On the Multicoding Schemes for the Interference Channel: An Interference-Dependent HK Region

The capacity of the two-user interference channel is a long-standing open problem in multiuser information theory. The classical Han–Kobayashi (HK) region remains the largest known achievable region. Recently, a multicoding scheme employing heterogeneous superposition coding and random binning was proposed and claimed to recover the same rate region as HK. However, subtle differences in the message variable-dependency assumptions and the use of random binning prompt a closer examination of the precise equivalence between these regions. This letter revisits the multicoding approach by considering a more general input distribution that allows for interdependent message variables, yielding a new, non-compact representation of the achievable region. Through a novel multicoding scheme involving homogeneous superposition coding, random binning, and joint decoding, we reveal the impact of interference-dependent constructions and establish a framework for direct comparison with the HK region. Inspired by Wyner’s and Gács–Körner’s common information theory, we adopt a simple dependency structure for the auxiliary variables, thereby showing that the proposed interference-dependent HK region generalizes the classical HK region and subsumes it as a special case.