Guruswami--Sudan List Decoding for Complex Reed--Solomon Codes
Mostafa H. Mohamed, Sven Puchinger, Martin Bossert

TL;DR
This paper extends the Guruswami--Sudan list decoding algorithm for complex Reed--Solomon codes, focusing on stabilizing numerical steps and enhancing decoding performance for applications like compressed sensing.
Contribution
It introduces methods to stabilize interpolation and root-finding steps, modifies the Roth--Ruckenstein algorithm, and integrates soft information for improved decoding accuracy.
Findings
Enhanced decoding stability over complex fields
Improved decoding performance compared to recent methods
Achieved unique solutions in sparse recovery scenarios
Abstract
We analyze the Guruswami--Sudan list decoding algorithm for Reed--Solomon codes over the complex field for sparse recovery in Compressed Sensing. We propose methods of stabilizing both the interpolation and the root-finding steps against numerical instabilities, where the latter is the most sensitive. For this purpose, we modify the Roth--Ruckenstein algorithm and propose a method to refine its result using Newton's method. The overall decoding performance is then further improved using Generalized Minimum Distance decoding based on intrinsic soft information. This method also allows to obtain a unique solution of the recovery problem. The approach is numerically evaluated and shown to improve upon recently proposed decoding techniques.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · graph theory and CDMA systems
