The minimum probability of error achievable by random codes on the arbitrarily varying channel (AVC) is investigated. New exponential error bounds are found and applied to the AVC with and without input and state constraints. Also considered is a simple subclass of random codes, called randomly modulated codes, in which encoding and decoding operations are separate from code randomization. A universal coding theorem is proved which shows the existence of randomly modulated codes that achieve the same error bounds as "fully" random codes for all AVCs.

It is well known that orthogonal signal sets approach the channel capacity and reliability function of the infinite bandwidth additive white Gaussian noise channel. It is shown that pseudonoise-modulated orthogonal signals play a similar role for the infinite bandwidth Gaussian arbitrarily varying channel.>

The main objective is to develop exponential bounds to the best error probability achievable with random coding on the Gaussian arbitrarily varying channel (GAVC) in the one case where a (strong) capacity exists (i.e., with peak time-averaged power constraints on both the transmitter and interference). The GAVC models a channel corrupted by thermal noise and by an unknown interfering signal of bounded power. The upper and lower bounds to the best error probability achievable on this channel with random coding are presented. The asymptotic exponents of these bounds agree in a range of rates near capacity. The exponents are universally larger than the corresponding exponents for the discrete-time Gaussian channel with the same capacity. It is further shown that the decoder can be taken to be the minimum Euclidean distance rule at all rates less than capacity.>