Generalized approximate message-passing decoder for universal sparse superposition codes
Date
2017-06Source Title
IEEE International Symposium on Information Theory - Proceedings
Print ISSN
2157-8095
Publisher
IEEE
Pages
1593 - 1597
Language
English
Type
Conference PaperItem Usage Stats
230
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Abstract
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 the 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. © 2017 IEEE.
Keywords
Channel codingCodes (symbols)
Decoding
Gaussian noise (electronic)
Information theory
White noise
Additive white Gaussian noise channel
Communication schemes
Memoryless channels
Message passing decoders
Optimal performance
Spatial couplings
State evolutions
Superposition codes
Message passing