Sparse superposition codes under VAMP decoding with generic rotational invariant coding matrices

Understand

Sparse superposition codes were originally proposed as a capacity-achieving communication scheme over the gaussian channel, whose coding matrices were made of i.i.d.

• gaussian entries.We extend this coding scheme to more generic ensembles of rotational invariant coding matrices with arbitrary spectrum, which include the gaussian ensemble as a special case.
• We further introduce and analyse a decoder based on vector approximate message-passing (VAMP).Our main findings, based on both a standard replica symmetric potential theory and state evolution analysis, are the superiority of certain structured ensembles of coding matrices (such as partial row-orthogonal) when compared to i.i.d.
• matrices, as well as a spectrum-independent upper bound on VAMP's threshold.