Capacity of the binomial channel, or minimax redundancy for memoryless sources

This paper computes the capacity of the binomial channel of order n, for any finite n via convex optimization and duality. The binomial channel capacity is also the minimax coding redundancy for a class of memoryless sources. The exact capacity for finite n computed here is compared to the asymptotic expression found by Xie and Barron (see IEEE Trans. Inform. Theory, vol.43, no.2, p.646-57 (March 1997)).