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Applying the max-product (and belief-propagation) algorithms to loopy graphs is now quite popular for constraint satisfaction 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 and/or the optimality of converged solutions. This paper presents an analysis of weighted...
We present improvements in linear programming decoding introduced by Feldman et al. with the help of generic integer programming methods. We propose a new IP formulation of the maximum likelihood decoding problem. This formulation makes use of indicator variables which help in detecting violated parity checks immediately. We derive Gomory cuts from our formulation and use them in a separation algorithm...
Simulations have shown that the outputs of min-sum (MS) decoding generally behave in one of two ways: either the output vector eventually stabilizes at a codeword or it eventually cycles through a finite set of vectors that may include both codewords and non-codewords. The latter behavior has significantly contributed to the difficulty in studying the performance of this decoder. To overcome this...
This paper explores ideas for fast linear programming (LP) decoding of low-density parity-check (LDPC) codes. We first propose a modification of adaptive LP decoding, and prove that it performs LP decoding by solving a number of linear programs that contain at most one linear constraint derived from each of the parity-check constraints. Then, as a step toward designing an efficient LP solver that...
The combination of low density parity check (LDPC) Codes and Automatic Repeat reQuest (ARQ) has shown to be a promising option to increase the throughput of a communication system. A recently proposed method uses the decoding result to request unreliable bits for retransmission (reliability-based Hybrid ARQ). Commonly, Belief Propagation is used to decode LDPC codes. The result of this algorithm naturally...
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