Performance bounds for nonbinary linear block codes over memoryless symmetric channels

  • Authors:

  • Eran Hof;Igal Sason;Shlomo Shamai

  • Affiliations:

  • Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel;Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel;Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

The performance of nonbinary linear block codes is studied in this paper via the derivation of new upper bounds on the block error probability under maximum-likelihood (ML) decoding. The transmission of these codes is assumed to take place over a memoryless and symmetric channel. The new bounds, which are based on the Gallager bounds and their variations, are applied to the Gallager ensembles of nonbinary and regular low-density parity-check (LDPC) codes. These upper bounds are also compared with sphere-packing lower bounds. This study indicates that the new upper bounds are useful for the performance evaluation of coded communication systems which incorporate nonbinary coding techniques.