uniform Multi-commodity Flow in Wireless Networks with Gaussian Fading Channels","authors":"O. Lévêque, Ritesh Madan, D. Shah","doi":"10.1109/ISIT.2006.261754","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261754","url":null,"abstract":"Starting with the seminal work of Gupta and Kumar (2000), there have been many interesting results that give information theoretic outer and inner approximations to the rate region for wireless networks. While these bounds are almost tight for geometric random networks, not much is known about their tightness for arbitrary wireless networks. In contrast, Leighton and Rao (1988) established a powerful result that uniform multi-commodity flow (UMCF) is within a factor of log n of the natural min-cut capacity for any graph (equivalent to a wireline network) of n nodes. Our motivation is to obtain a similar simple and general characterization for UMCF (shown to be equivalent to the characterization for a much wider class of traffic models) for any wireless network. In this paper, we apply and extend known results to obtain such characterization for networks with Gaussian fading channels. For channel state information (CSI) only at the receivers, we establish that UMCF is within a Delta2 log n factor of the information theoretic min-cut capacity of a wireless network, where Delta is the max-degree of a sub-graph induced by the underlying wireless network. For deterministic AWGN channels, we show that UMCF is within square root of the min-cut bound for any network","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114416094","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 : 2006-07-09DOI: 10.1109/ISIT.2006.262018
Kai Xie, Jing Li
Iterative analysis for low-density parity-check (LDPC) codes uses the prevailing assumption that messages exchanged between the variable nodes and the check nodes follow a Gaussian distribution. However, the justification is largely pragmatic rather than being based on any rigorous theory. This paper provides a theoretic support by investigating when and how well the Gaussian distribution approximates the real message density and the far subtler why. The analytical results are verified by extensive simulations
{"title":"On Accuracy of Gaussian Assumption in Iterative Analysis for LDPC Codes","authors":"Kai Xie, Jing Li","doi":"10.1109/ISIT.2006.262018","DOIUrl":"https://doi.org/10.1109/ISIT.2006.262018","url":null,"abstract":"Iterative analysis for low-density parity-check (LDPC) codes uses the prevailing assumption that messages exchanged between the variable nodes and the check nodes follow a Gaussian distribution. However, the justification is largely pragmatic rather than being based on any rigorous theory. This paper provides a theoretic support by investigating when and how well the Gaussian distribution approximates the real message density and the far subtler why. The analytical results are verified by extensive simulations","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114489140","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261911
L. Dolecek, V. Anantharam
We describe a method for enhancing the synchronization error correction properties of an array-based low density parity check (LDPC) code. The proposed method uses code expurgation: a linear subcode is retained for message encoding and additional input bits are used for protection against synchronization errors. The method is easy to implement and incurs minimal loss in rate
{"title":"A Synchronization Technique for Array-based LDPC Codes in Channels With Varying Sampling Rate","authors":"L. Dolecek, V. Anantharam","doi":"10.1109/ISIT.2006.261911","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261911","url":null,"abstract":"We describe a method for enhancing the synchronization error correction properties of an array-based low density parity check (LDPC) code. The proposed method uses code expurgation: a linear subcode is retained for message encoding and additional input bits are used for protection against synchronization errors. The method is easy to implement and incurs minimal loss in rate","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116900404","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261979
Rudi Cilibrasi, P. Vitányi
We consider similarity distances for two types of objects: literal objects that as such contain all of their meaning, like genomes or books, and names for objects. The latter may have literal embodiments like the first type, but may also be abstract like "red" or "Christianity". For the first type we consider a family of computable distance measures corresponding to parameters expressing similarity according to particular features between pairs of literal objects. For the second type we consider similarity distances generated by Web users corresponding to particular semantic relations between the (names for) the designated objects. For both families we give universal similarity distance measures, incorporating all particular distance measures in the family. In the first case the universal distance is based on compression and in the second case it is based on Google page counts related to search terms. In both cases experiments on a massive scale give evidence of the viability of the approaches
{"title":"Automatic Extraction of Meaning from the Web","authors":"Rudi Cilibrasi, P. Vitányi","doi":"10.1109/ISIT.2006.261979","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261979","url":null,"abstract":"We consider similarity distances for two types of objects: literal objects that as such contain all of their meaning, like genomes or books, and names for objects. The latter may have literal embodiments like the first type, but may also be abstract like \"red\" or \"Christianity\". For the first type we consider a family of computable distance measures corresponding to parameters expressing similarity according to particular features between pairs of literal objects. For the second type we consider similarity distances generated by Web users corresponding to particular semantic relations between the (names for) the designated objects. For both families we give universal similarity distance measures, incorporating all particular distance measures in the family. In the first case the universal distance is based on compression and in the second case it is based on Google page counts related to search terms. In both cases experiments on a massive scale give evidence of the viability of the approaches","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116946833","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 : 2006-07-09DOI: 10.1109/ISIT.2006.262120
A. Clark, Desmond P. Taylor, Peter J. Smith
Given digital transmission over two correlated Rician fading channels, we present a readily calculable expression for a tight approximation to the correlation between the probabilities of symbol error on each channel. For the Rayleigh fading channel the expression is exact. This correlation expression has applications in error performance analysis of fading systems, particularly multichannel systems and Markov modelling of error events. As an example we use these expressions to bound the block error rate of an OFDM system
{"title":"Simple Expressions for the Correlation between Fading Channel Error Rates","authors":"A. Clark, Desmond P. Taylor, Peter J. Smith","doi":"10.1109/ISIT.2006.262120","DOIUrl":"https://doi.org/10.1109/ISIT.2006.262120","url":null,"abstract":"Given digital transmission over two correlated Rician fading channels, we present a readily calculable expression for a tight approximation to the correlation between the probabilities of symbol error on each channel. For the Rayleigh fading channel the expression is exact. This correlation expression has applications in error performance analysis of fading systems, particularly multichannel systems and Markov modelling of error events. As an example we use these expressions to bound the block error rate of an OFDM system","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"32 3 Suppl 82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116006703","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 : 2006-07-09DOI: 10.1109/ISIT.2006.262081
R. Renner, S. Wolf, Jürg Wullschleger
In this paper we provide the answer to the following question: given a noisy channel PY|X and epsi > 0, how many bits can be transmitted with an error of at most epsi by a single use of the channel
{"title":"The Single-Serving Channel Capacity","authors":"R. Renner, S. Wolf, Jürg Wullschleger","doi":"10.1109/ISIT.2006.262081","DOIUrl":"https://doi.org/10.1109/ISIT.2006.262081","url":null,"abstract":"In this paper we provide the answer to the following question: given a noisy channel PY|X and epsi > 0, how many bits can be transmitted with an error of at most epsi by a single use of the channel","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"175 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116400778","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 : 2006-07-09DOI: 10.1109/ISIT.2006.262009
P. Moulin
Designing watermarking codes that can with stand geometric and other desynchronization attacks is a notoriously difficult problem. One may ask whether these difficulties are due to limitations of current codes, or rather to fundamental limitations on achievable performance. We model the attack channel as the cascade of a memoryless channel and a smooth, invertible mapping Tthetas, thetas isin thetasn, representing the geometric attack. The decoder does not known the value of thetas. We show that under regularity conditions, there exists a universal decoder for this problem, and we explicitly identify it
{"title":"Universal Decoding of Watermarks Under Geometric Attacks","authors":"P. Moulin","doi":"10.1109/ISIT.2006.262009","DOIUrl":"https://doi.org/10.1109/ISIT.2006.262009","url":null,"abstract":"Designing watermarking codes that can with stand geometric and other desynchronization attacks is a notoriously difficult problem. One may ask whether these difficulties are due to limitations of current codes, or rather to fundamental limitations on achievable performance. We model the attack channel as the cascade of a memoryless channel and a smooth, invertible mapping Tthetas, thetas isin thetasn, representing the geometric attack. The decoder does not known the value of thetas. We show that under regularity conditions, there exists a universal decoder for this problem, and we explicitly identify it","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122144283","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 : 2006-07-09DOI: 10.1109/ISIT.2006.261816
D. Donoho, Hossein Kakavand, J. Mammen
Consider a d times n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has infinitely many solutions (if there are any). Given y, the minimum Kolmogorov complexity solution (MKCS) of the input x is defined to be an input z (out of many) with minimum Kolmogorov-complexity that satisfies y = Az. One expects that if the actual input is simple enough, then MKCS will recover the input exactly. This paper presents a preliminary study of the existence and value of the complexity level up to which such a complexity-based recovery is possible. It is shown that for the set of all d times n binary matrices (with entries 0 or 1 and d < n), MKCS exactly recovers the input for an overwhelming fraction of the matrices provided the Kolmogorov complexity of the input is O(d). A weak converse that is loose by a log n factor is also established for this case. Finally, we investigate the difficulty of finding a matrix that has the property of recovering inputs with complexity of O(d) using MKCS
{"title":"The Simplest Solution to an Underdetermined System of Linear Equations","authors":"D. Donoho, Hossein Kakavand, J. Mammen","doi":"10.1109/ISIT.2006.261816","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261816","url":null,"abstract":"Consider a d times n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has infinitely many solutions (if there are any). Given y, the minimum Kolmogorov complexity solution (MKCS) of the input x is defined to be an input z (out of many) with minimum Kolmogorov-complexity that satisfies y = Az. One expects that if the actual input is simple enough, then MKCS will recover the input exactly. This paper presents a preliminary study of the existence and value of the complexity level up to which such a complexity-based recovery is possible. It is shown that for the set of all d times n binary matrices (with entries 0 or 1 and d < n), MKCS exactly recovers the input for an overwhelming fraction of the matrices provided the Kolmogorov complexity of the input is O(d). A weak converse that is loose by a log n factor is also established for this case. Finally, we investigate the difficulty of finding a matrix that has the property of recovering inputs with complexity of O(d) using MKCS","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129394004","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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