Ordered Statistics Derivative Decoding for Affine-Invariant Codes Without Gaussian Elimination

This paper introduces the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ordered statistics decoding</i> (OSD) without Gaussian elimination for affine-invariant codes based on their <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">derivative descendants</i> (DDs). Based on the affine-invariant property, the reliable bits can be permuted into the information positions for re-encoding by an affine permutation. Moreover, it makes the information bits more reliable to perform the re-encoding process on not the original codes, but their DDs. Thanks to the much smaller dimension of our defined affine DDs, OSD can be carried out more efficiently. Simulation results show that the proposed ordered statistics derivative decoding can provide good performance without Gaussian elimination, even better than the conventional OSD with higher order.