Source Coding with Side Information at the Decoder Revisited

A source coding system with side information at the decoder is a typical multiterminal source coding system where output sequences of two sources are independently encoded, but a decoder recovers only one output sequence from two codewords. Since Wyner, Ahlswede and Korner independently investigated this system, we call it as the WAK coding system. This paper investigates the epsilon-achievable rate region of the WAK coding system which allows the probability of error within a fixed tolerance epsilon (is an element of (0, 1)), and clarifies the epsilon-achievable rate region for correlated general sources in terms of the smooth max-entropy and the smooth max Renyi divergence. To this end, we show a new one-shot converse theorem for the WAK coding system, and a one-shot covering lemma which is a refined version of Warsi's result. Then, combining these results, we clarify the epsilon-achievable rate region of the WAK coding system.