Coding for Two Different Distributions. Consider two distributions $p(x)$ and $q(x)$ on the same alphabet

$x.$ We want to design a source code that works with either distribution. For any $lon>0,$ find a fixed$-$

to$-$fixed source code with probability of error less than $lon$ if the underlying distribution is either $p(x)$ or

$q(x),$ and where the number of compressed bits satisfies

$kn(max\{H_p(x),H_q(x)\}+lon)$

where $H_p$ and $H_q$ refer to the entropies under $p(x)$ and $q(x)$ respectively.