Recursive error correction for general Reed-Muller codes
Discrete Applied Mathematics - Special issue: Coding and cryptography
Unequal error protection and progressive decoding for JPEG2000
Image Communication
An improved list decoding algorithm for the second order Reed---Muller codes and its applications
Designs, Codes and Cryptography
Recursive error correction for general Reed-Muller codes
Discrete Applied Mathematics - Special issue: Coding and cryptography
Grassmannian packings from operator Reed-Muller codes
IEEE Transactions on Information Theory
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Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length n and fixed order r. An algorithm is designed that has complexity of order nlogn and corrects most error patterns of weight up to n(1/2-ε) given that ε exceeds n-12r/. This improves the asymptotic bounds known for decoding RM codes with nonexponential complexity. To evaluate decoding capability, we develop a probabilistic technique that disintegrates decoding into a sequence of recursive steps. Although dependent, subsequent outputs can be tightly evaluated under the assumption that all preceding decodings are correct. In turn, this allows us to employ second-order analysis and find the error weights for which the decoding error probability vanishes on the entire sequence of decoding steps as the code length n grows.