2023 Volume 17 Issue 1 Pages 52-58
Sparse superposition codes are error-correcting codes proposed in 2010, which construct codewords by sparsely superposing column vectors of a matrix called a dictionary. These codes can be directly applied to Gaussian channels and have been shown to achieve transmission rates arbitrarily close to the channel capacity. To understand a theoretical limitation, the error probability of optimal decoding (maximum likelihood decoding) without regard to computational complexity has been analyzed. Furthermore, efficient decoding methods have been studied for practical applications, such as approximate message passing (AMP), which is one of the solutions for compressed sensing. In this paper, these topics are introduced with the author's research, in which the performance of maximum likelihood decoding is evaluated when the distribution used for generating the dictionary is greatly simplified.
