Threshold Saturation of Spatially Coupled Sparse Superposition Codes for All Memoryless Channels

Understand

We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel.

• Here we generalize our analysis to a much broader setting.
• We show for any memoryless channel that spatial coupling allows generalized approximate message-passing (GAMP) decoding to reach the potential (or Bayes optimal) threshold of the code ensemble.
• Moreover in the large input alphabet size limit: i) the GAMP algorithmic threshold of the underlying (or uncoupled) code ensemble is simply expressed as a Fisher information; ii) the potential threshold tends to Shannon's capacity.