Efficient Majority-Logic Decoding of Short-Length Reed-Muller Codes at Information Positions
نویسندگان
چکیده
منابع مشابه
oft-decision majority decoding of Reed-Muller codes
We present a new soft-decision majority decoding algorithm for Reed–Muller codes RM ( ). First, the reliabilities of 2 transmitted symbols are recalculated into the reliabilities of 2 parity checks that represent each information bit. In turn, information bits are obtained by the weighted majority that gives more weight to more reliable parity checks. It is proven that for long low-rate codes R...
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The Reed-Muller (RM) code encoding n-variate degree-d polynomials over Fq for d < q, with its evaluation on Fq , has relative distance 1− d/q and can be list decoded from a 1−O( √ d/q) fraction of errors. In this work, for d ≪ q, we give a length-efficient puncturing of such codes which (almost) retains the distance and list decodability properties of the Reed-Muller code, but has much better r...
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OFDM, power, Reed-Muller code, decoding, algorithms, error correction Recently a class of generalised Reed-Muller codes has been suggested for use in power-controlled OFDM modulation. A number of approaches to decoding these codes have already been developed. Here we present low complexity alternatives which are inspired by the classical Reed decoding algorithm for binary Reed-Muller codes. We ...
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We construct list decoding algorithms for first order Reed-Muller codes RM [1,m] of length n = 2m correcting up to n(12 − 2) errors with complexity O(n2−3). Considering probabilistic approximation of these algorithms leads to randomized list decoding algorithms with characteristics similar to Goldreich-Levin algorithm, namely, of complexity O(m22−7 log 12 (log 12 +log 1 Perr +log m)), where Per...
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ژورنال
عنوان ژورنال: IEEE Transactions on Communications
سال: 2013
ISSN: 0090-6778
DOI: 10.1109/tcomm.2013.012313.110415