General formula for secrecy capacity of wiretap channel with noncausal state

The coding problem for a wiretap channel with a noncausal state is investigated, where the problem includes the coding problem for a channel with a noncausal state, which is known as the Gel´fand-Pinsker problem, and the coding problem for a wiretap channel introduced by Wyner. The secrecy capacity for this channel is derived, where an optimal code is constructed based on the hash property and a constrained-random-number generator. Since an ensemble of sparse matrices has a hash property, the rate of the proposed code using a sparse matrix can achieve the secrecy capacity.