Block Orthogonal Sparse Superposition (BOSS) codes are a promising class of joint coded modulation techniques that can closely approach the finite-blocklength capacity with low-complexity decoding at low code rates under Gaussian channels. However, in fading channels, the performance of BOSS codes degrades considerably due to varying channel fading effects on coded symbols. This paper presents a unified approach to extending BOSS codes to practical fading scenarios and introduces novel joint demodulation and decoding solutions. For fast-fading channels, we propose a minimum mean square error approximation maximum a posteriori (MMSE-A-MAP) algorithm that integrates demodulation and decoding when channel state information is available at the receiver (CSIR). Additionally, for block-fading channels without CSIR, we introduce a joint demodulation and decoding method, referred to as the non-coherent sphere decoding (NSD) algorithm. Simulation results demonstrate that BOSS codes with MMSE-A-MAP decoding outperform 5G polar codes, while the NSD algorithm achieves performance comparable to quasi-maximum likelihood decoding but with significantly reduced complexity. Both decoding methods can be implemented for parallel processing, allowing them to meet low-latency requirements. Furthermore, real-time simulations on a software-defined radio testbed validate the feasibility of using BOSS codes for low-power transmission.

Low-rate and short-packet transmissions are important for ultra-reliable low-latency communications (URLLC). In this paper, we put forth a new family of sparse superposition codes for URLLC, called block orthogonal sparse superposition (BOSS) codes. We first present a code construction method for the efficient encoding of BOSS codes. The key idea is to construct codewords by the superposition of the orthogonal columns of a dictionary matrix with a sequential bit mapping strategy. We also propose an approximate maximum a posteriori probability (MAP) decoder with two stages. The approximate MAP decoder reduces the decoding latency significantly via a parallel decoding structure while maintaining a comparable decoding complexity to the successive cancellation list (SCL) decoder of polar codes. Furthermore, to gauge the code performance in the finite-blocklength regime, we derive an exact analytical expression for block-error rates (BLERs) of single-layered BOSS codes in terms of relevant code parameters. Lastly, we present a cyclic redundancy check aided-BOSS (CA-BOSS) code with simple list decoding to boost the code performance. Our experiments verify that CA-BOSS codes with the simple list decoder outperform CA-polar codes with SCL decoding in the low-rate and finite-blocklength regimes while achieving the finite-blocklength capacity upper bound within one dB of signal-to-noise ratio.

Block orthogonal sparse superposition (BOSS) codes are a class of sparse superposition codes with orthogonality among sub-codewords. This orthogonal structure allows using a near-optimal maximum a posteriori (MAP) decoder with low complexity. Multi-path fading environments, however, destroy the intrinsic orthogonal property of BOSS codewords and result in a catastrophic loss of decoding performance. In this paper, we suggest a novel decoding algorithm of BOSS codes for multi-path fading channels. The proposed decoder comprises two-stage operations: i) minimum mean square error (MMSE) equalization and ii) approximate element-wise MAP decoding. The MMSE equalization restores the orthogonality in the codewords. Then, the element-wise MAP decoding identifies the non-zero positions of sparse message vectors. It turns out that BOSS codes with the proposed decoder provide a considerable performance improvement in terms of block error rate compared to polar codes in the short blocklength regime, while requiring polynomial time decoding complexity. To verify the performance gains, we provide simulation results. We also study the possibility of covert communications using BOSS codes.