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Ilya Dumer
Researcher at University of California, Riverside
Publications - 95
Citations - 1361
Ilya Dumer is an academic researcher from University of California, Riverside. The author has contributed to research in topics: Reed–Muller code & Linear code. The author has an hindex of 19, co-authored 95 publications receiving 1243 citations.
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Hardness of approximating the minimum distance of a linear code
TL;DR: In this paper, it was shown that the minimum distance d of a linear code is not approximable to within any constant factor in random polynomial time (RP), unless NP = RP.
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Soft-decision decoding of Reed-Muller codes: recursive lists
Ilya Dumer,Kirill Shabunov +1 more
TL;DR: Simulation results show that for all RM codes of length 256 and many subcodes of length 512, these algorithms approach maximum-likelihood (ML) performance within a margin of 0.1 dB.
Journal ArticleDOI
Recursive decoding and its performance for low-rate Reed-Muller codes
TL;DR: To evaluate decoding capability, a probabilistic technique is developed that disintegrates decoding into a sequence of recursive steps and subsequent outputs can be tightly evaluated under the assumption that all preceding decodings are correct.
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Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes
TL;DR: In this paper, a recursive decoding algorithm for Reed-Muller (RM) codes with growing length and fixed order was proposed. But the complexity of the algorithm was not asymptotic.
Journal ArticleDOI
Soft-decision decoding of Reed-Muller codes: a simplified algorithm
TL;DR: A recursive decoding algorithm is designed and its decoding threshold is derived for long RM codes and it corrects most error patterns of the Euclidean weight of order radicn/lnn, instead of the decoding threshold radicd/2 of the bounded distance decoding.