Asymptotic Error-Correcting Performance of Joint Source-Channel Schemes based on Arithmetic Coding

In joint source-channel (JSC) schemes based on arithmetic coding (AC), additional redundancy may be introduced in order to reduce transmission errors. The purpose of this work is to provide analytical tools to predict and evaluate the effectiveness of that redundancy. Integer binary AC is modeled by a reduced-state automaton in order to obtain a bit-clock trellis of the AC. Considering AC as a trellis code, distance spectra are then derived. In particular, an algorithm to compute the free distance of an arithmetic code is proposed. The obtained code properties allow to compute upper bounds on both bit error and symbol error probabilities and thus provide an objective criterion to analyze the behavior of JSCAC schemes when used on noisy channels