Editing Reed–Solomon error correction (section)

===Soft-decoding===

The algebraic decoding methods described above are hard-decision methods, which means that for every symbol a hard decision is made about its value. For example, a decoder could associate with each symbol an additional value corresponding to the channel [[demodulator]]'s confidence in the correctness of the symbol. The advent of [[low-density parity-check code|LDPC]] and [[turbo code]]s, which employ iterated [[soft-decision decoding|soft-decision]] belief propagation decoding methods to achieve error-correction performance close to the [[Shannon limit|theoretical limit]], has spurred interest in applying soft-decision decoding to conventional algebraic codes. In 2003, Ralf Koetter and [[Alexander Vardy]] presented a polynomial-time soft-decision algebraic list-decoding algorithm for Reed–Solomon codes, which was based upon the work by Sudan and Guruswami.<ref>{{cite journal | first1=Ralf | last1=Koetter | first2=Alexander | last2=Vardy | title=Algebraic soft-decision decoding of Reed–Solomon codes | journal=[[IEEE Transactions on Information Theory]] | volume=49 | issue=11 | year=2003 | pages=2809–2825 | doi=10.1109/TIT.2003.819332| citeseerx=10.1.1.13.2021 }}</ref>
In 2016, Steven J. Franke and Joseph H. Taylor published a novel soft-decision decoder.<ref>{{cite journal | first1=Steven J. | last1=Franke | first2=Joseph H. | last2=Taylor | title=Open Source Soft-Decision Decoder for the JT65 (63,12) Reed–Solomon Code | journal=QEX | issue=May/June | year=2016 | pages=8–17 | url=http://physics.princeton.edu/pulsar/K1JT/FrankeTaylor_QEX_2016.pdf | access-date=2017-06-07 | archive-date=2017-03-09 | archive-url=https://web.archive.org/web/20170309134627/http://www.physics.princeton.edu/pulsar/k1jt/FrankeTaylor_QEX_2016.pdf | url-status=live }}</ref>