Frequency-hop spread-spectrum packet radio with Hermitian codes

Hermitian codes are an attractive alternative to Reed-Solomon codes for use in frequency-hop (FH) spread-spectrum packet radio networks. For a given alphabet size, a Hermitian code has a much longer block length than a Reed-Solomon code. This and other considerations suggest that Hermitian codes may be superior for certain applications. Analytical results are developed for the evaluation of the packet error probability for FH transmissions using Hermitian coding. We find there are several situations for which Hermitian codes provide much lower packet error probabilities than can be obtained with Reed-Solomon codes. In general, as the code rate decreases or the symbol alphabet size increases, the relative performance of Hermitian codes improves with respect to Reed-Solomon codes. Performance evaluations are presented for an additive white Gaussian noise channel and for a catastrophic partial-band interference channel, and the packet error probability is evaluated for both errors-only and errors-and-erasures decoding.