Constructing Polar Codes Using Iterative Bit-Channel Upgrading

TL;DR

This paper introduces an iterative upgrading method for polar code construction that progressively refines bit-channels to closely approximate the original, enabling near-optimal code design with controlled complexity.

Contribution

It presents a novel iterative upgrading approach for polar code construction, improving accuracy while managing complexity compared to previous methods.

Findings

The method can produce channels arbitrarily close to the original.

It achieves near-optimal polar code construction.

The approach effectively controls the growth of alphabet size.

Abstract

The definition of polar codes given by Arikan is explicit, but the construction complexity is an issue. This is due to the exponential growth in the size of the output alphabet of the bit-channels as the codeword length increases. Tal and Vardy recently presented a method for constructing polar codes which controls this growth. They approximated each bit-channel with a better channel and a worse channel while reducing the alphabet size. They constructed a polar code based on the worse channel and used the better channel to measure the distance from the optimal channel. This paper considers the knowledge gained from the perspective of the better channel. A method is presented using iterative upgrading of the bit-channels which successively results in a channel closer to the original one. It is shown that this approach can be used to obtain a channel arbitrarily close to the original channel, and therefore to the optimal construction of a polar code.