{"title":"New Bounds on the Rate-Distortion Function of a Binary Markov Source","authors":"S. Jalali, T. Weissman","doi":"10.1109/ISIT.2007.4557286","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557286","url":null,"abstract":"This paper addresses the problem of bounding the rate-distortion function of a binary symmetric Markov source. We derive a sequence of upper and lower bounds on the rate- distortion function of such sources. The bounds are indexed by k, which corresponds to the dimension of the optimization problem involved. We obtain an explicit bound on the difference between the derived upper and lower bounds as a function of k. This allows to identify the value of k that suffices to compute the rate distortion function to a given desired accuracy. In addition to these bounds, a tighter lower bound which is also a function of k is derived. Our numerical results show that the new bounds improve on the Berger's upper and lower bounds even with small values of k.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133721958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Compound conditional source coding, Slepian-Wolf list decoding, and applications to media coding","authors":"S. Draper, E. Martinian","doi":"10.1109/ISIT.2007.4557436","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557436","url":null,"abstract":"We introduce a novel source coding problem, compound conditional source coding. We describe how a number of media coding problems can be cast into this framework. We develop the achievable rate region for this problem and error exponent results. We show that the reliability function of compound conditional source coding is as least as large as the list-decoding error exponent of Slepian-Wolf coding, which we develop in addition. A message of the paper is that a number of media coding scenarios where distributed source coding techniques are being used are more exactly stated as compound conditional problems. This insight can lead to improved system performance, as we demonstrate for error exponents.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"274 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115565384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Capacity Theorems for Relay Channels with Confidential Messages","authors":"Y. Oohama","doi":"10.1109/ISIT.2007.4557113","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557113","url":null,"abstract":"We consider a relay channel where a relay helps the transmission of messages from one sender to one receiver. The relay is considered not only as a sender that helps the message transmission but as a wire-tapper who can obtain some knowledge about the transmitted messages. In this paper we study the coding problem of the relay channel under the situation that some of transmitted messages are confidential to the relay. A security of such confidential messages is measured by the conditional entropy. The rate region is defined by the set of transmission rates for which messages are reliably transmitted and the security of confidential messages is larger than a prescribed level. In this paper we give two definition of the rate region. We first define the rate region in the case of deterministic encoder and call it the deterministic rate region. Next, we define the rate region in the case of stochastic encoder and call it the stochastic rate region. We derive explicit inner and outer bounds for the above two rate regions and present a class of relay channels where two bounds match. From the derived results, we can see that stochastic encoder can enlarge the rate region. We also evaluate the deterministic rate region of the Gaussian relay channel with confidential messages.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115840072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Turbo Decoding of Product Codes based on the Modified Adaptive Belief Propagation Algorithm","authors":"C. Jégo, W. Gross","doi":"10.1109/ISIT.2007.4557297","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557297","url":null,"abstract":"This paper introduces the Modified Adaptive Belief Propagation (m-ABP) algorithm, an innovative method for the turbo decoding of product codes based on BCH component codes. The Adaptive Belief Propagation algorithm of Jiang and Narayanan is simplified by moving the matrix adaptation step outside of the iteration loop, significantly reducing the complexity. Performance in terms of the bit- error-rate (BER) of the novel turbo decoding algorithm is given. Simulation results for the turbo decoding of product codes show that compared to the Chase-Pyndiah algorithm no significant BER deviation is observed while the highly- parallelizable graph-based structure of the algorithm enables high-throughput decoding.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"300 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124292894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effective LLL Reduction for Lattice Decoding","authors":"Cong Ling, Nick Howgrave-Graham","doi":"10.1109/ISIT.2007.4557226","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557226","url":null,"abstract":"The use of Lenstra-Lenstra-Lovasz (LLL) lattice reduction significantly improves the performance of zero-forcing (ZF) and successive interference cancellation (SIC) decoders in multi-input multi-output (MIMO) communications. Capitalizing on the observation that the decision region of SIC is determined by the Gram-Schmidt vectors rather than the basis itself, we propose the use of effective LLL reduction in SIC decoding, where size reduction is only performed for pairs of consecutive basis vectors. We establish the theoretic upper bound O(n3 log n) on the average complexity of effective LLL reduction for the i.i.d. Gaussian model of MIMO fading channels, which is an order lower than previously thought. Moreover, an effectively LLL-reduced basis can easily be transformed into the standard LLL-reduced basis for the purpose of ZF decoding.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114363220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Outage Capacity of MIMO Poisson Fading Channels","authors":"Kaushik Chakraborty, S. Dey, M. Franceschetti","doi":"10.1109/ISIT.2007.4557582","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557582","url":null,"abstract":"The information outage probability of a shot-noise limited direct detection multiple-input multiple-output (MIMO) optical channel subject to block fading is considered. Information is transmitted over this channel by modulating the intensity of a number of optical signals, one corresponding to each transmit aperture, and individual photon arrivals are observed at multiple receive photodetector apertures. The transmitted signals undergo multiplicative fading, and the fading occurs in coherence intervals of fixed duration in each of which the channel fade matrix remains constant. The channel fade matrix varies across successive coherence intervals in an independent and identically distributed fashion. The transmitter and the receiver are assumed to have perfect channel state information (CSI). The main contributions are a formulation of the outage probability problem as an optimization problem and an exact characterization of the optimal solution for the special case of the MIMO Poisson fading channel with two transmit apertures.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114522981","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}
Srinath Puducheri-Sundaravaradhan, J. Kliewer, T. Fuja
{"title":"Coding Schemes for an Erasure Relay Channel","authors":"Srinath Puducheri-Sundaravaradhan, J. Kliewer, T. Fuja","doi":"10.1109/ISIT.2007.4557301","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557301","url":null,"abstract":"This paper considers a simple network consisting of a source, a destination, and a relay. In this model, the source- relay and relay-destination links are lossless, while the source- destination link is subject to erasures. Four coding schemes for reliably conveying k symbols from the source to the destination are described. Three of these techniques are adapted directly from well-known point-to-point coding schemes - viz., the use of maximum-distance separable (MDS) codes and Luby Transform (LT) codes. The fourth approach is a new technique using uncoded transmission from the source in conjunction with a relay that transmits a sequence with this property: When the destination subtracts the effects of the unerased symbols from the sequence, what remains is an \"LT-like\" code for the erased symbols - and this property holds regardless of which symbols were erased on the source-destination link. The four approaches are compared in terms of their complexity and performance.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114652504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On The Duality Between Rate And Power Optimizations","authors":"Arun Padakandla, R. Sundaresan","doi":"10.1109/ISIT.2007.4557642","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557642","url":null,"abstract":"Sequence design problems are considered in this paper. The problem of sum power minimization in a spread spectrum system can be reduced to the problem of sum capacity maximization, and vice versa. A solution to one of the problems yields a solution to the other. Subsequently, conceptually simple sequence design algorithms known to hold for the white-noise case are extended to the colored noise case. The algorithms yield an upper bound of 2N - L on the number of sequences where N is the processing gain and L the number of non-interfering subsets of users. If some users (at most N - 1) are allowed to signal along a limited number of multiple dimensions, then N orthogonal sequences suffice.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115100215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integer Polar Coordinates for Compression","authors":"Demba E. Ba, Vivek K Goyal","doi":"10.1109/ISIT.2007.4557373","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557373","url":null,"abstract":"This paper introduces a family of integer-to-integer approximations to the Cartesian-to-polar coordinate transformation and analyzes its application to lossy compression. A high-rate analysis is provided for an encoder that first uniformly scalar quantizes, then transforms to \"integer polar coordinates,\" and finally separately entropy codes angle and radius. For sources separable in polar coordinates, the performance (at high rate) is shown to match that of entropy-constrained unconstrained polar quantization - where the angular quantization is allowed to depend on the radius. Thus, for sources separable in polar coordinates but not separable in rectangular coordinates - including certain Gaussian scale mixtures - the proposed system performs better than any transform code. Furthermore, unlike unconstrained polar quantization, integer polar coordinates are appropriate for lossless compression of integer-valued vectors. Combination of integer polar coordinates with integer-to-integer transform coding is also discussed.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117047339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Soft-Decision List Decoding with Linear Complexity for the First-Order Reed-Muller Codes","authors":"I. Dumer, G. Kabatiansky, C. Tavernier","doi":"10.1109/ISIT.2007.4557410","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557410","url":null,"abstract":"Soft-decision decoding on a memoryless channel is considered for the first-order Reed-Muller codes RM(1,m) of length 2m. We assume that different positions j of the received binary vector y can be corrupted by the errors of varying weight Wj. The generalized Hamming distance between vector y and any binary vector c is then defined as the sum of weighted differences Wj|yj - Cj| taken over all n positions. We obtain a tight upper bound Lt on the number of codewords located within generalized Hamming distance T from vector y, and design a decoding algorithm that outputs this list of codewords with complexity O(n In2 Lt)- In particular, all possible error weights wj equal 1 if this combinatorial model is applied to a binary symmetric channel. In this case, the well known Green algorithm performs full maximum likelihood decoding of RM(1,m) and requires O(n ln2 n) bit operations, whereas the Litsyn-Shekhovtsov algorithm operates within the bounded-distance decoding radius n/4 - 1 with linear complexity O(n). We close the performance-complexity gap between the two algorithms. Namely, for any fixed epsi isin (0, frac12), our algorithm outputs the complete list of codewords within the decoding radius n(frac12 - epsi) with linear complexity of order n ln2 epsi.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"7 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116860523","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}