On the condition of ∈-transmissible joint source-channel coding for general sources and general channels

The joint source-channel coding problem is considered. The joint source-channel coding theorem reveals the existence of a code for the pair of the source and the channel under the condition that the error probability is smaller than or equal to ∈ asymptotically. The separation theorem guarantees that we can achieve the optimal coding performance by using the two-stage coding. In the case that ∈ = 0, Han showed the joint source-channel coding theorem and the separation theorem for general sources and channels. Furthermore the ∈-coding theorem (0 ≤ ∈ < 1) in the similar setting was studied. However, the separation theorem was not revealed since it is difficult in general. So we consider the separation theorem in this setting.