Distributed Source Coding in Absence of Common Components

We introduce a scheme for the binary one-help-one distributed source coding problem using two layers of codes. The primary code is of constant finite block-length and the secondary code has a block-length approaching infinity. The achievable rate-distortion region for this scheme is derived for the binary one-help-one problem. It is shown that the scheme achieves the common component rate-distortion region in the case when the sources have a common component, while if a common component is not present (i.e. replaced with highly correlated functions of the two inputs) it improves upon existing achievable bounds. We show that as the block-length of the primary code is increased, the transmission rate required in the scheme decreases, reaches its minimum at some finite value and then increases. This phenomenon is not typically seen in traditional schemes used in multi-terminal source coding.