Polar Lattices for Lossy Compression

In this work, we propose a new construction of polar lattices to achieve the rate-distortion bound memoryless Gaussian source. The structure proposed allows integrate entropy coding into lattice quantizer, which greatly simplifies compression process. overall complexity encoding and decoding is O(N log 2 N) for any target distortion fixed rate larger than bound. Moreover, nesting provides solutions various multi-terminal problems. Wyner-Ziv problem source can be solved by using capacity-achieving channel, nested with achieving lattice, while Gelfand-Pinsker in reversed manner. quantizer further extended extract Wyner's common information pair sources or multiple sources.