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- W2189172750 abstract "TheGale-Berlekamp (inshort, GB)codeisthedual codeofthebinary product codeinwhichthehorizontal and vertical constituent codesareboththeparity code. Itisshown thattheproblem ofdeciding whether there isacodeword ofthe GBcodewithin aprescribed distance fromagiven received word, isNP-complete. Theproblemremains hard(ina well-defined sense) evenifthedecoder isallowed unlimited preprocessing thatdepends onlyonthecodelength. Whiletheintractability of maximum-likelihood decoding forspecific codes hasalready been shownbyBruckandNaorandLobstein, theresult herein seems tobethefirst thatshowshardness forfamiliar (ornatural) codes. Incontrast, itisalsoshownthat, withrespect toany memoryless binary symmetric channel withcrossover probability less than1/2, maximum-likelihood decoding canbeimplemented inlinear timeforallerror events except foraportion thatoccurs withvanishing probability." @default.
- W2189172750 created "2016-06-24" @default.
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- W2189172750 date "2007-01-01" @default.
- W2189172750 modified "2023-10-01" @default.
- W2189172750 title "On theHardness of Decoding theGale-Berlekamp Code" @default.
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