3 research outputs found
Optimal Threshold-Based Multi-Trial Error/Erasure Decoding with the Guruswami-Sudan Algorithm
Traditionally, multi-trial error/erasure decoding of Reed-Solomon (RS) codes
is based on Bounded Minimum Distance (BMD) decoders with an erasure option.
Such decoders have error/erasure tradeoff factor L=2, which means that an error
is twice as expensive as an erasure in terms of the code's minimum distance.
The Guruswami-Sudan (GS) list decoder can be considered as state of the art in
algebraic decoding of RS codes. Besides an erasure option, it allows to adjust
L to values in the range 1<L<=2. Based on previous work, we provide formulae
which allow to optimally (in terms of residual codeword error probability)
exploit the erasure option of decoders with arbitrary L, if the decoder can be
used z>=1 times. We show that BMD decoders with z_BMD decoding trials can
result in lower residual codeword error probability than GS decoders with z_GS
trials, if z_BMD is only slightly larger than z_GS. This is of practical
interest since BMD decoders generally have lower computational complexity than
GS decoders.Comment: Accepted for the 2011 IEEE International Symposium on Information
Theory, St. Petersburg, Russia, July 31 - August 05, 2011. 5 pages, 2 figure