In this paper, we propose enhanced Reed-Muller (RM) and Polar decoder for SDN-based C-RAN fronthaul. The simulation results show that our proposed algorithm outperforms traditional decoding algorithm in terms of average number of connected user equipment to RRHs, and the feasibility of decoding the RM codes by the Successive Cancellation (SC) decoding algorithm is verified by comparing the performance and decoding time of the RM and Polar codes under the SC and Belief Propagation (BP) iterative algorithm. The simulation results show that the decoding time of SC decoding algorithm is reduced about 98.98% compared with the BP decoding algorithm. For the BP decoding algorithm with excellent decoding performance but long decoding time, this paper proposes an improved BP decoding algorithm based on early terminating iteration criterion of the absolute values difference for the likelihood, which reduces the computational complexity of criterion. The simulation results illustrate that the early-terminating iteration criterion proposed in this paper reduces the computational complexity, thereby reducing the decoding delay and energy consumption effectively, and satisfying the low complexity and energy consumption decoding requirements.

In this paper, an efficient decoding algorithm is developed to facilitate faster decoding of the binary systematic quadratic residue (QR) codes. It is based on the difference of syndromes (DS), and hence, is called the DS algorithm hereinafter. This new method combines the advantages of the syndrome-weight algorithm and properties of the cyclic codes. Actually, it is a natural generalization of the cyclic weight (CW) algorithm for the (47, 24, 11) QR code developed by Lin et al., and its validity of decoding any binary systematic QR code is also proved. The complexity analysis and simulation results show that the DS algorithm dramatically reduces the decoding complexity without performance loss and considerably requires less memory when compared with previous ones. Utilizing the (47, 24, 11), the (71, 36, 11), the (73, 37, 13), and the (89, 45, 17) QR codes as examples, the DS algorithm not only significantly improves the decoding efficiency, but also saves the memory evidently. When the (23, 12, 7) QR code is considered, the DS algorithm performs almost as well as the currently known best algorithm in terms of decoding efficiency and memory requirements. Thus, all QR codes of lengths less than 100 can be decoded efficiently by using the proposed algorithm. Especially, when the proposed algorithm is applied to decode the (89, 45, 17) QR code, the best one among all the QR codes of lengths less than 100, the decoding speed is raised 26 times and the memory is saved up to 76.6% in comparison with the existing fastest decoding algorithm.

In this study, a new approach is developed to facilitate faster decoding of a binary systematic (71, 36, 11) quadratic residue (QR) code. In this decoder, it simplifies the step of calculating the condition and avoids calculating the unknown syndrome, thereby yielding a fast algebraic decoder for correcting four possible errors. Moreover, while using the proposed algorithm, if uses the channel measurement information proposed by Chase to sequentially invert the bits of the received word until one of the errors is cancelled for the five‐error case and apply the new algebraic decoding algorithm mentioned above to correct the remaining four errors, the algorithm has been verified through a software simulation in C‐language. The simulation shows that the decoding scheme developed here is more efficient than the previous decoding algorithm developed for the (71, 36, 11) QR code and it is naturally suitable for software implementation.

In this paper, a new algebraic method to decode the (71, 36, 11) QR code up to five errors is proposed. It completely avoids computing the unknown syndromes, and uses the previous scheme of decoding this QR code up to three errors, but corrects four and five errors with a new different method. In the four-error case, the new algorithm directly determines the coefficients of the error-locator polynomial by eliminating unknown syndromes in Newton identities. Subsequently, the shift-search algorithm can be utilized to decode the fifth error and the concept of bit reliability is also introduced to accelerate the decoding process. In other words, a weight-five-error pattern can be decoded in terms of the four-error case by inverting an incorrect bit of the received word in ascending order of reliability. Particularly, a threshold parameter γ can be preset to limit the number of inverting bits one by one, and a corresponding upper bound of the probability that decoding fails is derived. Finally, simulation and analysis show that the proposed new decoding algorithm for the abovementioned QR code not only significantly reduces the decoding complexity in terms of CPU time but also saves a lot of memory while maintaining the same error-rate performance. Additionally, the introduction of γ achieves a better tradeoff between the decoding performance and the computational complexity.

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.