Approximation of Initial Coset Cardinality Spectrum of Distributed Arithmetic Coding for Uniform Binary Sources

Distributed Arithmetic Coding (DAC) is a practical realization of Slepian-Wolf coding, one of whose properties is Coset Cardinality Spectrum (CCS). The initial CCS is especially important because it has many applications. Up to now, the initial CCS is calculable only for some discrete rates, while in general cases, the time-consuming numerical algorithm is needed. Though a polynomial approximation of the initial CCS has been proposed recently, its complexity becomes very high as code rate decreases. Hence, this letter aims at finding simpler approximations for the initial CCS at low rates by proposing two methods: interpolation approximation and bell-shaped approximation. The effectiveness of both methods is illustrated by simulation results.