One Shot Joint Source Channel Coding

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.