The Mismatched Multiple-Access Channel: General Alphabets

Abstract-This paper considers channel coding for the memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. Non-asymptotic bounds on the error probability are given, and a cost-constrained random-coding ensemble is used to obtain an achievable error exponent. The achievable rate region recovered by the error exponent coincides with that of Lapidoth in the discrete memoryless case, and remains valid for more general alphabets

Expurgated random-coding ensembles: Exponents, refinements, and connections

This paper studies expurgated random-coding bounds and exponents with a given (possibly suboptimal) decoding rule. Variations of Gallager’s analysis are presented, yielding new asymptotic and non-asymptotic bounds on the error probability for an arbitrary codeword distribution. A simple non-asymptotic bound is shown to attain an exponent which coincides with that of Csiszár and Körner for discrete alphabets, while also remaining valid for continuous alphabets. The method of type class enumeration is studied for both discrete and continuous alphabets, and it is shown that this approach yields improved exponents for some codeword distributions. A refined analysis of expurgated i.i.d. random prefactor, thus improving on Gallager’s O(1) prefactor. coding is given which yields an exponent with a O ( 1 √n I

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

Cost-Constrained Random Coding and Applications

Abstract—This paper studies a random coding ensemble in which each codeword is constrained to satisfy multiple cost constraints. Using this ensemble, an achievable second-order coding rate is presented for the mismatched single-user channel. Achievable error exponents are given for the mismatched singleuser channel and the matched multiple-access channel. I

Cost-constrained random coding and applications

This paper studies a random coding ensemble in which each codeword is constrained to satisfy multiple cost constraints. Using this ensemble, an achievable second-order coding rate is presented for the mismatched single-user channel. Achievable error exponents are given for the mismatched singleuser channel and the matched multiple-access channel. © 2013 IEEE