A Research On Sparse Superposition Codes And The Corresponding Decoding Algorithms

The demands for massive-user access and the ideas of “connecting everything” will be the focuses of the next generation wireless communication technologies.To solve these problems,a major difficulty lies in designing a low-complexity communication system which can guarantee high reliability as well as high rate simultaneously.An available solution is the usage of the sparse superposition codes,which can reduce the size of the codebook from the exponential level of the blocklength to the polynomial level of the blocklength by virtualizing a point-to-point channel as a multiple-access channel.The channel coding strategy incorporating the sparse superposition codes and the maximum likelihood decoder is demonstrated to be capacity-achieving.However,the cost of the maximum likelihood decoder is tremendous expensive,which is failing to dovetail with our wish of reducing the complexity.The AMP algorithm,which is used to solve sparsity recovery problems in the compressed sensing community at the very beginning,is an excellent algorithm for its ability to achieve the optimal performance and a lower complexity at the same time.Considering our desire to propose a low-complexity decoder,and the similarities of the sparsity recovery problems and the decoding problem of the sparse superposition codes,the classic AMP algorithm is generalized to solve our decoding problem.The consequential AMP decoder has a much lower complexity,of the level of a lower-order polynomial of the blocklength.A series of simulation experiments are conducted later in this thesis for the AMP decoder,by which some conclusions about the algorithm's performance are derived.First,the state evolution equation can predict the convergence performance of the AMP decoder,which is very helpful for the qualitative analysis.Second,the exponential power allocation strategy is optimal in the sense of information theory.Finally,AMP decoder can achieve the channel capacity based on our observation of the experiment results.In spite of these advantages,there is a shortage in the proposed decoder——it does not perform very well in the finite blocklength scheme.To fix this problem,some strategies and technologies in the algorithm need to be further modified.