The generalized stochastic likelihood decoder: Random coding and expurgated bounds

Correction to “The Generalized Stochastic Likelihood Decoder: Random Coding and Expurgated Bounds” [Aug 17 5039-5051]

“…In a recent article [1], random coding error exponents and expurgated exponents were analyzed for the generalized likelihood decoder (GLD), where the decoded message is randomly selected under a probability distribution that is proportional to a general exponential function of the empirical joint distribution of the codeword and the channel output vectors. In Section V of [1], Theorem 2 provides an expurgated exponent which is applicable to this decoder (and hence also to the optimal maximum likelihood decoder).…”

“…In Section V of [1], Theorem 2 provides an expurgated exponent which is applicable to this decoder (and hence also to the optimal maximum likelihood decoder). The proof of that theorem is based on two steps of a certain expurgation procedure.…”

“…When the transmitter wishes to convey a message m, it transmits the corresponding code-vector x m via the channel, which in turn, stochastically maps it into an n-vector y according to (1). Upon receiving y, the stochastic generalized likelihood decoder randomly selects the estimated messagem according to a generalized version of the induced posterior distribution of the transmitted message, i.e.,…”

“…As mentioned above, in Section V of [1], an expurgated error exponent is derived. Specifically, letting Q XY denote a generic joint distribution over X × Y, and letting I Q (X; Y ) denote the mutual information induced by Q XY , we define the following.…”

“…The proof in [1] contains two main steps of expurgation. In the first step, we confine attention to the subset of constant composition codes {C n } with the property…”