期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 67, 期 9, 页码 6140-6163出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2021.3097965
关键词
Lattices; Rate-distortion; Encoding; Channel coding; Quantization (signal); Distortion; Complexity theory; Vector quantization (VQ); source coding; lattices; network coding; polar codes
资金
- China Scholarship Council
- Engineering and Physical Sciences Research Council (EPSRC)
- National Natural Science Foundation of China [62001300]
- Natural Science Foundation of Guangdong Province of China [2021A1515011679]
- Start-Up Science Foundation of High-Caliber Personnel [RC00281, QNJS0178]
The proposed polar lattices achieve the rate-distortion bound of a memoryless Gaussian source by integrating entropy coding into the lattice quantizer. The complexity of encoding and decoding is O(N log(2) N) for any target distortion and fixed rate larger than the rate-distortion bound. Additionally, the nesting structure of polar lattices provides solutions to various multi-terminal coding problems.
In this work, we propose a new construction of polar lattices to achieve the rate-distortion bound of a memoryless Gaussian source. The structure of the proposed polar lattices allows to integrate entropy coding into the lattice quantizer, which greatly simplifies the compression process. The overall complexity of encoding and decoding is O(N log(2) N) for any target distortion and fixed rate larger than the rate-distortion bound. Moreover, the nesting structure of polar lattices provides solutions to various multi-terminal coding problems. The Wyner-Ziv coding problem for a Gaussian source can be solved by using a capacity-achieving polar lattice for the Gaussian channel, nested with a rate-distortion bound achieving lattice, while the Gelfand-Pinsker problem can be solved in a reversed manner. The polar lattice quantizer is further extended to extract Wyner's common information of a pair of Gaussian sources or multiple Gaussian sources.
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