Abstract
This work presents a modified extended key equation algorithm in list decoding of generalized Reed-Solomon (GRS) codes. A list decoding algorithm of generalized Reed-Solomon codes has two steps, interpolation and factorization. The extended key equation algorithm (EKE) is an interpolation-based approach with a lower complexity than Sudan's algorithm. To increase the decoding speed, this work proposes a modified EKE algorithm to perform codeword checking prior to such an interpolation process. Since the evaluation mapping is engaged in encoding, a codeword is not generated systematically. Thus, the transmission information is not directly obtained from a received codeword. Therefore, the proposed algorithm undertakes a matrix operation to obtain the transmission information once a received vector has been checked to be error-free. Simulation results demonstrate that the modified EKE algorithm in list decoding of a GRS code provides low complexity, particularly at high signal-to-noise ratios.
Highlights
Reed-Solomon (RS) codes are currently used in a wide variety of applications, ranging from data storage systems, mobile communications, to satellite communications
For CDMA2000 high-rate broadcast packet data air interface [1], they are expected to be adopted as outer codes in concatenated coding schemes for future fourthgeneration (4G) wireless systems
At a frame-error-rate (FER) of 10−5, the KV algorithm can achieve a coding gain of about 1 dB over the Guruswami and Sudan (GS) algorithm, for a (255, 144) generalized Reed-Solomon (GRS) code transmitted over an additive white Gaussian noise (AWGN) channel using 256-QAM modulation [13]
Summary
Reed-Solomon (RS) codes are currently used in a wide variety of applications, ranging from data storage systems, mobile communications, to satellite communications. A decoded codeword c∗ is chosen if the Hamming distance between c∗ and r is τ or less Because solving these interpolation equations of Sudan’s algorithm with a naıve Gaussian elimination requires the time complexity O(n3), an EKE algorithm has been presented to decrease this complexity [12]. At a frame-error-rate (FER) of 10−5, the KV algorithm can achieve a coding gain of about 1 dB over the GS algorithm, for a (255, 144) GRS code transmitted over an additive white Gaussian noise (AWGN) channel using 256-QAM modulation [13] Those approaches have a drawback, that is codeword checking is absent during decoding. Regardless of whether the received sequence is correct or not, the decoding algorithm proceeds to decode it This work overcomes this drawback by presenting a modified EKE algorithm with codeword checking.
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