List decoding of generalized reed-solomon codes by using a modified extended key equation algorithm

  • Authors:

  • Ta-Hsiang Hu;Ming-Hua Chang

  • Affiliations:

  • Department of Electrical Engineering, Da-Yeh University, Dacun, Changhua, Taiwan;Department of Electronic Engineering, Jinwen University of Science and Technology, Hsin-Tien, Taipei, Taiwan

  • Venue:
  • EURASIP Journal on Wireless Communications and Networking
  • Year:
  • 2011

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Abstract

This work presents a modified extended key equation algorithm in list decoding of generalized Reed-Solomon (GRS) codes. A list decoding algorithmof 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.