The Reliability Function of Lossy Source-Channel Coding of Variable-Length Codes with Feedback

We consider transmission of discrete memoryless sources (DMSes) across discrete memoryless channels (DMCs) using variable-length lossy source-channel codes with feedback. The reliability function (optimum error exponent) is shown to be equal to max{0, B(1-R(D)/C)}, where R(D) is the ratedistortion function of the source, B is the maximum relative entropy between output distributions of the DMC, and C is the Shannon capacity of the channel. We show that, in this setting and in this asymptotic regime, separate source-channel coding is, in fact, optimal.