The box-minus operator and its application to low-complexity belief propagation decoding

For iterative decoding of turbo codes and low-density parity check (LDPC) codes quite often log-likelihood ratios called L-values are used. A major role in the decoding algorithms is played by extrinsic information which is obtained as L-value of a modulo 2 combination of several bits. This leads in the L-domain to the so-called box-plus operation. In this paper we introduce a complementary box-minus operation. Based on it a low-complexity but powerful belief propagation algorithm for decoding of LDPC codes is described. This lookup-sum algorithm uses lookup-tables for correction functions to efficiently approximate box-plus and box-minus operations and its capabilities are demonstrated by complexity comparisons and simulation results.