Technical Program

Paper Detail

Paper Title Progressive Module Minimization for Re-encoding Transformed Soft Decoding of RS Codes
Paper IdentifierWE1.R8.3
Authors Jiongyue Xing, Li Chen, Sun Yat-sen University, China; Martin Bossert, Ulm University, Germany
Session Reed-Solomon Codes
Location Conseil, Level 5
Session Time Wednesday, 10 July, 09:50 - 11:10
Presentation Time Wednesday, 10 July, 10:30 - 10:50
Manuscript  Click here to download the manuscript
Abstract The interpolation based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance through constructing a minimum polynomial $Q(x,y)$ and finding its $y$-roots. The progressive algebraic soft decoding (PASD) constructs $Q(x,y)$ with a progressively enlarged $y$-degree and terminates once the message is decoded, adapting the decoding capability and computation to the channel. This paper proposes the re-encoding transformed PASD algorithm, in which $Q(x,y)$ is progressively constructed by the low-complexity module minimization (MM) technique. Re-encoding transform (ReT) results in a common divisor for polynomials of the image of the submodule basis. It can be removed, leading to a simpler image expansion and reduction. Consequently, $Q(x,y)$ is constructed through the isomorphic image of the progressively enlarged submodule basis. Our complexity analysis characterizes the complexity reduction brought by the transform and shows high rate codes benefit a greater complexity reduction.