# American Institute of Mathematical Sciences

August  2007, 1(3): 331-356. doi: 10.3934/amc.2007.1.331

## A weight-based characterization of the set of correctable error patterns under list-of-2 decoding

Received  January 2007 Revised  June 2007 Published  July 2007

List decoding of block codes is an alternative approach to the decoding problem with appealing qualities. The fairly recent development of efficient algorithms for list decoding of Reed-Solomon codes spur new fuel to the study of this decoding strategy. In this paper we give a weight-based characterization of the set of correctable error patterns under list-of-2 ecoding of $(\tau, 2$)-list-decodable linear codes with known weight distribution. We apply our characterization of the set of correctable error patterns to a few codes in a family of low-rate list-of-2 decodable Reed-Solomon codes. We study the increase in error-correction performance obtained in a symmetric AWGN channel by using list-of-2 decoding instead of traditional decoding for these codes. Some simulation results for list-of-2 decoding on QAM channels using the Guruswami-Sudan algorithm for decoding of Reed-Solomon codes are also presented.
Citation: Jonas Eriksson. A weight-based characterization of the set of correctable error patterns under list-of-2 decoding. Advances in Mathematics of Communications, 2007, 1 (3) : 331-356. doi: 10.3934/amc.2007.1.331
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