ABSTRACT This paper derives the asymptotic symbol error rate (SER) and outage probability of decode‐and‐forward (DF) cooperative communications over Rician fading channels. How to optimally allocate the total power is also addressed when the performance metric in terms of SER or outage probability is taken into consideration. Analysis reveals the insights that Rician factor has a great impact on the system performance as compared with the channel variance, and the relay–destination channel quality is of importance. In addition, the source–relay channel condition is irrelevant to the optimal power allocation design. Simulation and numerical evaluation substantiate the tightness of the asymptotic expressions in the high‐SNR regions and demonstrate the accuracy of our theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.

In this study, an efficient and fast algebraic decoding algorithm (ADA) for the binary systematic quadratic residue (QR) code of length 73 with the reducible generator polynomial to correct up to six errors is proposed. The S(I, J) matrix method given by He et al. (2001) is utilised to compute the unknown syndromes S5. A technique called swap base is proposed to correct the weight-4 error patterns. To correct the weight-5 error patterns, the new error-locator polynomials for decoding the five errors are derived. Finally, the modified shift-search algorithm (SSA) developed by Lin et al. (2010) is applied to correct the weight-6 error patterns. Moreover, the computations of all syndromes are achieved in a small finite field. Simulation results show that the proposed ADA is practical.

It is well-known that the Euclidean algorithm can be used o find the systematic errata-locator polynomial and the errata-evaluator polynomial simultaneously in Berlekamp's key equation that is needed to decode a Reed-Solomon (RS) codes. In this paper, a simplified decoding algorithm to correct both errors and erasures is used in conjunction with the Euclidean algorithm for efficiently decoding nonsystematic RS codes. In fact, this decoding algorithm is an appropriate modification to the algorithm developed by Shiozaki and Gao. Based on the ideas presented above, a fast algorithm described from Blahut's classic book is derivated and proved in this paper to correct erasures as well as errors by replacing the Euclidean algorithm by the Berlekamp-Massey (BM) algorithm. These facts lead to significantly reduce the decoding complexity of the proposed RS decoder. In addition, computer simulations show that this simple and fast decoding technique reduces the decoding time when compared with existing efficient algorithms including the new Euclidean-algorithm-based decoding approach proposed in this paper.