Low-Complexity Sparse Superimposed Coding for Ultra Reliable Low Latency Communications

TL;DR

This work addresses the challenge of achieving ultra-reliable low-latency communications with short packets by reducing the encoding and decoding complexity of sparse superimposed coding (SSC). It introduces a low-complexity SSC that employs a sparse Bernoulli codebook, enabling complexity reductions through a sparsity factor $R = D/M$ while maintaining reliable performance. Encoding splits information into an index part $b_I$ and a symbol part $b_S$, with $b_I = \left\lfloor \log_2(NK) \right\rfloor$ and $b_S = K \log_2(M_{\mathrm{mod}})$, and spreads the sparse vector via a sparse codebook $\bar{A} = \sqrt{1/R}\, G \odot A$. Decoding uses a Multipath Matching Pursuit (MMP) on the sparse measurement matrix $\Phi = \mathbf{F H_T F}^H \bar{A}$, leveraging sparsity to reduce complexity, and demonstrates that for $R$ around $0.3$–$0.5$ the scheme attains a favorable complexity-reliability trade-off, with robustness across block lengths and competitive performance relative to conventional SSC and SVC. The results suggest that the proposed sparse SSC is a practical URLLC candidate when sparsity is managed appropriately, offering substantial gains for resource-constrained scenarios.

Abstract

Sparse superimposed coding (SSC) has emerged as a promising technique for short-packet transmission in ultra-reliable low-latency communication scenarios. However, conventional SSC schemes often suffer from high encoding and decoding complexity due to the use of dense codebook matrices. In this paper, we propose a low-complexity SSC scheme by designing a sparse codebook structure, where each codeword contains only a small number of non-zero elements. The decoding is performed using the traditional multipath matching pursuit algorithm, and the overall complexity is significantly reduced by exploiting the sparsity of the codebook. Simulation results show that the proposed scheme achieves a favorable trade-off between BLER performance and computational complexity, and exhibits strong robustness across different transmission block lengths.

Figures (6)

• Figure 1: Diagram of the sparse mapping process of SSC scheme. $b$ bits of information are mapped to a sparse vector of length $N=8$ and containing $K=2$ non-zero elements.
• Figure 2: Encoding complexity vs. the value of $b_{\rm I}$.
• Figure 3: BLER performances of different schemes vs. SNR over Rayleigh channels with $K=2$, $N=257$, $M=128$ and $b=19$.
• Figure 4: BLER performances of different schemes vs. SNR over Rayleigh channels with $K=4$, $N=240$, $M=117$ and $b=35$.
• Figure 5: BLER performances vs. sparsity factor $R$ over Rayleigh channels with $K=4$, $N=240$, $M=117$ and $b=35$.