Augmented LT codes over binary extension fields with increased ratio of full‐degree columns

Abstract

This letter proposes an augmented scheme of LT codes to improve the decoding success rate. The method involves substituting the 1‐s in full‐degree columns of the generator matrix of conventional LT codes with binary extension field elements and simultaneously increasing the ratio of full‐degree columns in the ideal soliton distribution. For non‐full‐degree columns, we retain the nonzero elements as 1‐s in the conventional LT codes generator matrix to preserve computational efficiency. Compared to conventional LT codes, the proposed method enhances the linear independence of the generator matrix, leading to a higher decoding success rate with minimal data packets. Experimental results demonstrate the effectiveness of the method at improving the performance of LT codes, with close to 100% decoding success rate achieved with around 5% data redundancy.