  We recently showed in [1] the superiority of certain structured coding
matrices ensembles (such as partial row-orthogonal) for sparse superposition
codes when compared with purely random matrices with i.i.d. entries, both
information-theoretically and under practical vector approximate
message-passing decoding. Here we generalize this result to binary input
channels under generalized vector approximate message-passing decoding [2].We
focus on specific binary output channels for concreteness but our analysis
based on the replica symmetric method from statistical physics applies to any
memoryless channel. We confirm that the "spectral criterion" introduced in [1],
a coding-matrix design principle which allows the code to be capacity-achieving
in the "large section size" asymptotic limit, extends to generic memoryless
channels. Moreover, we also show that the vanishing error floor property [3] of
this coding scheme is universal for arbitrary spectrum of the coding matrix.
