High speed decoding of the binary (47, 24, 11) quadratic residue code

Decoding of the Five-Error-Correcting Binary Quadratic Residue Codes

In this paper, a new efficient syndrome-weight decoding algorithm (NESWDA) is presented to decode up to five possible errors in a binary systematic (47, 24, 11) quadratic residue (QR) code. The main idea of NESWDA is based on the property cyclic codes together with the weight of syndrome difference. The advantage of the NESWDA decoding algorithm over the previous table look-up methods is that i...

Algebraic Decoding of Quadratic Residue Codes Using Berlekamp-Massey Algorithm

In this paper, an algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey algorithm. By a modification of the technique developed by He et al., one can express the unknown syndromes as functions of the known syndromes. The unknown syndromes are determined by an efficient algorithm also developed in this paper. With the appearance of unknown syndro...

A cyclic weight algorithm of decoding the (47, 24, 11) quadratic residue code

Decoding the Ternary (23, 11, 9) Quadratic Residue Code

Quadratic residue (QR) codes are cyclic, nominally half-rate codes, that are powerful with respect to their error-correction capabilities. Decoding QR codes is in general a difficult task, but great progress has been made in the binary case since the work of Elia [1] and He et al. [2]. Decoding algorithms for certain nonbinary QR codes were proposed by Higgs and Humphreys in [3] and [4]. In [5]...

On the Pless-construction and ML decoding of the (48, 24, 12) quadratic residue code

We present a method for maximumlikelihood decoding of the (48; 24; 12) quadratic residue code. This method is based on projecting the code onto a subcode with an acyclic Tanner graph, and representing the set of coset leaders by a trellis diagram. This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule. We show that unlike the code does ...