Decoding Golay Codes and their Related Lattices: A PAC Code Perspective
Abstract
In this work, we propose a decoding method of Golay codes from the perspective of Polarization Adjusted Convolutional (PAC) codes. By invoking Forney's cubing construction of Golay codes and their generators G*(8,7)/(8,4), we found different construction methods of Golay codes from PAC codes, which result in an efficient parallel list decoding algorithm with near-maximum likelihood performance. Compared with existing methods, our method can get rid of index permutation and codeword puncturing. Using the new decoding method, some related lattices, such as Leech lattice 24 and its principal sublattice H24, can be also decoded efficiently.
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