Nested Lattice Coding With Algebraic Encoding and Geometric Decoding

Nested Lattice Coding (NLC) provides a generalized solution to Wyner-Ziv problems. Codebook of NLC is termed as the label-set. We find a significant difference between the label-set strictly satisfying coset's property and that predominantly used in existing NLC-related works. We name the former as Algebraic Label-Set (ALS), the latter as Geometric Label-Set (GLS), and present their enumeration strategies for practical implementation. Apart from random and coset binning, we name the enumeration of GLS as "geometric binning". By applying ALS for encoding and GLS for decoding, we propose a refined NLC scheme called Nested Lattice Coding with Algebraic Encoding and Geometric Decoding (NLC-AC-GD). NLC-AC-GD has the same decoding reliability and higher compression rate compared with the traditional NLC scheme.