Abstract:

Recently,the information bottleneck (IB) method has been successfully applied to the design of quantization decoders for LDPC codes.The resulting high performance quantization decoder can approach the performance of the floating-point SPA (Sum-Product Algorithm) decoder by using only 4 quantization bits.Moreover,the LDPC IB decoder deals only with unsigned integers and replaces complex check node operations by simple lookup tables,and thus is very suitable for practical implementations.However,the number of table lookups is proportional to the square of the node degrees,which is unfavorable for LDPC codes with large node degrees,such as the finite geometric LDPC codes and high-rate LDPC codes.To deal with this issue,an improved scheme for the design of IB decoders is proposed based on the forward-backward algorithm.In the proposed scheme,the node operations based on the forward-backward algorithm can be divided into three steps:forward table lookup pass,backward table lookup pass,and extrinsic information generation.To reduce the memory space,a careful design can be carried such that the forward and backward table look-up passes share the same set of lookup tables.When generating extrinsic information,nodes make full use of the intermediate messages generated by forward and backward table lookups,and effectively remove redundant calculations,thus resulting in a total number of table lookups linear with node degrees.Numerical results are provided to demonstrate the effectiveness of the proposed LDPC IB decoder.

Key words: low-density parity-check codes, quantization, the information-bottleneck algorithm, the forward-backward algorithm, iterative decoding