Optimized Distributed Quasi-GRS-Coded Cooperation with Split Labeling Diversity

In this paper, a distributed quasi-generalized Reed–Solomon (Q-GRS)-coded cooperative split labeling diversity (DQ-GRSCC-SLD) scheme is proposed to support reliable cooperative transmission of small-volume information in typical scenarios such as device-to-device (D2D) communication, vehicular ad hoc networks (VANETs) and wireless sensor networks. The system employs distinct labeling mappers at the source and the relay, enabling single-antenna transmission while constructing equivalently a dual-antenna labeling diversity model at the destination, which enhances interference resistance and reduces transmission costs. In addition, an ingenious design is proposed to ensure that the destination obtains the joint Q-GRS code. To optimize the weight distribution of the joint code, a traversal search (TS) algorithm is developed. Furthermore, a low-complexity joint decoding algorithm for Q-GRS codes, namely bracketing decoding, is presented by leveraging the efficient decoding algorithm of generalized Reed–Solomon (GRS) codes. Compared to the conventional maximum likelihood (ML) decoding, its complexity has been reduced from comparing qk codewords to evaluating q or q+1 promising codewords. A theoretical performance analysis of the DQ-GRSCC-SLD scheme is provided. Simulation results reveal that the proposed DQ-GRSCC-SLD scheme demonstrates its superior performance under practical scenarios.