{"title":"Fractal compression rate curves in lossless compression of balanced trees","authors":"Sang-youn Oh, J. Kieffer","doi":"10.1109/ISIT.2010.5513277","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513277","url":null,"abstract":"Let α be an integer ≥ 2. We define a finite rooted oriented tree to be α-balanced if (1) there is no vertex with > α children, (2) for each vertex having exactly α children, the subtrees rooted at these children have numbers of leaves differing by at most 1, and (3) each child of each internal vertex with < α children is a leaf. For each n ≥ 1, let H<inf>α</inf>(n) be logarithm to base two of the number of α-balanced trees having n leaves, which is roughly the codeword length needed to losslessly compress these trees via fixed-length binary codewords. Let {{x}} denote the fractional part of x. The compression rate curve C<inf>α</inf> is defined to be the set of limit points of the set of points of form ({{log<inf>α</inf> n}}, H<inf>α</inf>(n)/n). Two results about C<inf>α</inf> are presented. The first result is that C<inf>α</inf> is the graph of a unique realvalued nonconstant continuous function defined on [0, 1]. The second result is that C<inf>α</inf> is a 2-D fractal which is the attractor of an iterated function system S(α) consisting of α piecewise contractive 2-D mappings. For α = 2, 3, 4, we illustrate how a large number of points on C<inf>α</inf> can be rapidly generated via S(α).","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125643222","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":"Robust approximate lattice alignment design for K-pairs quasi-static MIMO interference channels with imperfect CSI","authors":"Huang Huang, V. Lau, Yinggang Du, Sheng Liu","doi":"10.1109/ISIT.2010.5513781","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513781","url":null,"abstract":"In this paper, we consider a robust approximate lattice alignment design for K-pairs quasi-static MIMO interference channels. The traditional interference alignment on the signal space is infeasible for K > 3 and perfect channel state information (CSI) is required for all the alignment schemes in the literature, which is impractical in practice. Furthermore, the structured lattice, widely used in the practical communications, can create a structured interference space compared with random Gaussian symbols. However, the existing alignment schemes on the lattice codes either require infinite SNR or require symmetric interference channel coefficients. Furthermore, they all assume perfect CSI knowledge. In this paper, we propose an approximate lattice alignment scheme for general complex interference channels in the general SNR regimes as well as a two-stage decoding algorithm to decode the desired signal from the approximated structured interference space. We derive the achievable data rate based on the approximate lattice alignment scheme and formulated the precoder, equalizer as well as the interference quantization design as a mixed integer and continuous optimization problem. By exploiting specific problem structures and incorporating CSI errors in the design, we derive low complexity robust solutions. We show that the proposed scheme has significant gain compared with the existing baselines.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116014921","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":"Diversity-multiplexing tradeoff in MIMO Gaussian interference channels","authors":"Hsiao-feng Lu","doi":"10.1109/ISIT.2010.5513470","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513470","url":null,"abstract":"In this paper we analyze the generalized degrees of freedom (GDOF) and the DMT performances of both the symmetric and asymmetric MIMO Gaussian interference fading channel with a fixed-power-split HK scheme for two transmit-receive pairs. Exact characterizations of both the GDOF and DMT performance measures are given. It is shown in the SIMO case that when the number of receive antennas is at least two, full region of GDOF can be achieved, as if the non-intending transmitter does not exist. The same conclusion is applied to the DMT measure as well. In particular, if the channel is symmetric, both receivers are able to achieve the single-user performance regime.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116389011","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":"Multiuser switched scheduling systems with per-user threshold and post-user selection","authors":"Haewoon Nam, Mohamed-Slim Alouini","doi":"10.1109/ISIT.2010.5513467","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513467","url":null,"abstract":"A multiuser switched diversity scheduling scheme with per-user feedback threshold is proposed in this paper. Unlike the conventional multiuser switched diversity scheduling scheme where a single threshold is used by all the users in order to determine whether to transmit a feedback, the proposed scheme deploys per-user threshold, where each user uses a potentially different threshold than other users thresholds. This paper first provides a generic analytical framework for the optimal feedback thresholds in a closed form. Then we investigates the impact of user sequence strategies and post selection strategies on the performance of the multiuser switched scheduling scheme with per-user threshold. Numerical and simulation results show that the proposed scheme provides a higher system capacity compared to the conventional scheme.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116357080","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":"Patterns and exchangeability","authors":"N. Santhanam, M. Madiman","doi":"10.1109/ISIT.2010.5513581","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513581","url":null,"abstract":"In statistics and theoretical computer science, the notion of exchangeability provides a framework for the study of large alphabet scenarios. This idea has been developed in an important line of work starting with Kingman's study of population genetics, and leading on to the paintbox processes of Kingman, the Chinese restaurant processes and their generalizations. In information theory, the notion of the pattern of a sequence provides a framework for the study of large alphabet scenarios, as developed in work of Orlitsky and collaborators. The pattern is a statistic that captures all the information present in the data, and yet is universally compressible regardless of the alphabet size. In this note, connections are made between these two lines of work- specifically, patterns are examined in the context of exchangeability. After observing the relationship between patterns and Kingman's paintbox processes, and discussing the redundancy of a class of mixture codes for patterns, alternate representations of patterns in terms of graph limits are discussed.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127197248","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":"Diversity-multiplexing-tradeoff-optimal 2-user scheduling in an M-user Gaussian multiple-access channel","authors":"Manav Garg, M. Varanasi","doi":"10.1109/ISIT.2010.5513478","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513478","url":null,"abstract":"The problem of user scheduling in a Gaussian i.i.d. Rayleigh faded multiple-access channel (MAC) is considered, whereby the receiver uses perfect knowledge of the channels of all the transmitters to select and schedule two-out-of-M users. The transmitters are assumed to have one antenna each and the two selected users are allocated equal rates. The receiver is equipped with Nr antennas. For user selection that is based on minimizing outage probability (say via an exhaustive search over (M over 2)possibilities), the diversity-multiplexing tradeoff (DMT) of the corresponding outage probability is computed. Moreover, a novel user-selection algorithmis proposed that achieves the same DMT as does the minimum outage probability method, but with only a O(M) complexity instead of O(M2) required for an exhaustive search to minimize outage probability. The DMT optimality of the proposed algorithm is also proved for 2-user scheduling in the dual M-user Gaussian broadcast channel assuming availability of global channel state information. Simulation results are presented which demonstrate that the proposed algorithm achieves an outage probability close to that of the exhaustive search.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124103464","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}
L. A. Lastras-Montaño, A. Jagmohan, M. Franceschini
{"title":"Algorithms for memories with stuck cells","authors":"L. A. Lastras-Montaño, A. Jagmohan, M. Franceschini","doi":"10.1109/ISIT.2010.5513786","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513786","url":null,"abstract":"We present a class of algorithms for encoding data in memories with stuck cells. These algorithms rely on earlier code constructions termed cyclic Partitioned Linear Block Codes. For the corresponding q-ary BCH-like codes for u stucks in a codeword of length n, our encoding algorithm has complexity O((u logq n)2) Fq operations, which we will show compares favorably to a generic approach based on Gaussian elimination. The computational complexity improvements are realized by taking advantage of the algebraic structure of cyclic codes for stucks. The algorithms are also applicable to cyclic codes for both stucks and errors.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124239594","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}
Bharath K. Sriperumbudur, K. Fukumizu, A. Gretton, B. Scholkopf, Gert R. G. Lanckriet
{"title":"Non-parametric estimation of integral probability metrics","authors":"Bharath K. Sriperumbudur, K. Fukumizu, A. Gretton, B. Scholkopf, Gert R. G. Lanckriet","doi":"10.1109/ISIT.2010.5513626","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513626","url":null,"abstract":"In this paper, we develop and analyze a nonparametric method for estimating the class of integral probability metrics (IPMs), examples of which include the Wasserstein distance, Dudley metric, and maximum mean discrepancy (MMD). We show that these distances can be estimated efficiently by solving a linear program in the case of Wasserstein distance and Dudley metric, while MMD is computable in a closed form. All these estimators are shown to be strongly consistent and their convergence rates are analyzed. Based on these results, we show that IPMs are simple to estimate and the estimators exhibit good convergence behavior compared to ø-divergence estimators.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124357403","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":"Rate-of-decay of probability of isolation in dense sensor networks with bounding constraints","authors":"A. Singh, P. Elia, D. Slock","doi":"10.1109/ISIT.2010.5513315","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513315","url":null,"abstract":"The work establishes the asymptotic rate of decay for the probability of node isolation in bounded wireless sensor networks, in the high density regime. In this regime, the exposition reveals the role of the most isolated neighborhoods of the bounding region in exponentially increasing the average probability of isolation. The problem is treated for a large family of random spatial distributions of nodes, random shapes of node coverage areas, and random topography of the network's bounding region. Different examples are presented to insightfully describe the detrimental effect of boundedness in network isolation. Finally we address different aspects relating to extremely isolating bounding regions, and densities that vary exponentially in time.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128932375","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":"New Restricted Isometry results for noisy low-rank recovery","authors":"Karthika Mohan, Maryam Fazel","doi":"10.1109/ISIT.2010.5513471","DOIUrl":"https://doi.org/10.1109/ISIT.2010.5513471","url":null,"abstract":"The problem of recovering a low-rank matrix consistent with noisy linear measurements is a fundamental problem with applications in machine learning, statistics, and control. Reweighted trace minimization, which extends and improves upon the popular nuclear norm heuristic, has been used as an iterative heuristic for this problem. In this paper, we present theoretical guarantees for the reweighted trace heuristic. We quantify its improvement over nuclear norm minimization by proving tighter bounds on the recovery error for low-rank matrices with noisy measurements. Our analysis is based on the Restricted Isometry Property (RIP) and extends some recent results from Compressed Sensing. As a second contribution, we improve the existing RIP recovery results for the nuclear norm heuristic, and show that recovery happens under a weaker assumption on the RIP constants.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121554615","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}