One Shot Joint Source Channel Coding

Nir Elkayam, Meir Feder

Abstract: This paper presents a one shot analysis to the lossless joint source channel coding problem. Achievable and converse bounds are derived. Both bound are given in term of $F(z)$, the CDF of the random variable $Z=-\log p_{e}(V, X, Y)$ where $p_{e}(V, X, Y)$ is the the pairwise error probability between two codewords associated with two source symbols. This is an information functional that resembles a similar quantity in the meta-converse form of one shot channel coding, but it depends also on the source $V$ in addition to the input $X$ and the output $Y$ of the channel. The role of $F(z)$ is analogous to the role of the information spectrum, but our treatment does not include any asymptotic analysis. Relation to other known bounds is also demonstrated.