Low-Complexity Belief Propagation Decoding by Approximations with Lookup-Tables

Belief propagation decoding of low-density parity-check codes or one-step majority logic decodable codes has been proven to be a very powerful coding scheme. In this paper an approximation for the belief propagation algorithm, also known as sumproduct decoding, is presented which uses correction functions, implemented as precomputed lookup-tables, to significantly reduce the computational complexity. The new lookup-sum algorithm requires no multiplications, divisions, exponential or logarithmic operations in the iterative process. Already for lookup-tables containing a single entry simulation results show that the performance of non-approximated belief propagation can be approached by 0.1 dB in / 0. With slightly larger tables a performance not noticeably differing from nonapproximated belief propagation can be achieved.

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