Cooperative Transmission Through Signal-Superposition-Based Braid Coding

Abstract

This paper investigates a cooperative transmission scheme for a multisource single-destination system through superposition modulation based on braid coding. The source nodes take turns transmitting, and each time, a source “overlays” its new data together with (some or all of) what it overhears from its partner(s), in a way similar to French braiding the hair. We show that the proposed “braid coding” cooperative scheme benefits not only from the cooperative diversity but from the bit error rate (BER) performance gain as well. We introduce two subclasses of braid coding, namely, the nonregenerative and regenerative cases, and, using the pairwise error probability (PEP) as a figure of merit, derive the optimal weight parameters for each one. By exploiting the structure relevance of braid codes with trellis codes, we propose a Viterbi maximum-likelihood (ML) decoding method of linear complexity for the regenerative case; we also investigate and compare several linear detectors for the nonregenerative case. We analyze the theoretical BER performance of the proposed scheme and prove that the full diversity order can be achieved using braid coding. Moreover, we discuss the memory size that strikes the best balance between performance and complexity by considering both the (Euclidean) free distance and the diversity order. The proposed braid coding can be viewed as a special case of network coding. Finally, we present soft-iterative joint channel–network decoding. The overall decoding process is divided into forward message passing and backward message passing, which makes effective use of the available reliability information from all the received signals. Simulation results confirm the efficacy and efficiency of the proposed scheme.