Polar Lattices for Lossy Compression

Liu, Ling; Shi, Jinwen; Ling, Cong

doi:10.48550/arxiv.1501.05683

Cited by 5 publications

(1 citation statement)

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“…Polar lattice codes obtained from polar lattices with discrete Gaussian shaping is then shown to be capacity-achieving [39]. Polar lattices are also shown to be able to achieve the rate distortion bound of memoryless Gaussian source in [40]. One variant of Construction D called Construction by Code Formula has attracted a lot of attention since its introduction by Forney in [41], see for example [42], [43].…”

Section: Construction πmentioning

confidence: 99%

Construction πA and πD Lattices: Construction, Goodness, and Decoding Algorithms

Huang

Narayanan

2017

IEEE Trans. Inform. Theory

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A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of L linear codes over F p1 , . . . , F pL , respectively, and hence is referred to as Construction π A . The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction π A lattices is proposed and its achievable rate for the additive white Gaussian channel is analyzed. A generalization named Construction π D is also investigated which subsumes Construction A with codes over prime fields, Construction D, and Construction π A as special cases.

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Section: Construction πmentioning

confidence: 99%