Design Of Rate Compatible Spatially Coupled LDPC Codes

Channel coding is one of the key technology of 5G new radio,which plays an important role in improving the network coverage and transmission rate.How to design a channel coding with flexible rate and higher reliability has been a hotspot in this field.Due to the "threshold saturation" property,spatially coupled LDPC codes provide a new way to design capacityapproaching rate-compatible codes.The conventional way to construct rate-compatible spatially coupled LDPC codes is coupling the pre-designed rate-compatible LDPC codes.However,the parity check matrix for each member code needs to be designed,which complicates both the design and the implementation.This paper mainly proposes the construction of the ratecompatible spatially coupled LDPC codes with low complexity and capacity approaching threshold.The details are as follows:(1)Based on the "threshold saturation" property of spatially coupled LDPC codes,we designed a rate-compatible spatially coupled LDPC code that can approach the capacity with low complexity.At each coupling position,a certain fraction of variable nodes is randomly selected and then repeat them for certain times.Rate compatibility is achieved by adjusting the selection fraction and repetition times.The results obtained by the improved differential evolution algorithm show that the optimal thresholds can be obtained when selecting the same fraction of variable nodes and repeating them for the same times at each position.Secondly,we analyzed the decoding complexity of the proposed rate-compatible spatially coupled LDPC codes by computing the number of logarithmic/exponential operations at one iteration and compared it with the classical rate-compatible spatially coupled LDPC codes.The comparison results show that the decoding complexity of the proposed rate-compatible spatially coupled LDPC code is obviously lower than that of the classical rate-compatible spatially coupled LDPC codes.(2)We analyzed the threshold performances of the proposed rate-compatible spatially coupled LDPC codes over the binary erasure channel and the additive white gaussian noise channel.For the binary erasure channel,we derived the density evolution algorithm to calculate the thresholds of the designed rate-compatible spatially coupled LDPC codes.On this basis,we make analysis of the impacts of the selection fraction and repetition times on the threshold performances.Secondly,we derived the extrinsic information transfer function of the designed rate-compatible spatially coupled LDPC code and compute the thresholds for the additive white gaussian noise channel.The results show that the threshold performances of the designed ratecompatible spatially coupled LDPC code are better than those of the classical rate-compatible spatially coupled LDPC code over the binary erasure channel and the additive white gaussian noise channel especially in the lower rate region.Finally,the bit error rate simulation results of the designed rate-compatible spatially coupled LDPC codes are consistent with the threshold results.