Convergence of weighted min-sum decoding via dynamic programming on trees
Applying the max-product (and sum-product) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence or optimality of converged solutions or both. This paper presents an analysis of both attenuated max-product decoding and weighted min-sum decoding for low-density paritycheck (LDPC) codes, which guarantees convergence to a fixed point when a weight factor, β is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-programming (LP) and maximumlikelihood (ML) decoding solution. For (dv, dc)-regular LDPC codes, the weight factor must satisfy.©2013 IEEE.
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