  This paper focuses on the problem of $L-$channel quadratic Gaussian multiple
description (MD) coding. We recently introduced a new encoding scheme in [1]
for general $L-$channel MD problem, based on a technique called `Combinatorial
Message Sharing' (CMS), where every subset of the descriptions shares a
distinct common message. The new achievable region subsumes the most well known
region for the general problem, due to Venkataramani, Kramer and Goyal (VKG)
[2]. Moreover, we showed in [3] that the new scheme provides a strict
improvement of the achievable region for any source and distortion measures for
which some 2-description subset is such that the Zhang and Berger (ZB) scheme
achieves points outside the El-Gamal and Cover (EC) region. In this paper, we
show a more surprising result: CMS outperforms VKG for a general class of
sources and distortion measures, which includes scenarios where for all
2-description subsets, the ZB and EC regions coincide. In particular, we show
that CMS strictly extends VKG region, for the $L$-channel quadratic Gaussian MD
problem for all $L\geq3$, despite the fact that the EC region is complete for
the corresponding 2-descriptions problem. Using the encoding principles
derived, we show that the CMS scheme achieves the complete rate-distortion
region for several asymmetric cross-sections of the $L-$channel quadratic
Gaussian MD problem, which have not been considered earlier.
