Distributed Arithmetic Coding for the Slepian–Wolf Problem

Distributed joint source-channel arithmetic coding

“…The coding rate increases to r(X; ǫ) = H(X) − log 2 (1 − ǫ) and the presence of µ allows one to drive the MAP decoding algorithm. The second AC modification is based on the insertion of an ambiguity in the encoding process [1] and leads to the definition of the distributed arithmetic coding (DAC). The DAC is obtained using larger probability intervals, i.e., proportional to the modified probabilities p j = α j p j , j = 0, 1 and α j ≥ 1.…”

“…We note that, while the joint encoder is a relatively simple combination of [5] and [1], the joint decoder requires a new design and will be described in Sect. 2.2.…”

“…This complementary approach has led to the design of the DAC decoder [1] evaluating conditional probabilities along a binary search tree where branches are triggered when the numerical value of C falls in the overlapped, i.e. ambiguous, sub-interval.…”

“…The metric (3) can be recast into an additive metric in the logarithmic domain. The term P (X|Y, C) depends on the correlation with the side information and it is the MAP metric used in [1] for the DAC. The term P (R|C)/P (R) depends on the channel transition probability and can be evaluated as in [5].…”

“…a low-density parity-check (LDPC) or turbo code. Alternatively, distributed arithmetic coding (DAC) has also been proposed [1]. DAC uses interval overlap during the arithmetic coding (AC) process to yield and ambiguous compressed description of X; sequential decoding of X with branch metric depending on Y yields results better than turbo and LDPC codes at relatively short block lengths.…”