Binary Polar Codes Based on Bit Error Probability

TL;DR

This paper presents methods for constructing binary polar codes using bit error probability, enabling improved code design and error bound estimation based on successive-cancellation decoding performance.

Contribution

It introduces a novel approach to polar code construction based on bit error probability and reconstructs the polarization lemma accordingly.

Findings

Techniques for computing bit error probability are developed.

Methods for constructing polar codes using bit error probability are proposed.

Bounds on block decoding error probability are derived.

Abstract

This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then techniques to compute the bit error probability are introduced. These techniques can be applied to the construction of polar codes and the computation of lower and upper bounds of the block decoding error probability.