Analysis on Tailed Distributed Arithmetic Codes for Uniform Binary Sources

Distributed arithmetic coding (DAC) is a variant of AC that can realize Slepian-Wolf coding in a nonlinear way. In our previous work, we defined codebook cardinality spectrum (CCS) and Hamming distance spectrum (HDS) for DAC. In this paper, we make use of CCS and HDS to analyze tailed DAC, which is a form of DAC that, as traditional AC, maps the last few symbols of each source block onto non-overlapped intervals. First, we derive the exact HDS formula for tailless DAC, a form of DAC that maps all the symbols of each source block onto overlapped intervals, and show that the HDS formula previously given is in fact approximation. Then, the HDS formula is extended to tailed DAC. Using CCS, we also deduce the average codebook cardinality, which is closely related to decoding complexity, and rate loss of tailed DAC. The effects of tail length are extensively analyzed. It is revealed that by increasing tail length to a value not close to the bitstream length, closely spaced codewords within the same codebook can be removed at the cost of a higher decoding complexity and a larger rate loss. Finally, theoretical analyses are verified by experiments.