Construction of Simultaneously Good Polar Codes and Polar Lattices
🤖 AI Summary
This work addresses the long-standing challenge of simultaneously achieving both channel coding capacity and source coding mean-square error (MSE) optimality with polar codes and polar lattices. We propose an explicit multi-level concatenated polar construction, integrating polar theory, lattice coding, and discrete Gaussian distribution analysis. Our design is the first to yield polar codes and polar lattices that are provably optimal for both channel and source coding. Unlike prior existence proofs based on random ensembles, our framework is fully constructive and operates in polynomial time. Under the AWGN channel, it attains the Shannon capacity; under quadratic distortion constraints, it approaches the fundamental MSE lower bound. This constitutes the first explicitly constructible, polynomial-complexity polar framework that is rigorously dual-optimal—achieving both channel capacity and source coding MSE limits—thereby enabling efficient joint source-channel coding.
Application Category
📝 Abstract
In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of such kind of lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.
Problem
Research questions and friction points this paper is trying to address.
Polarization Technology
Polar Codes
Channel and Source Encoding
Innovation
Methods, ideas, or system contributions that make the work stand out.
Polarization Technique
Optimal Polar Lattices
Simultaneous Channel and Source Coding
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