{"title":"Asymptotic Rate versus Design Rate","authors":"C. Méasson, A. Montanari, R. Urbanke","doi":"10.1109/ISIT.2007.4557441","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557441","url":null,"abstract":"The rate of a code is one of its most important parameters. We consider sparse graph codes and ask whether the rate of a random element of an ensemble is typically close to the design rate of the ensemble. For regular LDPC ensembles this question was answered in the affirmative in (Miller and Cohen, 2003). We start by giving an alternative proof of this statement. We then show that essentially the same type of argument applies not only to regular ensembles but also to ensembles that are derived from regular ensembles in the sense that their degree distribution is the result of applying the peeling decoder to a regular code. As an immediate consequence we prove that for regular ensembles the asymptotic MAP EXIT value coincides with the asymptotic BP EXIT value. We then give a systematic construction of ensembles for which rate and design rate differ. To accomplish this, we first show that the duality theorem (Ashikhminet al., 2004) implies that the asymptotic BP EXIT and the MAP EXIT functions are identical for any channel parameter for which the density evolution (DE) equations have a unique fixed point.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"75 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":"134011406","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":"ML decoding via mixed-integer adaptive linear programming","authors":"S. Draper, J. Yedidia, Yige Wang","doi":"10.1109/ISIT.2007.4557459","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557459","url":null,"abstract":"Linear programming (LP) decoding was introduced by Feldman et al. (IEEE Trans. Inform. Theory Mar. 2005) as a novel way to decode binary low-density parity-check codes. Taghavi and Siegel (Proc. ISIT 2006) describe a computationally simplified decoding approach they term \"adaptive\" LP decoding. Adaptive LP decoding starts with a sub-set of the LP constraints, and iteratively adds violated constraints until an optimum of the original LP is found. Usually only a tiny fraction of the original constraints need to be reinstated, leading to huge efficiency gains compared to ordinary LP decoding. Here we describe a modification of the adaptive LP decoder that results in a maximum likelihood (ML) decoder. Whenever the adaptive LP decoder returns a pseudo-codeword rather than a codeword, we add an integer constraint on the least certain symbol of the pseudo-codeword. For certain codes, and especially in the high-SNR (error floor) regime, only a few integer constraints are required to force the resultant mixed-integer LP to the ML solution. We demonstrate that our approach can efficiently achieve the optimal ML decoding performance on a (155,64) LDPC code introduced by Tanner et al.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"58 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":"134284685","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":"Precoding of Space-Time Block Codes in Multiuser MIMO Channels with Outdated Channel State Information","authors":"Jane Wei Huang, E. Au, V. Lau","doi":"10.1109/ISIT.2007.4557519","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557519","url":null,"abstract":"Motivated by the fact that combining space-time block codes with channel precoding can make the system robust against channel fading while achieving both coding and diversity gains, we propose a joint set of linear precoder designs for uplink multiuser space-time block coded multiple-input multiple-output systems with multipacket reception by exploiting outdated channel state information. In particular, we formulate the design as an optimization problem of minimizing pairwise error probability subject to transmit power constraint for each user. Due to non-convex nature of the optimization problem, we devise an iterative algorithm to solve for linear precoding structure for general space-time block code. For orthogonal space-time block code, we also propose a simplified distributed algorithm to solve for a closed-form solution. Asymptotic analysis of the effect of channel quality on the precoder structure is also presented. Simulation results are provided to demonstrate the effectiveness of the proposed designs for orthogonal and quasi-orthogonal space-time block codes over the conventional beamforming system.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"23 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":"131580115","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":"Broadcasting with Feedback","authors":"Sibi Raj Bhaskaran","doi":"10.1109/ISIT.2007.4557259","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557259","url":null,"abstract":"The availability of noiseless feedback in an additive white Gaussian noise channel can considerably improve the rate of decay of error-probability with block length. A doubly exponential error decay can be attained even in the presence of an additive interference term non-causally known at the transmitter alone. Adapting this result, we show that the capacity region of a Gaussian broadcast channel (GBC) can be enlarged even when the feedback is available from only one of the receivers. We also demonstrate an explicit capacity achieving transmission strategy for the physically degraded GBC with feedback, with the decay of error doubly exponential in the number of transmissions specific to a given message.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"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":"129374451","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 Information Theoretic View of Stochastic Resonance","authors":"V. Anantharam, V. Borkar","doi":"10.1109/ISIT.2007.4557349","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557349","url":null,"abstract":"We are motivated by the widely studied phenomenon called stochastic resonance, namely that in several sensing systems, both natural and engineered, the introduction of noise can enhance the ability of the system to perceive signals in the environment. We adopt an information theoretic viewpoint, evaluating the quality of sensing via the mutual information rate between the environmental signal and the observations. Viewing what would be considered noise in stochastic resonance as an open loop control and using Markov decision theory techniques, we discuss the problem of optimal choice of this control in order to maximize this mutual information rate. We determine the corresponding dynamic programming recursion: it involves the conditional law of certain conditional laws associated to the dynamics. We prove that the optimal control may be chosen as a deterministic function of this law of laws.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"88 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":"130941113","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":"Equivalence classes of boolean functions for first-order correlation","authors":"J. L. Bars, Alfredo Viola","doi":"10.1109/ISIT.2007.4557223","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557223","url":null,"abstract":"Boolean functions are very important cryptographic primitives in stream or block ciphers. In this context, these functions need to satisfy good properties like high algebraic degree, nonlinearity and correlation immunity. We present here an original and efficient method to enumerate all the correlation-immune functions of a fixed Hamming weight, in particular the class of 1-resilient functions. The key idea consists in defining equivalent classes to split boolean functions along their distance from correlation-immune boolean functions. These classes, called first-order correlation classes, are built using a recursive decomposition of smaller classes. We derive from this method several algorithms to enumerate their elements and to count their cardinality. We first show that the exact number of 1-resilient boolean functions with 7 variables is 23478015754788854439497622689296 and we obtain a tight estimation of their number with 8 variables, between 4 1067 and 5.6 1068. We then present a general lower bound for the number of 1-resilient boolean functions and improve Schneider's upper bound. We also propose a general lower bound for the number of k-resilient functions. Most of the bounds presented in this paper, substantially improve the best known bounds in the literature. We finally establish that the probability of a Boolean function being 1-resilient is asymptotically between (npi)n/2/2n2-3/2n-1en-1/2.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"47 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":"133019940","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}
Yuval Cassuto, Moshe Schwartz, V. Bohossian, Jehoshua Bruck
{"title":"Codes for Multi-Level Flash Memories: Correcting Asymmetric Limited-Magnitude Errors","authors":"Yuval Cassuto, Moshe Schwartz, V. Bohossian, Jehoshua Bruck","doi":"10.1109/ISIT.2007.4557123","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557123","url":null,"abstract":"Several physical effects that limit the reliability and performance of Multilevel Flash memories induce errors that have low magnitude and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions for such channels when the number of errors is bounded by t. The construction uses known codes for symmetric errors over small alphabets to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. An extension of the construction is proposed to include systematic codes as a benefit to practical implementation.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"515 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133557390","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":"A Note on Error Correction Schemes using LDPC codes with a High-Capacity Feedback Channel","authors":"Naoto Kobayashi, T. Matsushima, S. Hirasawa","doi":"10.1109/ISIT.2007.4557575","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557575","url":null,"abstract":"In this paper, transmission schemes with noiseless and high capacity feedback channel is considered. We propose two types of transmission schemes using LDPC codes and clarify the density evolution analysis method for these proposed schemes. We investigate the performance of the proposed schemes by the density evolution analysis and computer simulations. The result shows some interesting characteristics for schemes with high capacity feedback channel.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"160 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":"132046699","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":"Joint Beamforming and Power Control for Optimal SIR Assignment in Cellular Uplinks","authors":"T. Lan, P. Hande, M. Chiang","doi":"10.1109/ISIT.2007.4557584","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557584","url":null,"abstract":"This paper considers the nonconvex and globally coupled problem of joint antenna beamforming and transmit power control, in order to maximize the network-wide utility as a function of attained SIRs. Using a spillage-load characterization for power control [13], we assign utility as a function of attained SIRs and formulate the joint optimization as a utility maximization problem. Despite the highly coupled structure of the problem, we propose an efficient distributed algorithm that is proved to be convergent in general. Despite nonconvexity in the joint optimization, we prove global optimality in the two user case. We find in simulations the algorithm always converges to the global optimal allocation, and the Pareto-optimal tradeoff between power and antenna beamforming in maximizing network utility is illustrated.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"241 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":"131857017","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":"Sum-Capacity and MMSE for the MIMO Broadcast Channel without Eigenvalue Decompositions","authors":"R. Hunger, D. Schmidt, W. Utschick","doi":"10.1109/ISIT.2007.4557107","DOIUrl":"https://doi.org/10.1109/ISIT.2007.4557107","url":null,"abstract":"In this paper, we present a novel algorithm for determining the sum-rate optimal transmit covariance matrices for the MIMO broadcast channel. Instead of optimizing the covariances directly, our algorithm operates on the preceding matrices, i.e., the square roots of the covariances. As a result, no eigenvalue decompositions are required in the iterations, and the complexity per iteration is significantly lower. A look at the convergence over the required number of computations shows a visible advantage over the state-of-the-art sum power iterative waterfilling algorithm. Also, our algorithm allows us to find the optimal sum-rate for an arbitrarily limited number of data streams per user. Finally, with a simple modification, our algorithm can also be used for sum-MSE minimization.","PeriodicalId":193467,"journal":{"name":"2007 IEEE International Symposium on Information Theory","volume":"51 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":"133734726","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}