  We present a joint source-channel multiple description (JSC-MD) framework for
resource-constrained network communications (e.g., sensor networks), in which
one or many deprived encoders communicate a Markov source against bit errors
and erasure errors to many heterogeneous decoders, some powerful and some
deprived. To keep the encoder complexity at minimum, the source is coded into K
descriptions by a simple multiple description quantizer (MDQ) with neither
entropy nor channel coding. The code diversity of MDQ and the path diversity of
the network are exploited by decoders to correct transmission errors and
improve coding efficiency. A key design objective is resource scalability:
powerful nodes in the network can perform JSC-MD distributed
estimation/decoding under the criteria of maximum a posteriori probability
(MAP) or minimum mean-square error (MMSE), while primitive nodes resort to
simpler MD decoding, all working with the same MDQ code. The application of
JSC-MD to distributed estimation of hidden Markov models in a sensor network is
demonstrated. The proposed JSC-MD MAP estimator is an algorithm of the longest
path in a weighted directed acyclic graph, while the JSC-MD MMSE decoder is an
extension of the well-known forward-backward algorithm to multiple
descriptions. Both algorithms simultaneously exploit the source memory, the
redundancy of the fixed-rate MDQ, and the inter-description correlations. They
outperform the existing hard-decision MDQ decoders by large margins (up to
8dB). For Gaussian Markov sources, the complexity of JSC-MD distributed MAP
sequence estimation can be made as low as that of typical single description
Viterbi-type algorithms.
