منابع مشابه
Channel capacities of classical and quantum list decoding
We focus on classical and quantum list decoding. The capacity of list decoding was obtained by Nishimura in the case when the number of list does not increase exponentially. However, the capacity of the exponential-list case is open even in the classical case while its converse part was obtained by Nishimura. We derive the channel capacities in the classical and quantum case with an exponential...
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Whenever variable-length entropy codes are used in the presence of a noisy channel, any channel errors will propagate and cause significant harm. Despite using channel codes, some residual errors always remain, whose effect will get magnified by error propagation. Mitigating this undesirable effect is of great practical interest. One approach is to use the residual redundancy of variable-length...
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We study the list-decodability of multiplicity codes. These codes, which are based on evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while simultaneously allowing for sublinear-time error-correction. In this paper, we show that multiplicity codes also admit powerful list-decoding and local list-decoding algorithms correcting a large fraction of errors. Sta...
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We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding algorithms with nonexponential complexity known for RM codes. Decoding performance is further enhanced by using intermediate code lists and permutation procedures....
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This paper presents a list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n− p n(n− 2t− 2) errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomialtime list-decoding algorithms for the same codes, the new algorithm corrects approximately t/2n extra errors.
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 1973
ISSN: 0021-9002,1475-6072
DOI: 10.2307/3212384