Abstract
Separate source and channel coding is known to be sub-optimal for communicating correlated sources over a Gaussian multiple access channel (GMAC). This paper presents an approach to designing distributed joint source-channel (DJSC) codes for encoding correlated binary sources over a two-user GMAC, using systematic irregular low-density parity check (LDPC) codes. The degree profile defining the LDPC code is optimized for the joint source probabilities using extrinsic information transfer (EXIT) analysis and linear programming. A key issue addressed is the Gaussian modeling of log-likelihood ratios (LLRs) generated by nodes representing the joint source probabilities in the combined factor graph of the two LDPC codes, referred to as source-channel factor (SCF) nodes. It is shown that the analytical expressions based on additive combining of incoming LLRs, as done in variable nodes and parity check nodes of the graph of a single LDPC code, cannot be used with SCF nodes. To this end, we propose a numerical approach based on Monte-Carlo simulations to fit a Gaussian density to outgoing LLRs from the SCF nodes, which makes the EXIT analysis of the joint decoder tractable. Experimental results are presented which show that LDPC codes designed with the proposed approach outperforms previously reported DJSC codes for GMAC. Furthermore, they demonstrate that when the sources are strongly dependent, the proposed DJSC codes can achieve code rates higher than the theoretical upper-bound for separate source and channel coding.
Highlights
Wireless communication of multiple correlated information sources to a common receiver has become an important research problem due to potential applications in emerging information gathering systems such as wireless sensor networks (WSNs) [1]
In contrast to a previous work, in this paper, we present a distributed joint source-channel (DJSC) code design approach for a pair of correlated binary sources, in which the degree profile of a systematic irregular low-density parity check (LDPC) (SI-LDPC) code is optimized for the joint distribution of the two sources and the signal-tonoise ratio (SNR) of the Gaussian multiple access channel (GMAC)
6 Conclusions An approach to designing a DJSC code with symmetric rates for a pair of correlated binary sources transmitted over a GMAC, based on SI-LDPC codes has been developed
Summary
Wireless communication of multiple correlated information sources to a common receiver has become an important research problem due to potential applications in emerging information gathering systems such as wireless sensor networks (WSNs) [1]. An improved system design based on LDGM codes is presented in [10], which requires an additional channel between each source and the common receiver In another closely related work, Roumy et al [11] consider the joint design of LDPC codes for independent sources transmitted over a two-input GMAC. One of the key issues addressed here is the mutual information computation (as required for EXIT analysis) for messages passed from factor nodes in the joint factor graph of the two LDPC codes, referred to as source channel factor (SCF) nodes, which represent the joint probabilities of the two sources and the output conditional probability density function (pdf ) of the GMAC.
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