Polar Codes for Multiple Descriptions

Abstract

<p>Two coding schemes based on polar codes are proposed for the multiple description (MD) problem. The first scheme is an adaptation of the one developed by \c{S}a\c{s}o\u{g}lu {\em et al.} for the multiple access channel to the MD setting. Specifically, it is shown that the scheme is able to achieve certain rate pairs on the dominant line of the achievable rate region determined by El Gamal and Cover (EGC) when the associated auxiliary random variables have different prime alphabet sizes. Different from polar coding for the multiple access channel considered by \c{S}a\c{s}o\u{g}lu {\em et al.}, the auxiliary random variables in the MD problem can be dependent, and their alphabet sizes play an unexpected important role in the construction. The second scheme is based on the idea of rate splitting. We show that it can achieve the entire EGC rate region. The effectiveness of the proposed polar coding schemes is verified by the experimental results.</p>