Design Of Nested QC-LDPC Codes For Compute-forward Multiple Access

Multiple access channel（MAC）is a kind of common channel which is widely concerned and studied in the field of wireless communication.Many communication links can be modeled as this channel,such as uplink link of cellular mobile communication system and satellite communication system.In the traditional multiple access scheme,the whole capacity region of MAC channel can be realized by successive interference cancellation and time sharing or rate-splitting multiple access technique,at the cost of increasing system complexity and communication delay.With the comprehensive deployment and promotion of 5th generation mobile communication technology（5G）,the number of devices and the amount of data in wireless channel will increase sharply.In order to ensure that multiple devices can com-municate stably and efficiently with base stations at the same time,it is necessary to find a multi-access scheme with low complexity and low communication delay.Compute-forward multiple access（CFMA）is a new-type of multiple access scheme devel-oped in recent years.The advantage of this scheme is that the capacity region of the whole MAC channel can be realized without time sharing or rate splitting,which can greatly sim-plify the processing process of the detection and decoding module of the receiver.Low density parity check（LDPC）code is a kind of error correction code with excellent perfor-mance,and has been adopted as a coding scheme for 5G data channel.This paper aims to analyze and design nested QC-LDPC codes suitable for CFMA,and give an efficient and low-complexity soft detection algorithm.The specific research content is as follows:In the CFMA system with high quadrature amplitude modulation（QAM）and LDPC code,it is necessary to convey the bit-order soft decision information into the iterative decoder.Therefore,the detector at the front of the decoder needs to calculate the log-likelihood ratio（LLR）.When the original algorithm is used,the computational complexity is higher and it is not suitable for implementation by hardware.Based on the orthogonality and symmetry of QAM modulation constellation,a soft detection algorithm with low complexity is proposed in this paper.Compared with the original algorithm,the new one can greatly reduce the number of exponential operations in the calculation formulas.Furthermore,we obtain a soft detection algorithm with lower complexity and easier hardware implementation by elimi-nating the logarithm and exponential operations in the formulas by means of mathematical approximation.On the other hand,this paper aims to analyze and construct nested irregular QC-LDPC codes suitable for CFMA.Based on the Gaussian consistency hypothesis,an modified protograph-based extrinsic information transfer（P-EXIT）technique is proposed firstly.This technique can not only be used to compute the iterative decoding threshold in the first decoding stage of CFMA system,but also be used to generate the basis matrix or masking matrix with optimal degree distribution under given conditions.In order to simplify the calculation of P-EXIT,we derive a formula for calculating the standard deviation of channel output LLR based on Monte Carlo method.And then,a extending technique with constant code length is applied to construct nested QC-LDPC codes.The numerical simulation results show that the irregular QC-LDPC code constructed by the scheme proposed in our paper have good iterative decoding performance at low signal-noise ratio,and the error floor does not appear when the bit error rate reaches 10^-6.