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

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...

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

Similar to algebraic decoding schemes, the (23, 12, 7) Golay code can be decoded by applying the step-by-step decoding algorithm. In this work, a modified step-by-step algorithm for decoding the Golay code is presented. Logical analysis yielded a simple rule for directly determining whether a bit in the received word is correct. The computational complexity can be reduced significantly using th...

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.

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...