Block Markov Superposition Transmission of Non-uniform Q-ary Sources - Wang, Yinchu; Ma, Qianli; Mo, Zhaohao; Zheng, Xiangping; Ma, Xiao (IEEE transactions on communications, 2025)
In this paper, we propose a fixed-to-fixed length coding approach to near-lossless compression by leveraging block Markov superposition transmission (BMST) of generalized Reed-Solomon (GRS) codes. To compress non-uniform non-binary sources, we propose two schemes: multi-level coding with a natural mapper and single-level coding with a mapper called sparsifier. The multi-level coding can be proved to achieve the source entropy, while the single-level coding is more suitable for practical use. Both the natural mapper and the sparsifier map non-binary symbols with higher probability to sparser binary vectors of fixed length. When compared with variable-length coding, the most distinguished feature of the proposed coding is that the error propagation caused by a few erroneous bits can be controlled. Even more, the proposed scheme can be easily extended as joint source-channel coding (JSCC) with a wide range of code rates by fixing the input while lengthening the output. Numerical results show that the proposed codes can approach the Shannon limits for transmitting non-uniform sources over noisy channels, providing a universal way to trade off bandwidth and the transmission power.