Pub Date : 2006-07-09DOI: 10.1109/ISIT.2006.261725
Kwang Taik Kim, T. Berger
In critical distortion range, the MSE rate-distortion function of time-discrete stationary Gaussian first-order autoregressive source is equal to that of related time-discrete i.i.d. Gaussian source. For 0 < D les Dc it is necessary to provide additional information of non-negligible positive rate in order to obtain a D-admissible code for the original source via the R-D coding of the innovations process and additional post-processing at the decoder. In this scenario, we provide an explicit expression of additional description rate about the original source to find the degree of suboptimality of sending a lossy version of the innovations process in Gauss-Markov rate-distortion. It is shown that additional description rate is monotone increasing on alpha isin [0,1) and is constant on all critical distortion range
{"title":"The Degree of Suboptimality of Sending a Lossy Version of the Innovations Process in Gauss-Markov Rate-Distortion","authors":"Kwang Taik Kim, T. Berger","doi":"10.1109/ISIT.2006.261725","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261725","url":null,"abstract":"In critical distortion range, the MSE rate-distortion function of time-discrete stationary Gaussian first-order autoregressive source is equal to that of related time-discrete i.i.d. Gaussian source. For 0 < D les Dc it is necessary to provide additional information of non-negligible positive rate in order to obtain a D-admissible code for the original source via the R-D coding of the innovations process and additional post-processing at the decoder. In this scenario, we provide an explicit expression of additional description rate about the original source to find the degree of suboptimality of sending a lossy version of the innovations process in Gauss-Markov rate-distortion. It is shown that additional description rate is monotone increasing on alpha isin [0,1) and is constant on all critical distortion range","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"258 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":"129801878","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.2006.261897
E. Rosnes, O. Takeshita
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Also, the recently proposed quadratic permutation polynomial (QPP) based interleavers by Sun and Takeshita (IEEE Trans. Inform. Theory, Jan. 2005) provide excellent performance for short-to-medium block lengths. In this work the minimum distance of turbo codes with QPP-based interleavers is considered in detail. Large tables of optimum (in terms of turbo code minimum distance and multiplicity) QPPs for turbo codes with 8-state and 16-state constituent codes are presented. The minimum distances are compared to existing results in the literature on dithered relative prime (DRP) interleavers. The optimality of the new tables makes them an excellent source of information to advance the understanding of permutation polynomial (PP) based interleavers
{"title":"Optimum Distance Quadratic Permutation Polynomial-Based Interleavers for Turbo Codes","authors":"E. Rosnes, O. Takeshita","doi":"10.1109/ISIT.2006.261897","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261897","url":null,"abstract":"An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Also, the recently proposed quadratic permutation polynomial (QPP) based interleavers by Sun and Takeshita (IEEE Trans. Inform. Theory, Jan. 2005) provide excellent performance for short-to-medium block lengths. In this work the minimum distance of turbo codes with QPP-based interleavers is considered in detail. Large tables of optimum (in terms of turbo code minimum distance and multiplicity) QPPs for turbo codes with 8-state and 16-state constituent codes are presented. The minimum distances are compared to existing results in the literature on dithered relative prime (DRP) interleavers. The optimality of the new tables makes them an excellent source of information to advance the understanding of permutation polynomial (PP) based interleavers","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":"130406798","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.2006.261543
Jia Wang, Xiaolin Wu, Songyu Yu, Jun Sun
We propose a new scheme of multiple descriptions in the Wyner-Ziv setting (MD-WZ). The two side decoders of MD-WZ use two different side information (SI) streams. Both SI streams are available to the central decoder, but none to the encoder. We derive an achievable region (inner bound) for this MD-WZ system for general source and SI. If the source and SI are correlated Gaussian and for quadratic distortion metric, the tight bound is obtained. Our result is an extension of Ozarow's result on multiple descriptions of Gaussian source without SI. The MD-WZ coding scheme is shown to have a property of practical significance. For symmetric case where the joint distributions of the source and the two SI are the same and the two channels are balanced, interchanging the two channels causes no performance loss for Gaussian source. Considering that the existing multi-description video coding methods suffer from the notorious drifting problem induced by channels interchange, this work lends a theoretical support to distributed multi-description video coding in the Wyner-Ziv setting
{"title":"Multiple Descriptions in the Wyner-Ziv Setting","authors":"Jia Wang, Xiaolin Wu, Songyu Yu, Jun Sun","doi":"10.1109/ISIT.2006.261543","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261543","url":null,"abstract":"We propose a new scheme of multiple descriptions in the Wyner-Ziv setting (MD-WZ). The two side decoders of MD-WZ use two different side information (SI) streams. Both SI streams are available to the central decoder, but none to the encoder. We derive an achievable region (inner bound) for this MD-WZ system for general source and SI. If the source and SI are correlated Gaussian and for quadratic distortion metric, the tight bound is obtained. Our result is an extension of Ozarow's result on multiple descriptions of Gaussian source without SI. The MD-WZ coding scheme is shown to have a property of practical significance. For symmetric case where the joint distributions of the source and the two SI are the same and the two channels are balanced, interchanging the two channels causes no performance loss for Gaussian source. Considering that the existing multi-description video coding methods suffer from the notorious drifting problem induced by channels interchange, this work lends a theoretical support to distributed multi-description video coding in the Wyner-Ziv setting","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"38 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":"126979417","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.2006.262047
B. Nazer, M. Gastpar
We study the problem of multicasting over a network of multiple-access channels (MACs). The separation-based solution to this problem is to reduce each MAC to a set of noiseless bit pipes via a channel code and then employ network coding. Sometimes, however, the physical-layer structure of the MAC can be exploited more advantageously. In many cases of interest, the MAC output is a (deterministic) function of its inputs, corrupted by noise. We develop structured codes to exploit the natural function of a MAC to reliably compute functions as part of a network code and show that in many scenarios of interest our scheme outperforms the separation-based solution. If each MAC can be written as a sum over some finite field plus noise, then our achievable rate coincides with the max-flow min-cut bound
{"title":"Computing over Multiple-Access Channels with Connections to Wireless Network Coding","authors":"B. Nazer, M. Gastpar","doi":"10.1109/ISIT.2006.262047","DOIUrl":"https://doi.org/10.1109/ISIT.2006.262047","url":null,"abstract":"We study the problem of multicasting over a network of multiple-access channels (MACs). The separation-based solution to this problem is to reduce each MAC to a set of noiseless bit pipes via a channel code and then employ network coding. Sometimes, however, the physical-layer structure of the MAC can be exploited more advantageously. In many cases of interest, the MAC output is a (deterministic) function of its inputs, corrupted by noise. We develop structured codes to exploit the natural function of a MAC to reliably compute functions as part of a network code and show that in many scenarios of interest our scheme outperforms the separation-based solution. If each MAC can be written as a sum over some finite field plus noise, then our achievable rate coincides with the max-flow min-cut bound","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":"129186234","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.2006.261836
Po-Ning Chen, Tsang-Yi Wang, Y. Han, P. Varshney, C. Yao, Shin-Lin Shieh
In this work, we analyze the performance of a wireless sensor network with distributed classification codes, where independence across sensors, including local observations, local classifications and sensor-fusion link noises, is assumed. In terms of large deviations technique, we establish the necessary and sufficient condition under which the minimum Hamming distance fusion error vanishes as the number of sensors tends to infinity. With the necessary and sufficient condition and the upper performance bounds, the relation between the fault-tolerance capability of a distributed classification code and its pair-wise Hamming distances is characterized
{"title":"Fault-Tolerance Analysis of a Wireless Sensor Network with Distributed Classification Codes","authors":"Po-Ning Chen, Tsang-Yi Wang, Y. Han, P. Varshney, C. Yao, Shin-Lin Shieh","doi":"10.1109/ISIT.2006.261836","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261836","url":null,"abstract":"In this work, we analyze the performance of a wireless sensor network with distributed classification codes, where independence across sensors, including local observations, local classifications and sensor-fusion link noises, is assumed. In terms of large deviations technique, we establish the necessary and sufficient condition under which the minimum Hamming distance fusion error vanishes as the number of sensors tends to infinity. With the necessary and sufficient condition and the upper performance bounds, the relation between the fault-tolerance capability of a distributed classification code and its pair-wise Hamming distances is characterized","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":"123399813","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.2006.261970
S. B. Korada, N. Macris
An important quantity in the analysis of MAP decoding for LDPC codes is the conditional entropy of the input given the output. There exist conjectured formulas for this entropy derived from the replica technique and one sided bounds derived with the help of the interpolation method. In this paper we compute exactly such a quantity for a simpler spin model which retains the essential features of the communications problem. The result is a step towards a proof of the conjectured replica formula for the conditional entropy under MAP decoding
{"title":"Exact solution of a p-spin model and its relationship to error correcting codes","authors":"S. B. Korada, N. Macris","doi":"10.1109/ISIT.2006.261970","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261970","url":null,"abstract":"An important quantity in the analysis of MAP decoding for LDPC codes is the conditional entropy of the input given the output. There exist conjectured formulas for this entropy derived from the replica technique and one sided bounds derived with the help of the interpolation method. In this paper we compute exactly such a quantity for a simpler spin model which retains the essential features of the communications problem. The result is a step towards a proof of the conjectured replica formula for the conditional entropy under MAP decoding","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"71 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":"121327873","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.2006.261718
C. Chekuri, C. Fragouli, E. Soljanin
A non-uniform demand network consists of a source and a set of receivers that have different min-cut values from the source. We look at the case where each receiver would like to receive information from the source at a rate that is equal to its min-cut value. This problem has been formulated before, and in contrast to the uniform case, it has been shown that the non-uniform case does not admit a good characterization. Motivated by this, we formulate relaxations of the problem and present some preliminary results
{"title":"On Achievable Information Rates in Single-Source Non-Uniform Demand Networks","authors":"C. Chekuri, C. Fragouli, E. Soljanin","doi":"10.1109/ISIT.2006.261718","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261718","url":null,"abstract":"A non-uniform demand network consists of a source and a set of receivers that have different min-cut values from the source. We look at the case where each receiver would like to receive information from the source at a rate that is equal to its min-cut value. This problem has been formulated before, and in contrast to the uniform case, it has been shown that the non-uniform case does not admit a good characterization. Motivated by this, we formulate relaxations of the problem and present some preliminary results","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"73 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":"114233564","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.2006.261945
R. Tandra, A. Sahai
We consider a point to point communication system facing interference from other systems, with a particular focus on the case when this interference is undecodable. It is well known that when the interference is non-interactive, we can certainly treat it as additional noise at the receiver and thereby achieve certain rates. This paper asks whether any higher rates could be achieved by exploiting knowledge of the interferer's codebook. The main contribution of this paper is to study the converse: if the interference is undecodable, then we cannot do better than treating it as additional noise. This is proved for almost all interference codebooks when viewed under the random Gaussian codebook measure. When the interference signal is strong enough to be decodable, then codebook knowledge can be exploited at our receiver to allow higher rates to be achieved by appropriately structuring our own codebooks. Finally, we give an example of an interference codebook that cannot be completely decoded, but whose knowledge is still useful. However, this interference codebook is bad from the perspective of the interferer's own communication system. This leads us to conjecture that when the interference signal is undecodable, the only interference codebooks worth knowing are those that are not worth using from the interfering system's point of view
{"title":"Is interference like noise when you know its codebook?","authors":"R. Tandra, A. Sahai","doi":"10.1109/ISIT.2006.261945","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261945","url":null,"abstract":"We consider a point to point communication system facing interference from other systems, with a particular focus on the case when this interference is undecodable. It is well known that when the interference is non-interactive, we can certainly treat it as additional noise at the receiver and thereby achieve certain rates. This paper asks whether any higher rates could be achieved by exploiting knowledge of the interferer's codebook. The main contribution of this paper is to study the converse: if the interference is undecodable, then we cannot do better than treating it as additional noise. This is proved for almost all interference codebooks when viewed under the random Gaussian codebook measure. When the interference signal is strong enough to be decodable, then codebook knowledge can be exploited at our receiver to allow higher rates to be achieved by appropriately structuring our own codebooks. Finally, we give an example of an interference codebook that cannot be completely decoded, but whose knowledge is still useful. However, this interference codebook is bad from the perspective of the interferer's own communication system. This leads us to conjecture that when the interference signal is undecodable, the only interference codebooks worth knowing are those that are not worth using from the interfering system's point of view","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":"116472673","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.2006.261928
Y. Zhong, F. Alajaji, L. Campbell
For a memoryless Gaussian source under the squared-error distortion fidelity criterion and a memoryless additive Gaussian noise channel with a quadratic power constraint at the channel input, upper and lower bounds for the joint source-channel coding excess distortion exponent (which is the exponent of the probability of excess distortion) are established. A necessary and sufficient condition for which the two bounds coincide is provided, thus exactly determining the exponent. This condition is observed to hold for a wide range of source-channel parameters
{"title":"On the Excess Distortion Exponent for Memoryless Gaussian Source-Channel Pairs","authors":"Y. Zhong, F. Alajaji, L. Campbell","doi":"10.1109/ISIT.2006.261928","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261928","url":null,"abstract":"For a memoryless Gaussian source under the squared-error distortion fidelity criterion and a memoryless additive Gaussian noise channel with a quadratic power constraint at the channel input, upper and lower bounds for the joint source-channel coding excess distortion exponent (which is the exponent of the probability of excess distortion) are established. A necessary and sufficient condition for which the two bounds coincide is provided, thus exactly determining the exponent. This condition is observed to hold for a wide range of source-channel parameters","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"98 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":"114711687","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.2006.261878
A. Ashikhmin, A. Calderbank, Wjatscheslaw Kewlin
We derive a generalization of a result in representation theory. Using this generalization, we construct new families of Grassmannian packings associated with binary Reed-Muller codes and we develop a low complexity decoding algorithm by modifying standard decoding algorithms for these binary codes. The subspaces are associated with projection operators which arise in the theory of quantum stabilizer codes. These Grassmannian packings find application as highly structured examples of dictionaries that admit fast algorithms for identifying sparse representations, and in noncoherent wireless communication with multiple antennas. The capacity of the noncoherent MIMO channel at both low and moderate SNR (under the constraint that only isotropically distributed unitary matrices are used for information transmission) is closely approximated by these packings
{"title":"Multidimensional Second Order Reed-Muller Codes as Grassmannian Packings","authors":"A. Ashikhmin, A. Calderbank, Wjatscheslaw Kewlin","doi":"10.1109/ISIT.2006.261878","DOIUrl":"https://doi.org/10.1109/ISIT.2006.261878","url":null,"abstract":"We derive a generalization of a result in representation theory. Using this generalization, we construct new families of Grassmannian packings associated with binary Reed-Muller codes and we develop a low complexity decoding algorithm by modifying standard decoding algorithms for these binary codes. The subspaces are associated with projection operators which arise in the theory of quantum stabilizer codes. These Grassmannian packings find application as highly structured examples of dictionaries that admit fast algorithms for identifying sparse representations, and in noncoherent wireless communication with multiple antennas. The capacity of the noncoherent MIMO channel at both low and moderate SNR (under the constraint that only isotropically distributed unitary matrices are used for information transmission) is closely approximated by these packings","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"29 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":"124140130","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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