Abstract
This paper considers Bose-Chaudhuri-Hocquenghem (BCH) codes for distributed source coding. A feedback channel is employed to adapt the rate of the code during the decoding process. The focus is on codes with short block lengths for independently coding a binary source X and decoding it given its correlated side information Y. The proposed codes have been analyzed in a high-correlation scenario, where the marginal probability of each symbol, X i in X, given Y is highly skewed (unbalanced). Rate-adaptive BCH codes are presented and applied to distributed source coding. Adaptive and fixed checking strategies for improving the reliability of the decoded result are analyzed, and methods for estimating the performance are proposed. In the analysis, noiseless feedback and noiseless communication are assumed. Simulation results show that rate-adaptive BCH codes achieve better performance than low-density parity-check accumulate (LDPCA) codes in the cases studied.
Highlights
1 Introduction In this paper, we address the use of Bose-ChaudhuriHocquenghem (BCH) codes in distributed source coding (DSC) with feedback
An initial study on RA BCH codes was presented in [15], where we proposed a model for RA BCH codes: we demonstrated that BCH codes were able to outperform low-density parity-check accumulate (LDPCA)
We compare our methods with LDPCA codes
Summary
Rate adaptation is performed incrementally and controlled by the decoder by means of a feedback channel This is a quite common assumption in LDPCA and Turbo code-based DVC [5,6]. A check of the decoded result may be requested and performed based on additional syndromes of the RA BCH code or cyclic redundancy checking (CRC). When performing the check through the request of extra syndromes, we can request δ(s) extra syndrome(s) (whose transmission requires c(s) bits) and let the Berlekamp-Massey algorithm continue one or more steps: if the result is not consistent with the extra check syndrome(s), the RA BCH decoder is forced to start the decoding process again.
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