Progressive Algebraic Soft Decoding of Reed-Solomon Codes Using Module Minimization
Jiongyue Xing, Li Chen, Martin Bossert · 2018
The algebraic soft decoding (ASD) algorithm achieves advanced decoding performance for Reed-Solomon (RS) codes. However, its complexity remains high making it impractical. This is due to the interpolation. The progressive ASD (PASD) algorithm adjusts the decoding computation to the reliability of received information. Its interpolation generates the intended polynomial Q(x, y) with a progressively enlarged y- degree, and terminates once the message is decoded. But this progressive decoding is realized at the cost of memorizing the intermediate decoding information. This paper proposes a new PASD algorithm, in which the progressive interpolation is realized by the module minimization (MM) technique. Polynomial Q(x, y) can be found through the progressively enlarged images of submodule's basis without memorizing the intermediate decoding information. The MM interpolation also grants it a significantly lower complexity than the original PASD algorithm that uses Koetter's interpolation. Our simulation results will verify its advanced decoding performance and low-complexity feature.