  This paper presents a new class of sparse superposition codes for low-rates
and short-packet communications over the additive white Gaussian noise channel.
The new code is orthogonal sparse superposition (OSS) code. A codeword of OSS
codes is represented as a superposition of sparse sub-codewords whose support
sets are mutually non-overlapping. To construct such codewords in a
computationally efficient manner, a successive encoding method is presented.
Harnessing the orthogonal property among sub-codewords, a simple yet
near-optimal decoding method is proposed, which performs element-wise maximum a
posterior decoding with successive support set cancellation. This decoder is
super-fast by a linear decoding complexity in block lengths, far less than the
commercially used channel decoders for modern channel codes. The upper bounds
for the block error rates (BLERs) are analytically derived for few-layered OSS
codes as a function of block lengths and code rates. It turns out that a
single-layered OSS code achieves the ultimate Shannon limit in the
power-limited regime, even with the linear complexity decoder. Via simulations,
the proposed OSS codes are shown to perform better than commercially used coded
modulation techniques for low-rate and short-latency communication scenarios.
