7 research outputs found
Mismatched Multi-Letter Successive Decoding for the Multiple-Access Channel
This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is considered, and achievable rate regions and error exponents are derived both for the standard MAC (independent codebooks), and for the cognitive MAC (one user knows both messages) with superposition coding. In the cognitive case, the rate region and error exponent are shown to be tight with respect to the ensemble average. The rate regions are compared with those of the commonly considered decoder that chooses the message pair maximizing the decoding metric, and numerical examples are given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions.This work was supported in part by the European Research Council through ERC under Grant 259663 and Grant 725411, in part by the European Union’s 7th Framework Programme under Grant 303633, and in part by the Spanish Ministry of Economy and Competitiveness under Grant RYC-2011-08150, Grant TEC2012-38800-C03- 03, and Grant TEC2016-78434-C3-1-R
Random Coding Error Exponents for the Two-User Interference Channel
This paper is about deriving lower bounds on the error exponents for the
two-user interference channel under the random coding regime for several
ensembles. Specifically, we first analyze the standard random coding ensemble,
where the codebooks are comprised of independently and identically distributed
(i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is
in contrast to other, suboptimal decoding rules that have been used in the
literature (e.g., joint typicality decoding, treating interference as noise,
etc.). The fact that the interfering signal is a codeword, rather than an
i.i.d. noise process, complicates the application of conventional techniques of
performance analysis of the optimum decoder. Also, unfortunately, these
conventional techniques result in loose bounds. Using analytical tools rooted
in statistical physics, as well as advanced union bounds, we derive
single-letter formulas for the random coding error exponents. We compare our
results with the best known lower bound on the error exponent, and show that
our exponents can be strictly better. Then, in the second part of this paper,
we consider more complicated coding ensembles, and find a lower bound on the
error exponent associated with the celebrated Han-Kobayashi (HK) random coding
ensemble, which is based on superposition coding.Comment: accepted IEEE Transactions on Information Theor
Mismatched Multi-Letter Successive Decoding for the Multiple-Access Channel
This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is considered, and achievable rate regions and error exponents are derived both for the standard MAC (independent codebooks), and for the cognitive MAC (one user knows both messages) with superposition coding. In the cognitive case, the rate region and error exponent are shown to be tight with respect to the ensemble average. The rate regions are compared with those of the commonly considered decoder that chooses the message pair maximizing the decoding metric, and numerical examples are given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions
Mismatched multi-letter successive decoding for the multiple-access channel
Abstract—This paper studies channel coding for the discrete memoryless multiple-access channel with a given decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative function q(x1, x2, y) is considered, and an achiev-able rate region and error exponent are derived. The rate region is compared with that of the maximum-metric decoder which uses the function q(x1, x2, y), and a numerical example is given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions. I
Mismatched multi-letter successive decoding for the multiple-access channel
This paper studies channel coding for the discrete memoryless multiple-access channel with a given decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative function q(x1, x2, y) is considered, and an achievable rate region and error exponent are derived. The rate region is compared with that of the maximum-metric decoder which uses the function q(x1, x2, y), and a numerical example is given for which successive decoding yields a strictly higher sum rate for a given pair of input distributions. © 2014 IEEE
Information-Theoretic Foundations of Mismatched Decoding
Shannon's channel coding theorem characterizes the maximal rate of
information that can be reliably transmitted over a communication channel when
optimal encoding and decoding strategies are used. In many scenarios, however,
practical considerations such as channel uncertainty and implementation
constraints rule out the use of an optimal decoder. The mismatched decoding
problem addresses such scenarios by considering the case that the decoder
cannot be optimized, but is instead fixed as part of the problem statement.
This problem is not only of direct interest in its own right, but also has
close connections with other long-standing theoretical problems in information
theory. In this monograph, we survey both classical literature and recent
developments on the mismatched decoding problem, with an emphasis on achievable
random-coding rates for memoryless channels. We present two widely-considered
achievable rates known as the generalized mutual information (GMI) and the LM
rate, and overview their derivations and properties. In addition, we survey
several improved rates via multi-user coding techniques, as well as recent
developments and challenges in establishing upper bounds on the mismatch
capacity, and an analogous mismatched encoding problem in rate-distortion
theory. Throughout the monograph, we highlight a variety of applications and
connections with other prominent information theory problems.Comment: Published in Foundations and Trends in Communications and Information
Theory (Volume 17, Issue 2-3