Optimized-Goppa Codes Based on the Effective Selection of Goppa Polynomials for Coded-Cooperative Generalized Spatial Modulation Network

This paper proposes a novel optimized-Goppacoded cooperative generalized spatial modulation (OGCCGSM) scheme for short -to -medium information block transmission. In the proposed OGCC-GSM scheme, an efficient Goppa polynomial selection approach is designed to ensure that the selected Goppa codes applied in the source and relay nodes both have the largest minimum Hamming distance (MHD) and the optimal weight distribution. Compared to conventional coded cooperation (CC) with a single antenna, the proposed scheme employs the generalized spatial modulation (GSM) technique to achieve more diversity gains, where each node is equipped with multiple antennas and more than one transmit antenna (TA) is activated at each time -instant transmission. As a benchmark comparison, the OGCC spatial modulation (OGCC-SM) scheme is also investigated with a single TA active. Moreover, the reduced -complexity transmit antenna combination (RC-TAC) selection algorithm utilized in GSM is first developed with the aid of the channel state information (CSI) to reconcile computational complexity and system performance. In addition, joint decoding is conducted on the destination terminal to further enhance the performance of the proposed scheme. The simulated results indicate the performance of the proposed OGCCGSM scheme is superior to that of its benchmark OGCC-SM scheme, with a substantial reduction in the number of TAs. Besides, Monte Carlo simulations demonstrate that the proposed OGCC-GSM scheme prevails over its counterparts by a margin of over 4.2 dB under identical conditions.