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.

In this paper, we propose a new coding approach to near-lossless compression of$Q$-ary sources by utilizing a sparsifier and block Markov superposition transmission (BMST) codes. The symbols from a$Q$-ary source are mapped to fixedlength binary vectors by the sparsifier such that the symbols with higher probabilities are mapped to vectors of lower weights. The binary sparse sequences are then compressed in a BMST manner. The most distinguished feature of the proposed source coding is that the error propagation can be mitigated in the presence of noise. Numerical results show that the proposed scheme performs well for$Q$-ary sources, providing a universal but simple way to achieve near-lossless coding at rates approaching the source entropy.