Optimization of short sparse regression codes for gaussian and rayleigh fading channels

Abstract

As a 5G service category, ultra-reliable low-latency communication (URLLC) raises the challenge of dramatically improving the reliability of short message transmission, for which sparse regression codes (SRCs) and their variations, e.g., sparse vector codes (SVCs), have emerged as promising solutions. SRCs have attracted much attention because they are capacity-achieving under the approximate message-passing decoder in polynomial time when power allocation or spatial coupling is applied. However, they suffer from small minimum Euclidean distance and diversity order for the short block length regime, which are crucial measures characterizing their error performance in Gaussian and Rayleigh fading channels. Since the codewords of SRCs are generated by a coding matrix left-multiplying a sparse vector, we first optimize the minimum Euclidean distance of SRCs concerning careful choices of sparse vectors. Then we optimize the diversity order of SRCs by designing a unitary matrix to left-multiply the codewords of SRCs. For the Gaussian channel, we propose the SD-MinVC algorithm to search for a sparse vector set that satisfies a certain minimum Euclidean distance constraint, which is a constant weight code (CWC) design problem. To improve the code rate of CWC, we generalize CWC to M-ary CWC (M-CWC) in which the 1’s in the codewords are generalized to be M-ary phase symbols. By our search algorithm, the codebook size of M-CWC is at least 4 times that of CWC. In addition, we formulate a theorem to construct the M-CWC from CWC and theoretically analyze the improvement in the minimum Euclidean distance. Then we apply the M-CWC to M-CWC SVCs (M-CWC-SVC), and the anticipated performance gain of the resultant M-CWC-SVC over SVCs is verified by simulation. Additionally, our simulation results show that the proposed M-CWC-SVC outperforms the state-of-the-art SVC-based schemes by about 1 dB gain in E_b/N₀ at BLER of 1e-5 under the maximum likelihood (ML) decoder. For the Rayleigh fading channel, we proposed an enhanced version of M-CWC-SVC, abbreviated as M-CWC-uSVC, by introducing a unitary matrix transform. While maintaining the minimum Euclidean distance of M-CWC-SVC, the diversity order of M-CWC-uSVC is optimized concerning the design of the unitary matrix. The genetic algorithm is applied to search for a good unitary matrix. Simulation results show the M-CWC-uSVC achieves a 3dB gain in E_s/N₀ at BLER of 1e-3 over the Rayleigh fading channel under the ML decoder. Furthermore, we developed the multi-path matching pursuit-maximum likelihood (MMP-ML) decoder, which can be specialized as either a multi-path matching pursuit (MMP) decoder for decoding simplicity or an ML decoder for enhanced performance, simply by adjusting a specific parameter. It provides a flexible trade-off between the decoding complexity and its error performance. This allows the M-CWC-uSVC to cater to varying requirements and scenarios when integrated with the MMP-ML decoder. Our simulation results demonstrate that M-CWC-uSVC achieves lower BLER than SVCs with affordable complexity over the Gaussian and Rayleigh fading channels.

Date of Award	2024
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Wai Ho MOW (Supervisor)