Study On Sparse Superposition Codes Based On Compressed Sensing

Sparse superposition codes are a recent class of communication schemes for efficient communication over the AWGN channel and other any memoryless channels.They integrate the encoding and modulation steps into a single process,so they can directly apply in the AWGN channel without a separate modulation process.What's more,they have some properties including encoding easily and decoding in low-complexity.Similar to LDPC codes,there is a phase transition phenomenon produced in the decoding process,it will prevent sparse superposition codes from approaching the channel capacity.Power allocation and spatial coupling can improve this phenomenon,which help sparse superposition codes get a better performance under the condition of finite signal length.In a nutshell,it is of great significance to study these two methods of sparse superposition codes.This thesis focuses on the problems of power allocation and spatial coupling in sparse superposition codes based on the knowledge of compressed sensing and channel coding,and the main innovations shown as follows:1.To solve the problem of unreasonable power allocation among the sections in existing power allocation schemes,a hybrid iterative power allocation scheme is proposed in this thesis.At first,the required minimum power of every section for successful decoding is calculated and allocated to corresponding sections.Then,the remaining power is allocated to all sections in average,and all sections will get sufficient power to against the interference from the noise with the proposed power allocation scheme.The theoretical analysis and simulation results show that,under the condition of low signalto-noise ratio and coding rates approaching the capacity,a stronger ability to against the noise will be obtained with the proposed power allocation scheme,so the decoding accuracy will be higher.2.For finite length signal,it is also a concern to reduce the decoding iterative times in addition to improving the decoding precision for sparse superposition codes.To solve these problems,a double-seeds spatial coupling design matrix which combines the decoding promotion effect of seeds and the propagation effect of coupling structure is proposed in this thesis.A propagation wave is produced by setting the first subsystem and last subsystem a high sampling ratio,which propagates from the seeds at the two ends to the center.Besides,every block matrix is constructed with a matrix constructed method based on the Hadamard square matrix,it can reduce the decoding computation complexity.Then,different variance is allocated to each block to strengthen the coupling structure.Finally,the matrix performance is verified by implementing over different channels with the utilization of generalized approximate message passing decoding algorithm.Theoretical analysis and simulation results show that,under the condition of the same global sampling ratio,a lower decoding error will be obtained with the double-seeds spatial coupling matrix compared to the matrix with only one seed.Besides,the iterative times of the decoding algorithm will be reduced and the probability of successful decoding will be increased.