Algebraic and linear programming decoding of the (73, 37, 13) quadratic residue code

Abstract

In this paper 1 , a method to search the subsets I and J needed in computing the unknown syndromes for the (73, 37, 13) quadratic residue (QR) code is proposed. According to the resulting I and J, one computes the unknown syndromes, and thus finds the corresponding error-locator polynomial by using an inverse-free BM algorithm. Based on the modified Chase-II algorithm, the performance of soft-decision decoding for the (73, 37, 13) QR code is given. This result is never seen in the literature, to our knowledge. Moreover, the error-rate performance of linear programming (LP) decoding for the (73, 37, 13) QR code is also investigated, and LP-based decoding is shown to be significantly superior in performance to the algebraic soft-decision decoding while requiring almost the same computational complexity.Index Terms-Berlekamp-Massey algorithm, quadratic residue code, Chase algorithm, linear programming.

Eight Error Correction for (57,29,17) Quadratic Residue Code Over Binary Field

“…Truong et al devised a method to compute unknown syndromes for the (73,37,13) QR code, with a focus on enhancing decoding performance using soft decisions. A comprehensive study was conducted to evaluate error-rate performance [4]. Furthermore, the author elaborated on numerous decoding algorithm techniques and error correction coding utilizing a mathematical approach [14].…”