Generalized Approximate Message-Passing Decoder for Universal Sparse Superposition Codes

Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it was discovered that these codes are universal, in the sense that they achieve capacity over any memoryless channel under generalized approximate message-passing (GAMP) decoding [2], although this decoder has never been stated for SS codes. In this contribution we introduce the GAMP decoder for SS codes, we confirm empirically the universality of this communication scheme through its study on various channels and we provide the main analysis tools: state evolution and potential. We also compare the performance of GAMP with the Bayes-optimal MMSE decoder. We empirically illustrate that despite the presence of a phase transition preventing GAMP to reach the optimal performance, spatial coupling allows to boost the performance that eventually tends to capacity in a proper limit. We also prove that, in contrast with the AWGNC case, SS codes for binary input channels have a vanishing error floor in the limit of large codewords. Moreover, the performance of Hadamard-based encoders is assessed for practical implementations

Replica Analysis and Approximate Message Passing Decoder for Superposition Codes

Superposition codes are efficient for the Additive White Gaussian Noise channel. We provide here a replica analysis of the performances of these codes for large signals. We also consider a Bayesian Approximate Message Passing decoder based on a belief-propagation approach, and discuss its performance using the density evolution technic. Our main findings are 1) for the sizes we can access, the message-passing decoder outperforms other decoders studied in the literature 2) its performance is limited by a sharp phase transition and 3) while these codes reach capacity as $B$ (a crucial parameter in the code) increases, the performance of the message passing decoder worsen as the phase transition goes to lower rates.Comment: 5 pages, 5 figures, To be presented at the 2014 IEEE International Symposium on Information Theor

a novel physical layer scheme based on superposition codes

Abstract The recently proposed superposition codes (SCs) have been mathematically proved to be decoded at any rate below the capacity, for additive white Gaussian noise (AWGN) channels. The main objective of this paper is to study the feasibility of a novel SC approach as an alternative to the traditional way of designing modern physical (PHY) layer schemes. Indeed, currently, PHY solutions are based on the decomposition into two separate problems of modulation shaping and coding over finite alphabets. Since superposition codes are defined over real numbers, modulation and coding can be jointly realized. Moreover, a fast decoding method is developed and tested by comparing the obtained results with both the uncoded system performance and two approximate message passing (AMP) algorithms. Finally, possible perspective to fifth generation (5G) applications exploiting SC solutions are outlined in the paper, and some interesting relations with sparse signal recovery are analyzed for further future research lines