Chained Successive Cancellation Decoding of the Extended Golay code

TL;DR

This paper demonstrates that the extended Golay code can be decoded using chained successive cancellation algorithms, leveraging polar subcode representations and fast Hadamard transforms to achieve complexity comparable to existing algorithms.

Contribution

It introduces a novel approach to decode the extended Golay code via chained polar subcodes and simplifies the decoder with fast Hadamard transforms.

Findings

Decoding complexity is comparable to the Vardy algorithm.

The extended Golay code can be represented as a chained polar subcode.

Fast Hadamard transform simplifies the decoding process.

Abstract

The extended Golay code is shown to be representable as a chained polar subcode. This enables its decoding with the successive cancellation algorithm and its stack generalization. The decoder can be further simplified by employing fast Hadamard transform. The complexity of the obtained algorithm is comparable with that of the Vardy algorithm.