This paper presents a general approach to designing distributed joint source channel (DJSC) codes with arbitrary rates for communication of a pair of correlated binary sources over noisy channels. In this approach, both distributed compression and channel error correction are simultaneously achieved by transmitting, for each source, a fraction of the information bits together with the parity bits of a systematic channel code. This approach is shown to be asymptotically optimal, i.e., any rate-pair in the achievable rate-region can be approached as the codeword length is increased. The practical realization of such a code requi res the design of a pair of channel codes with unequal error protection (UEP) properties determined by the inter-source correlation and the channel capacity available to each source. Towards this end, a linear programming based procedure for jointly optimizing the degree profiles of a pair of irregular LDPC codes to achieve the required UEP properties is presented. Experimental results obtained with both binary symmetric channels and binary-input Gaussian channels are presented, which demonstrate that the proposed UEP-DJSC codes can significantly outperform separate source-channel codes, as well as previously reported joint source-channel coding schemes, particularly for short codeword lengths.

A practical approach to designing distributed joint source channel (DJSC) codes for correlated binary sources using LDPC codes is presented. In this approach, both distributed compression and channel error protection are achieved by optimally puncturing bits of a systematic channel code to match the source correlation and channel error probability. This requires the design of a channel code with a specific unequal error protection (UEP) property. Towards this end, we present a linear-programming based algorithm for optimizing an irregular LDPC code for a given level of source correlation and channel noise. Experimental results are presented for both binary symmetric channels and Gaussian channels, which demonstrate that the proposed DJSC codes can significantly outperform the best code found through random search, tandem source-channel codes and previously reported schemes based on turbo codes when the encoding delay is constrained.