Block Markov Superposition Transmission of Non-uniform Q-ary Sources

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 m...

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Veröffentlicht in:IEEE transactions on communications S. 1
Hauptverfasser: Wang, Yinchu, Ma, Qianli, Mo, Zhaohao, Zheng, Xiangping, Ma, Xiao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 2025
Schlagworte:
Block Markov superposition transmission (BMST)
Channel coding
Codes
Encoding
Entropy
fixed-to-fixed source coding
Image coding
Iterative decoding
joint source-channel coding (JSCC)
Polynomials
Source coding
Symbols
transmission of non-uniform sources
Vectors
ISSN:0090-6778, 1558-0857
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Zusammenfassung: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.
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2025.3631568