{"title":"On the vector Gaussian L-terminal CEO problem","authors":"Jia Wang, Jun Chen","doi":"10.1109/ISIT.2012.6284256","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6284256","url":null,"abstract":"We derive an outer bound of the rate region of the vector Gaussian L-terminal CEO problem by establishing a lower bound on each supporting hyperplane of the rate region. To this end we prove a new extremal inequality by exploiting the connection between differential entropy and Fisher information as well as some fundamental estimation-theoretic inequalities. It is shown that the outer bound matches the Berger-Tung inner bound in the high-resolution regime.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115170066","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 uncertainty of information retrieval in associative memories","authors":"Eitan Yaakobi, Jehoshua Bruck","doi":"10.1109/ISIT.2012.6283016","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6283016","url":null,"abstract":"We (people) are memory machines. Our decision processes, emotions and interactions with the world around us are based on and driven by associations to our memories. This natural association paradigm will become critical in future memory systems, namely, the key question will not be “How do I store more information?” but rather, “Do I have the relevant information? How do I retrieve it?” The focus of this paper is to make a first step in this direction. We define and solve a very basic problem in associative retrieval. Given a word W, the words in the memory that are t-associated with W are the words in the ball of radius t around W. In general, given a set of words, say W, X and Y, the words that are t-associated with {W, X, Y} are those in the memory that are within distance t from all the three words. Our main goal is to study the maximum size of the t-associated set as a function of the number of input words and the minimum distance of the words in memory - we call this value the uncertainty of an associative memory. We derive the uncertainty of the associative memory that consists of all the binary vectors with an arbitrary number of input words. In addition, we study the retrieval problem, namely, how do we get the t-associated set given the inputs? We note that this paradigm is a generalization of the sequences reconstruction problem that was proposed by Leven-shtein (2001). In this model, a word is transmitted over multiple channels. A decoder receives all the channel outputs and decodes the transmitted word. Levenshtein computed the minimum number of channels that guarantee a successful decoder - this value happens to be the uncertainty of an associative memory with two input words.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"07 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127196840","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":"Projected subcodes of the second order binary Reed-Muller code","authors":"Matthieu Legeay, P. Loidreau","doi":"10.1109/ISIT.2012.6283977","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6283977","url":null,"abstract":"In this paper we construct new subcodes of the second-order binary Reed-Muller code by using the permutation group and by projecting the code onto codes with smaller parameters. The permutation group of Reed-Muller codes is the general affine group and can be decomposed into the semi-direct product of the translation group and the general linear group. The action of the translation group projects the second order Reed-Muller code onto copies of the first order Reed-Muller code. The general linear group projects the code onto codes for which we can control the useful length and the dimension. These parameters depend on the dimension of the eigenspace of the chosen element of the general linear group for the eigenvalue 1.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127549887","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":"Guiding blind transmitters: Relay-aided interference alignment for the X channel","authors":"Ye Tian, A. Yener","doi":"10.1109/ISIT.2012.6283517","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6283517","url":null,"abstract":"This paper investigates the impact of half-duplex relays on the degrees of freedom (DoF) of the K-user X channel when the transmitters are blind in the sense that no channel state information (CSI) at the transmitter (CSIT) is available. It is shown that adding relay nodes with CSI to the communication model is sufficient to recover the optimal DoF with CSIT. In particular, the relay nodes help steer the directions of the transmitted signals to facilitate interference alignment to achieve optimal DoF. It is shown that one relay node with K-1 antennas is sufficient to achieve the optimal DoF. When relays do not have multiple antennas, it is sufficient to have (K - 1)2 relays to achieve the optimal DoF. The achievability is established using partial interference alignment and joint beamforming. DoF for the case when relays only have delayed CSI is also investigated.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124910763","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":"Codes over non-Abelian groups: Point-to-point communications and computation over MAC","authors":"A. G. Sahebi, S. Pradhan","doi":"10.1109/ISIT.2012.6284269","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6284269","url":null,"abstract":"In this paper, we show that good structured codes over non-Abelian groups do exist. Specifically, we construct codes over the smallest non-Abelian group D6 and show that the performance of these codes is superior to the performance of Abelian group codes of the same alphabet size. This promises the possibility of using non-Abelian codes for multi-terminal settings where the structure of the code can be exploited to gain performance. We also show that for the problem of computation over MAC, these codes are superior to random codes in certain cases.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124951918","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 achievable rates for nonlinear Volterra channels via martingale inequalities","authors":"Kostis Xenoulis, N. Kalouptsidis, I. Sason","doi":"10.1109/ISIT.2012.6283497","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6283497","url":null,"abstract":"This paper establishes new achievable rates for nonlinear Volterra communication channels using refined versions of the Azuma-Hoeffding inequality. The characteristics of these rates are illuminated in special cases of interest that include time invariant linear channels with memory, memoryless non-linear channels, and Volterra channel models.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125798265","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":"Linear-programming decoding of Tanner codes with local-optimality certificates","authors":"N. Halabi, G. Even","doi":"10.1109/ISIT.2012.6284007","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6284007","url":null,"abstract":"Given a channel observation y and a codeword x, we are interested in a one-sided error test that answers the questions: is x optimal with respect to y? is it unique? A positive answer for such a test is called a certificate for the optimality of a codeword. We present new certificates that are based on combinatorial characterization for local-optimality of a codeword in irregular Tanner codes. The certificate is based on weighted normalized trees in computation trees of the Tanner graph. These trees may have any finite height h (even greater than the girth of the Tanner graph). In addition, the degrees of local-code nodes are not restricted to two (i.e., skinny trees). We prove that local-optimality in this new characterization implies ML-optimality and LP-optimality, and show that a certificate can be computed efficiently. We apply the new local-optimality characterization to regular Tanner codes, and prove lower bounds on the noise thresholds of LP-decoding in MBIOS channels. When the noise is below these lower bounds, the probability that LP-decoding fails decays doubly exponentially in the girth of the Tanner graph.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126166091","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":"Genie chains and the degrees of freedom of the K-user MIMO interference channel","authors":"Chenwei Wang, Hua Sun, S. Jafar","doi":"10.1109/ISIT.2012.6283961","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6283961","url":null,"abstract":"We explore the degrees of freedom (DoF) of the K >; 3 user M<sub>T</sub> × M<sub>R</sub> MIMO Gaussian interference channel where each transmitter is equipped with M<sub>T</sub> and each receiver is equipped with M<sub>R</sub> antennas. Expressing the DoF characterization as a function of the ratio γ = M/N, where M = min(M<sub>T</sub>, M<sub>R</sub>) and N = max(M<sub>T</sub>, M<sub>R</sub>), we find that when γ ≤ γ<sub>o</sub> = K-1/K(K-2) = γ<sub>o</sub>, the DoF value per user is piecewise linear depending on M and N alternately, similar to the DoF characterization for K = 3 which has been previously obtained. The regime γ >; γ<sub>o</sub>, which is the dominant regime for K >; 3 users and is not encountered in the K = 3 user setting, is the main focus of this paper. Our DoF results in this regime are obtained through a novel “genie chains” approach, which is the main contribution of this work. It is a chain of mappings from genie signals provided to a receiver to the exposed signal spaces at that receiver, which then serve as the genie signals for the next receiver in the chain, until an acceptable genie with the required number of dimensions is obtained, essentially converting an information theoretic problem into a linear algebra problem.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125258347","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":"Upper bound for the capacity of multiple access protocols on multipacket reception channels","authors":"D. Chan, T. Berger","doi":"10.1109/ISIT.2012.6283545","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6283545","url":null,"abstract":"While there has been much research on the capacity of the collision channel for multiple access protocols, there has been little investigation on their fundamental performance with multipacket reception (MPR)-capable channels, which allow more than one simultaneous transmissions to be successfully received. In this paper we investigate the properties of these MPR channels and provide an upper bound for their multiaccess capacities with a genie-aided argument. Our results not only give insights into the limiting efficiency with which multiaccessing can be performed in the MPR environment, but also generalize familiar results from classical multiaccess theory.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125436376","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":"An analytic upper bound on T-complexity","authors":"U. Speidel, T. Gulliver","doi":"10.1109/ISIT.2012.6284014","DOIUrl":"https://doi.org/10.1109/ISIT.2012.6284014","url":null,"abstract":"The Titchener T-complexity CT of a string has applications in, e.g., randomness testing, event detection and similarity comparison. Like the Lempel-Ziv production complexity, the upper bound of CT is demonstrably not a linear function of the string length. Knowledge of the bound for a given length is however required in order to convert CT into a measure with linear upper bound such as Titchener's T-information. For this reason, the upper bound of CT has been investigated before by several authors, with various asymptotic solutions proposed. We present a new analytic closed-form asymptotic upper bound for CT based on the Hurwitz-Lerch zeta function.","PeriodicalId":300161,"journal":{"name":"2012 IEEE International Symposium on Information Theory Proceedings","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125444568","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}