Fast Decoding of the (41,21,9) Quadratic Residue Code Without Computing Unknown Syndromes

In this paper, an improved hard-decision scheme is proposed to facilitate a faster decoding of the binary (41, 21, 9) quadratic residue (QR) code. Based on eliminating the unknown syndromes in Newton's identities, the proposed algorithm can directly calculate the coefficients of the error-locator polynomials when there are 2, 3 or 4 errors in the received word. Additionally, compared to the conventional works, the simplification of the occurrence conditions for 1, 2 or 3 errors in the received word is also presented in our proposed algorithm, which can further reduce the decoding time. Simulation results show that the proposed algorithm can achieve a significant reduction in computational complexity in comparison with the conventional algebraic decoding algorithms (ADAs) like Lin's algorithm in [8], while maintaining the good error performance.