Achieving the Capacity of any DMC using only Polar Codes

TL;DR

This paper presents a polar coding scheme that achieves the capacity of any discrete memoryless channel by combining source polarization, randomness extraction, and channel coding, maintaining low complexity and offering a new conceptual approach.

Contribution

The paper introduces a novel polar coding scheme that achieves channel capacity for any DMC using only polar techniques, including source polarization and shaping.

Findings

Successfully achieves capacity for any DMC

Maintains low complexity of polar codes

Provides a new conceptual approach compared to Gallager's method

Abstract

We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be employed to "shape" uniformly-distributed i.i.d. random variables into approximate i.i.d. random variables distributed ac- cording to the capacity-achieving distribution. We then combine this shaper with a variant of polar channel coding, constructed by the duality with source coding, to achieve the channel capacity. Our scheme inherits the low complexity encoder and decoder of polar coding. It differs conceptually from Gallager's method for achieving capacity, and we discuss the advantages and disadvantages of the two schemes. An application to the AWGN channel is discussed.