To code or not to code: Revisited

We revisit the dilemma of whether one should or should not code when operating under delay constraints. In those curious cases when the source and the channel are probabilistically matched so that symbol-by-symbol coding is optimal in terms of the average distortion achieved, we show that it also achieves the dispersion of joint source-channel coding. Moreover, even in the absence of such probabilistic matching between the source and the channel, symbol-by-symbol transmission, though asymptotically suboptimal, might outperform not only separate source-channel coding but also the best known random-coding joint source-channel coding achievability bound in the finite blocklength regime.