New Coding Schemes for the Symmetric $K$-Description Problem

We propose novel coding schemes for the $K$-description problem with symmetric rates and symmetric distortion constraints. There are two main new ingredients in these schemes: the first one is akin to the method seen in the well-known butterfly network of network coding literature, and systematic erasure channel codes are applied on certain carefully chosen source coding component; the second approach is built on the quantization splitting technique which was previously proven useful in the Gaussian CEO problem. We first focus on a special case of the three description problem, where any two descriptions are rate-distortion optimal jointly, referred to as the no two description excess rate case. For this special case and the quadratic Gaussian source, we show that the two aforementioned approaches lead to rate-distortion points outside the achievable region based on the source-channel erasure codes, previously proposed by Pradhan, Puri, and Ramchandran. Interestingly, though only the symmetric problem is considered in our work, the proposed schemes in fact benefit from time-sharing several asymmetric rate-distortion points. The insights gained through the no two description excess rate case lead to strategic combination of the new ingredients with the existing coding scheme, yielding new coding schemes for the symmetric $K$-description problem.