  Sparse regression codes (SPARC) connect the sparse signal recovery framework
of compressive sensing with error control coding techniques. SPARC encoding
produces codewords which are \emph{sparse} linear combinations of columns of a
dictionary matrix. SPARC decoding is accomplished using sparse signal recovery
algorithms. We construct dictionary matrices using Gold codes and mutually
unbiased bases and develop suitable generalizations of SPARC (GSPARC). We
develop a greedy decoder, referred as match and decode (MAD) algorithm and
provide its analytical noiseless recovery guarantees. We propose a parallel
greedy search technique, referred as parallel MAD (PMAD), to improve the
performance. We describe the applicability of GSPARC with PMAD decoder for
multi-user channels, providing a non-orthogonal multiple access scheme. We
present numerical results comparing the block error rate (BLER) performance of
the proposed algorithms for GSPARC in AWGN channels, in the short block length
regime. The PMAD decoder gives better BLER than the approximate message passing
decoder for SPARC. GSPARC with PMAD gives comparable and competitive BLER
performance, when compared to other existing codes. In multi-user channels,
GSPARC with PMAD decoder outperforms the sphere packing lower bounds of an
orthogonal multiple access scheme, which has the same spectral efficiency.
