Daniel Kariuki Waweru

This paper presents a multi-relay Coded-Cooperative system that integrates Hybrid Automatic Repeat Request and Coded Cooperative Cooperation. It utilizes powerful cyclic Totally Decomposed Cumulative Goppa codes (TDCG codes) known for exceptional performance as best-known linear codes. The destination code is jointly designed by combining TDCG codes from relay and source codes. Optimized relay channel codes improve overall system bit-error-rate performance, aided by a proposed optimization technique. Numerical simulations assess BER performance under various channel conditions with BPSK modulation and coherence detection over flat Rayleigh fading channels. Results show that the TDCG coded-cooperative scheme outperforms non-cooperative approaches and similar coded cooperation techniques with comparable code rates. The integration of HARQ and Coded Cooperative Cooperation enhances wireless communication system reliability and efficiency.

The distributed Goppa coded spatial modulation (DGC‐SM) scheme is proposed in cooperative scenarios. In the proposed DGC‐SM scheme, the relay chooses the partial information from the source by using the idea of information selection, and then re‐encodes the selected information. At the destination, a distributed Goppa code is obtained corresponding to each selection. In order to get the best possible code, an optimal information selection algorithm is proposed at the relay. In the proposed optimal algorithm, all selections and source message sequences are considered, which results in high complexity. Thus, another optimized information selection algorithm with low complexity is proposed at the relay. To further enhance the capability to get the source information, two efficient joint decoding algorithms called smart decoding algorithm and improved smart decoding algorithm are proposed. Moreover, the bit error rate (BER) performance bound of the proposed DGC‐SM scheme is derived. Through the simulations, the effectiveness of the proposed two optimized information selection algorithms is confirmed. Also, it is observed that the simulation and analytical results closely match at high signal‐to‐noise ratio (SNR).

The distributed Goppa-coded generalized spatial modulation (DGC-GSM) scheme with the source, relay, and destination in cooperative communications is proposed, where the source and relay adopt different Goppa codes. Goppa codes have many advantages such as the flexible codeword length, excellent code construction, and easy encoding and decoding complexity. At the relay, we select portions of the source information bits for further encoding. For each selection, the destination constructs a channel code. To obtain the best code in the destination, we propose the optimal information bit selection algorithm at the relay to choose the source information. However, Goppa codes with a large block length will impose high complexity on the optimal algorithm. Thus, the locally optimized selection algorithm is further proposed. At the destination, the joint decoding algorithm is adopted to recover the source information. Our simulated results indicate that the two selection algorithms proposed achieve better performance than the random selection method. This is because the optimized algorithms can generate the code with a larger minimum distance at the destination. Moreover, the proposed DGC-GSM scheme outperforms the non-cooperative system. Moreover, the DGC-GSM scheme can obtain the approximate performance with the distributed Goppa-coded spatial modulation (DGC-SM) scheme but has a significantly reduced transmit antenna number.