{"title":"Fixed-length lossy compression in the finite blocklength regime: Discrete memoryless sources","authors":"V. Kostina, S. Verdú","doi":"10.1109/ISIT.2011.6034159","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6034159","url":null,"abstract":"This paper studies the minimum achievable source coding rate as a function of blocklength n and tolerable distortion level d. Tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength. For stationary memoryless sources with separable distortion, the minimum rate achievable is shown to be q closely approximated by equation, where R(d) is the rate-distortion function, V (d) is the rate dispersion, a characteristic of the source which measures its stochastic variability, Q−1 (·) is the inverse of the standard Gaussian complementary cdf, and ε is the probability that the distortion exceeds d. The new bounds and the second-order approximation of the minimum achievable rate are evaluated for the discrete memoryless source with symbol error rate distortion. In this case, the second-order approximation reduces to equation if the source is non-redundant.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115273185","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 asymptotic error probability of composite relay channels","authors":"A. Behboodi, P. Piantanida","doi":"10.1109/ISIT.2011.6033798","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6033798","url":null,"abstract":"Consider the composite relay channel consisting of a set of relay channels associated to a probability measure. The current channel is a draw from its probability and in some cases arbitrary small error probability cannot be guaranteed for all channels in the set. In this paper, instead of finding the maximum achievable rate subject to a small error probability (EP) for all the channels in the set, we look at the asymptotic behavior of EP for a given rate. The notion of achievable EP is introduced as a novel performance measure for wireless relay channels. We can intuitively define it as the smallest EP that can be asymptotically achieved for a given rate. The behavior of EP is directly related to the ∈-capacity of each channel in the set. It is shown that the behavior of EP is upper and lower bounded by the outage probability of a region which is referred to as the full error region. Then every code with a rate belonging to this region yields EP equal to one. Finally, new coding for oblivious cooperation simultaneously exploiting both Decode-and-Forward (DF) and Compress-and-Forward (CF) strategies is investigated. The Gaussian relay channel with slow fading is also discussed.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116882318","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}
Or Ordentlich, Jiening Zhan, U. Erez, M. Gastpar, B. Nazer
{"title":"Practical code design for compute-and-forward","authors":"Or Ordentlich, Jiening Zhan, U. Erez, M. Gastpar, B. Nazer","doi":"10.1109/ISIT.2011.6033876","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6033876","url":null,"abstract":"The Compute-and-Forward approach has been proven to be very beneficial for communication over Gaussian networks. While the theoretical results are promising, it is still not completely understood how to best apply this scheme in practice. The objective of this work is to provide a low complexity scheme suitable for Compute-and-Forward. The scheme is based on utilizing linear codes over ℤq where q is not restricted to be prime and allows to achieve high transmission rates following Ungerboeck's set partitioning principle.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121116205","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":"Secret sharing via noisy broadcast channels","authors":"L. Lai, Yingbin Liang, Wenliang Du, S. Shamai","doi":"10.1109/ISIT.2011.6033894","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6033894","url":null,"abstract":"We consider the secret sharing problem, in which a dealer distributes a secret among a set of participants in such a manner that only qualified sets of users can recover the secret by pooling their shares together while non-qualified sets of users will obtain no information about the secret even if they pool their shares together. In contrast to the existing solutions that are mainly based on number theoretic tools, we propose a physical layer approach that exploits the presence of random noise inherent to wireless channels for secret sharing. Two different scenarios are considered. In the first scenario, the classic secret sharing problem with a single secret message is considered, in which qualified sets are specified by a general access structure. A secret sharing scheme is proposed by constructing a secure coding scheme for an equivalent compound wiretap channel. Based on this approach, both lower and upper bounds on the secret sharing capacity are obtained. For some special cases, the secret sharing capacity is fully characterized. In the second scenario, a generalization of the classic secret sharing problem is proposed, in which multiple secret messages are required to be recovered at different qualified sets. A secret sharing scheme is provided by constructing an equivalent broadcast channel with compound eavesdroppers and constructing a secure coding scheme for the equivalent channel.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127306239","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":"Channels with intermittent errors","authors":"A. Mazumdar, A. Barg","doi":"10.1109/ISIT.2011.6033849","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6033849","url":null,"abstract":"We study coding for binary channels in which out of any two consecutive transmitted bits at most one can be affected by errors. We consider a set of basic coding problems for such channels, deriving estimates on the size of optimal codes and providing some constructions. We also study a generalization to errors separated by at least s = 2, 3, … error-free channel uses. Finally, we define a probabilistic model of a binary channel with non-adjacent errors and find the capacity of this channel.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"188 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127343440","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":"Max-flow min-cut theorem for Rényi entropy in communication networks","authors":"M. Gadouleau, Søren Riis","doi":"10.1109/ISIT.2011.6034200","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6034200","url":null,"abstract":"A symbolic approach to communication networks, where the topology of the underlying network is contained in a set of formal terms, was recently introduced. Many communication problems can be recast as dispersion problems in this setup. The so-called min-cut of a term set represents its number of degrees of freedom. For any assignment of function symbols, its dispersion measures the amount of information sent to the destinations. It was proved that the maximum dispersion asymptotically reaches the min-cut of the term set. In this paper, we refine this result in two ways. First, we prove a max-flow min-cut theorem for the Rényi entropy with order less than one, given that the inputs are equiprobably distributed; conversely, there is no max-flow min-cut theorem for Rényi entropy with order greater than one. Second, although linear coding functions have the practical appeal of low complexity, we prove that they are insufficient in general to reach the min-cut. More specifically, there exist term sets which have an arbitrarily large dispersion for non-linear coding functions, yet limited dispersion when linear coding functions are considered. Conversely, we show that if there is a solution based on low degree polynomials, then there exists a linear solution.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125064182","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 completing the degrees of freedom characterization of MIMO interference networks with No CSIT","authors":"C. Vaze, M. Varanasi","doi":"10.1109/ISIT.2011.6034164","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6034164","url":null,"abstract":"The two-user multi-input, multi-output (MIMO) interference and cognitive radio channels are studied under the assumption of no channel state information at the transmitter (CSIT) from the degrees of freedom (DoF) region perspective. With M<inf>i</inf> and N<inf>i</inf> denoting the number of antennas at transmitter i and receiver i respectively, the DoF region of the MIMO interference channel was recently characterized by Huang et al., Zhu and Guo, and by the authors of this paper for all values of the 4-tuple (M<inf>1</inf>,M<inf>2</inf>,N<inf>1</inf>,N<inf>2</inf>), except when min(M<inf>1</inf>,N<inf>1</inf>) > N<inf>2</inf> > M<inf>2</inf> (or min(M<inf>2</inf>,N<inf>2</inf>) > N<inf>1</inf> > M<inf>1</inf>). This latter case was solved more recently by Zhu and Guo, who provided a tight outer-bound. Here, a simpler and more widely applicable proof of that outer-bound is given based on the idea of interference localization. Using it, the DoF region is also established for the class of MIMO cognitive radio channels (under certain restrictions on the fading distributions) when min(M<inf>1</inf> + M<inf>2</inf>,N<inf>1</inf>) > N<inf>2</inf> > M<inf>2</inf> (with the second transmitter cognitive) - the only class for which the inner and outer bounds previously obtained by the authors were not tight.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125948062","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":"Error exponents in asynchronous communication","authors":"Da Wang, V. Chandar, Sae-Young Chung, G. Wornell","doi":"10.1109/ISIT.2011.6033695","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6033695","url":null,"abstract":"Based on recent work on asynchronous communication, this paper proposes a slotted asynchronous channel model and investigates the fundamental limits of asynchronous communication, in terms of miss and false alarm error exponents. We propose coding schemes that are suitable for various asynchronous communication scenarios, and quantify more precisely the suboptimality of training-based schemes, i.e., communication strategies that separate synchronization from information transmission. In particular, we show that under a broad set of conditions, training-based schemes are suboptimal at all positive rates. Finally, we demonstrate these performance differences by specializing our results to BSCs and AWGN channels.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123320955","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":"The diversity of MMSE receiver over frequency-selective MIMO channel","authors":"A. Mehana, Aria Nosratinia","doi":"10.1109/ISIT.2011.6033706","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6033706","url":null,"abstract":"This paper analyzes the MMSE receiver in MIMO frequency-selective channels. This expands our understanding of the MMSE MIMO channel, whose diversity was only recently characterized in the MIMO flat-fading regime. Specifically, in this paper lower and upper bounds on the diversity of the MMSE receiver operating over frequency selective MIMO channel under block transmission with zero-padding (ZP) or cyclic-prefix (CP) are produced. The tightness of the bounds is demonstrated for both ZP/CP for the special case of SIMO channel.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115574169","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":"Weighted sum rate maximization for the MIMO X channel through MMSE precoding","authors":"A. Agustin, J. Vidal","doi":"10.1109/ISIT.2011.6034033","DOIUrl":"https://doi.org/10.1109/ISIT.2011.6034033","url":null,"abstract":"Recent results elucidate the optimality of the interference alignment concept in attaining the degrees of freedom of the MIMO X channel. However, in the low-medium SNR regime optimizing the weighted sum-rate seems more meaningful. Since the MIMO X channel subsumes the MIMO interference channel, MIMO multiple access, parallel MIMO point-to-point and MIMO broadcast channel, it is desirable to have a procedure that designs the linear transmitters and receivers in all cases. In this work we have observed that an algorithm based on alternate optimization, along with the proper initialization, is able to provide MMSE precoders attaining the degrees of freedom and significant gains in terms of SNR offset with respect the conventional interference alignment solution.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"714 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122992327","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}