Bounds on redundancy in constrained delay arithmetic coding

We address the problem of a finite delay constraint in an arithmetic coding system. Due to the nature of the arithmetic coding process, source sequences causing arbitrarily large encoding or decoding delays exist. Therefore, to meet a finite delay constraint, it is necessary to intervene with the normal flow of the coding process, e.g., to insert fictitious symbols. This results in an inevitable coding rate redundancy. In this paper, we derive an upper bound on the achievable redundancy for a memory less source. We show that this redundancy decays exponentially as a function of the delay constraint, and thus it is clearly superior to block to variable methods in that aspect. The redundancy-delay exponent is shown to be lower bounded by log(1/α), where α is the probability of the most likely source symbol. Our results are easily applied to practical problems such as the compression of English text.