Multiuser Coding Techniques for Mismatched Decoding

This paper studies multiuser coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, error exponents are obtained which are tight with respect to the ensemble average, and positive within the interior of Lapidoth’s achievable rate region. In the special case of maximum-likelihood decoding, the ensemble tightness of the exponent of Liu-Hughes is proved. Alternative expressions for the error exponents and rate regions are given, including expressions obtained using Lagrange duality which extend immediately to general alphabets. In the setting of single-user mismatched decoding, similar analysis techniques are applied to two types of superposition coding. The standard version is shown to yield an achievable rate which is at least as high as that of Lapidoth’s expurgated parallel coding rate after the optimization of the parameters. A refined version of superposition coding is shown to achieve rates at least as good as the standard version for any set of random-coding parameters, and it is shown that the gap between the two can be significant when the input distribution is fixed. Index Terms Mismatched decoding, multiple-access channels, superposition coding, random coding, error exponents, ensemble tightness, duality, maximum-likelihood decoding.