# Source Symbol Purging-Based Distributed Conditional Arithmetic Coding
## 1 Introduction
Coding methods of DSC schemes based on channel codes are apparently indifferent with the statistical characteristics of the source. This means that DSC schemes based on channel codes can only use the correlation between the sources, but cannot utilize the internal correlation among symbols of source \(X\). Furthermore, DSC schemes based on channel codes can only exhibit better performances when coding longer blocks of source symbols. In addition to DSC schemes based on channel codes, many scholars have also carried out research on DSC based on source codes. The DSC scheme based on arithmetic coding is the most popular method. Distributed arithmetic coding (DAC) [15] makes use of the characteristics of arithmetic coding that can freely adjust the encoding probability distribution of symbols during the encoding process; it ensures a shorter codelength by purposely expanding the probability interval of each symbol. However, the probability intervals during the coding will be overlapped after the probability interval of each symbol is expanded, which may cause the decoding ambiguity because the received codewords may fall into the overlapping areas during decoding. The decoder needs to create a decoding tree to save all possible decoding results, and use the maximum a posterior (MAP) decoding algorithm with the assistance of a side information sequence to find the decoding sequence with the largest cumulative product of posterior probabilities. Compared with DSC schemes based on channel codes, DAC can better adapt to non-stationary sources, and the coding performance for smaller data blocks will be better [9]. After DAC was proposed, a series of DSC schemes similar to DAC, which are based on expanding the probability intervals, were also successively proposed. In [16], a Slepian-Wolf code which is a quasi-arithmetic code based on coding interval overlapping is described, and this scheme is also applied to a distributed coding platform. Two non-binary DAC compression schemes, multi-interval DAC and Huffman coded DAC, are proposed in [17], which extend DAC from the compression of binary sources to the compression of non-binary sources. In [18], another DAC scheme was proposed which makes the encoder imitate the operation of the decoder and put ambiguous symbols in a list. If the decoder detects that the decoding has failed (e.g., by using a cyclic redundancy check code), the decoder can request the encoder to send the stored ambiguous symbols through a feedback channel. In [19], the DAC scheme was extended to a scenario of noisy communication, and introduced a 'forbidden symbol' to DAC; it is referred to as DJSCAC. This is a very convenient way to improve decoding error performance. On the basis of DAC, the scheme adds a non-coding interval into the original probability intervals, the non-coding interval does not correspond to any symbol that can be practically encoded. The decoder determines whether the codeword is wrong by judging whether the 'forbidden symbol' is obtained during the decoding process. However, when a DSC scheme based on expanding probability intervals encodes a biased source (the probability of one of the encoded symbol is relatively large), the large probability will make the expandable range of the probability interval very limited. This problem limits the potential compression gain that DSC schemes based on expanding probability intervals can obtain when the source has a highly skewed probability distribution \(p0=p(x_{i}=0)\) or \(p1=p(x_{i}=1)\gg 0.5\), especially when a context model is used. Another idea to implement the DSC scheme based on arithmetic coding is to puncture the output bitstream of the arithmetic encoder. This is a very convenient solution to obtain the additional compression gain, which will not be affected by the skewed probability distribution of the source. A DSC scheme using the punctured quasi-arithmetic code was proposed in [20].