Modified OSD Algorithm With Reduced Gaussian Elimination

Abstract

In this letter, the OSD algorithm is modified to perform a limited GE with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N^{3} \min \{R, 1-R\}^{3})$ </tex-math></inline-formula> complexity for an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(N,K)$ </tex-math></inline-formula> linear block code of rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R=K/N$ </tex-math></inline-formula>.