Two-level decoding of (32, 16, 8) quadratic residue code

Abstract

The Pless construction of the (24, 12, 8) extended Golay code can be modified to construct the (32, 16, 8) extended QR code. Some structural similarities are discovered between the (32, 16, 8) QR code and the (24, 12, 8) Golay code. A simple decoder is developed based on the two-level structure of the (32, 16, 8) QR code. In addition to correcting all three or less bit errors, the proposed algorithm is able to correct some four-bit error patterns. Recently, soft-logic decoding of block codes has found increasing practical applications. The two-level structure renders an extension of Vardy and Be‘ery’s fast algorithm to the (32, 16, 8) QR code. The Vardy-Be‘ery’s algorithm is, so far, the most efficient scheme for the Golay code in the literature, with direct application impact. Its extension to the (32, 16, 8) code is also computationally efficient, as analysed in detail.