  We study joint source-channel coding (JSCC) of compressed sensing (CS)
measurements using vector quantizer (VQ). We develop a framework for realizing
optimum JSCC schemes that enable encoding and transmitting CS measurements of a
sparse source over discrete memoryless channels, and decoding the sparse source
signal. For this purpose, the optimal design of encoder-decoder pair of a VQ is
considered, where the optimality is addressed by minimizing end-to-end mean
square error (MSE). We derive a theoretical lower-bound on the MSE performance,
and propose a practical encoder-decoder design through an iterative algorithm.
The resulting coding scheme is referred to as channel- optimized VQ for CS,
coined COVQ-CS. In order to address the encoding complexity issue of the
COVQ-CS, we propose to use a structured quantizer, namely low complexity
multi-stage VQ (MSVQ). We derive new encoding and decoding conditions for the
MSVQ, and then propose a practical encoder-decoder design algorithm referred to
as channel-optimized MSVQ for CS, coined COMSVQ-CS. Through simulation studies,
we compare the proposed schemes vis-a-vis relevant quantizers.
