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arXiv:1801.06315 · Iran Workshop on Communication and Information Theory (IWCIT)

Chained successive cancellation decoding of the extended Golay code

Peter Trifonov

Published Apr 1, 2018• 0 citations
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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 sequential 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.

DOI
10.1109/iwcit.2018.8405038

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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 sequential 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.
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This letter proposes a reinterpretation of the classical binary Golay codes as Polar codes with additional inner permutations and puncturing. This establishes a novel relationship between algebraic codes and codes based on Kronecker products, like polar codes. Naturally, this construction also allows for polar-code-type decoding of the Golay codes using successive cancellation list decoding. Using the Golay code as a driving example, we conjecture that other algebraic codes may be represented in a similar way.