Distributed Arithmetic Coding (DAC) is an effective implementation ofSlepian-Wolf coding, especially for short data blocks. To research itsproperties, the concept of DAC codeword distribution along proper and wrongdecoding paths has been introduced. For DAC codeword distribution ofequiprobable binary sources along proper decoding paths, the problem wasformatted as solving a system of functional equations. However, up to now, onlyone closed form was obtained at rate 0.5, while in general cases, to find theclosed form of DAC codeword distribution still remains a very difficult task.This paper proposes three kinds of approximation methods for DAC codeworddistribution of equiprobable binary sources along proper decoding paths:numeric approximation, polynomial approximation, and Gaussian approximation.Firstly, as a general approach, a numeric method is iterated to find theapproximation to DAC codeword distribution. Secondly, at rates lower than 0.5,DAC codeword distribution can be well approximated by a polynomial. Thirdly, atvery low rates, a Gaussian function centered at 0.5 is proved to be a good andsimple approximation to DAC codeword distribution. A simple way to estimate thevariance of Gaussian function is also proposed. Plenty of simulation resultsare given to verify theoretical analyses.
展开▼
