Performance Bounds for Nonbinary Linear Block Codes Over Memoryless Symmetric Channels

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.