Gallager-Type Bounds for Non-Binary Linear Block Codes over Memoryless Symmetric Channels

The performance analysis of non-binary linear block codes is studied under ML decoding where it is assumed that the transmission takes place over memoryless symmetric channels. Gallager-type bounds are derived, and the proposed bounds are exemplified for expurgated regular ensembles of non-binary low-density parity-check (LDPC) codes. These bounds are also compared with classical and recent improved sphere-packing bounds, indicating that these bounding techniques are informative for the performance evaluation of coded communication systems which incorporate non-binary coding techniques.