本课题将具有良好代数结构且简单适用的Reed-Muller码应用于多中继协作系统中，首先研究双RM码的联合最优设计方法和单中继协作系统目的点译码器联合译码的性能。基于任意RM码的直和生成原理，中继协作系统的源点和中继点分别采用两个低阶RM码，目的点译码器等效采用一个由两个低阶RM通过直和产生的一个高阶RM码。由于中继点RM码“信息位”是源点RM码信息位的子集，因此利用抽象代数中的陪集分解原理并辅以计算机搜索可以寻找到该高阶RM码满足子集条件的具有最大自由距离和最小错误系数的子码，实现双RM码的联合最优设计并基于此研究单中继协作系统目的点译码器的性能。以上双RM码最优设计方法可推广到采用多RM码的任意中继协作系统中。由于具有良好的性能和译码复杂度折衷RM编码中继协作在实际通信系统中具有非常良好的潜在应用价值。

In this research Reed-Muller codes with desirable agebraic properties are first applied to a single-relay cooperation system to perform the jointly optimized double RM codes design and investigate the error performance of joint decoding in the destination. Based on a fundamental principle that any higher order RM code can be decomposed by two lower order RM codes, thus two lower order RM codes employed by the souruce and relay can resulted in an equivalent higher orderer RM code in the destination, whose optimimum subcode with maximum free Hamming distance and least error coefficient can be found out by coset decomposition based on abstract algebraic and by the aid of the proper computer search. In this sense a jointly optimized double RM codes design and the performance of joint decoding in the destination can be carried out. These optimum RM codes construction and performance study can be naturally extended to any relay cooperation with multiple optimized RM codes. This proposed RM coded relay cooperation has great potentials in practical applications due the very good tradeoff between the performance and decoding complexity in the destination.