Information Theory and Reliable Communication
Information Theory and Reliable Communication
Decoding error-correcting codes via linear programming
Decoding error-correcting codes via linear programming
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
Adaptive Methods for Linear Programming Decoding
IEEE Transactions on Information Theory
Nonlinear programming approaches to decoding low-density parity-check codes
IEEE Journal on Selected Areas in Communications
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In this paper we present a three-stage decoding strategy that combines quantized and un-quantized belief propagation (BP) decoders with a mixed-integer linear programming (MILP) decoder. Each decoding stage is activated only when the preceding stage fails to converge to a valid codeword. The faster BP decoding stages are able to correct most errors, yielding a short average decoding time. Only in the rare cases when the iterative stages fail is the slower but more powerful MILP decoder used. The MILP decoder iteratively adds binary constraints until either the maximum likelihood codeword is found or some maximum number of binary constraints has been added. Simulation results demonstrate a large improvement in the word error rate (WER) of the proposed multi-stage decoder in comparison to belief propagation. The improvement is particularly noticeable in the low crossover probability (error floor) regime. Through introduction of an accelerated "active-set" version of the quantized BP decoder we significantly speed up the pace of simulation to simulate low density parity check (LDPC) codes of length up to around 2000 down to a WER of around 10-10 on the binary symmetric channel. We demonstrate that for certain codes our approach can efficiently approach the optimal ML decoding performance for low crossover probabilities.