  Block orthogonal sparse superposition (BOSS) code is a class of joint coded
modulation methods, which can closely achieve the finite-blocklength capacity
with a low-complexity decoder at a few coding rates under Gaussian channels.
However, for fading channels, the code performance degrades considerably
because coded symbols experience different channel fading effects. In this
paper, we put forth novel joint demodulation and decoding methods for BOSS
codes under fading channels. For a fast fading channel, we present a minimum
mean square error approximate maximum a posteriori (MMSE-A-MAP) algorithm for
the joint demodulation and decoding when channel state information is available
at the receiver (CSIR). We also propose a joint demodulation and decoding
method without using CSIR for a block fading channel scenario. We refer to this
as the non-coherent sphere decoding (NSD) algorithm. Simulation results
demonstrate that BOSS codes with MMSE-A-MAP decoding outperform CRC-aided polar
codes, while NSD decoding achieves comparable performance to quasi-maximum
likelihood decoding with significantly reduced complexity. Both decoding
algorithms are suitable for parallelization, satisfying low-latency
constraints. Additionally, real-time simulations on a software-defined radio
testbed validate the feasibility of using BOSS codes for low-power
transmission.
