Decoding the (23, 12, 7) Golay Code Using a Low-Complexity Scheme

On high-speed decoding of the (23, 12, 7) Golay code

Decoding the Golay code with Venn diagrams

A decoding algorithm based on Venn diagrams to decode the [23, 12, 71 Golay code is presented. The decoding algorithm is based on the “design” properties of the parity sets of the code. As for other decoding algorithms for the Golay code, decoding can be easily done by hand.

Soft decoding of the (23, 12, 7) Golay-code up to five errors

A new decoder is proposed to decode the (23, 12, 7) binary Golay-code up to five errors. It is based on the algorithm that can correct up to four errors for the (24, 12, 8) extended Golay-code proposed by Lin et al., thereby achieving the soft decoding in the real sense for the Golay-code. For a weight-2 or weight-3 error pattern decoded by the hard decoder for correcting up to three errors, on...

Efficient decoding of the (23, 12, 7) Golay code up to five errors

Article history: Received 5 May 2009 Received in revised form 29 June 2013 Accepted 31 July 2013 Available online 8 August 2013

The Golay Code Outperforms the Extended Golay Code Under Hard-Decision Decoding

We show that the binary Golay code is slightly more power efficient than the extended binary Golay code under maximum-likelihood (ML), hard-decision decoding. In fact, if a codeword from the extended code is transmitted, one cannot achieve a higher probability of correct decoding than by simply ignoring the 24th symbol and using an ML decoder for the non-extended code on the first 23 symbols. T...