Exponential Strong Converse for One Helper Source Coding Problem.

We consider the one helper source coding problem posed and investigated by Ahlswede, Körner and Wyner. Two correlated sources are separately encoded and are sent to a destination where the decoder wishes to decode one of the two sources with an arbitrary small error probability of decoding. In this system, the error probability of decoding goes to one as the source block length goes to infinity. This implies that we have a strong converse theorem for the one helper source coding problem. In this paper, we provide the much stronger version of this strong converse theorem for the one helper source coding problem. We prove that the error probability of decoding tends to one exponentially and derive an explicit lower bound of this exponent function.