On Lossless Coding With Coded Side Information

This paper considers the problem, first introduced by Ahlswede and Korner in 1975, of lossless source coding with coded side information. Specifically, let
X
and
Y
be two random variables such that
X
is desired losslessly at the decoder while
Y
serves as side information. The random variables are encoded independently, and both descriptions are used by the decoder to reconstruct
X
. Ahlswede and Korner describe the achievable rate region in terms of an auxiliary random variable. This paper gives a partial solution for an optimal auxiliary random variable, thereby describing part of the rate region explicitly in terms of the distribution of
X
and
Y
.