This talk builds on our recently introduced multiple descriptions coding
paradigm, combinatorial message sharing (CMS), where each subset of the
descriptions is allowed to share a distinct common message, and whose achievable
region subsumes the one due to Venkataramani et al. We show that CMS provides
strict improvement for a general class of settings, including the quintessential
Gaussian source under mean squared error, for which CMS achieves the complete
region for several asymmetric cross-sections. Finally, a random binning scheme
is proposed whose achievable region subsumes the one due to Pradhan et al. By
unifying random binning and conditional codebook techniques, it exploits the
underlying symmetry, while maintaining adaptability to partial asymmetry in
rates and distortions.