Journal ArticleDOI
Lattice codes can achieve capacity on the AWGN channel
Rudiger Urbanke,Bixio Rimoldi +1 more
- Vol. 44, Iss: 1, pp 273-278
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TLDR
It is shown that lattice codes can achieve capacity on the additive white Gaussian noise channel and there exists a lattice code with rate no less than R and average error probability upper-bounded by e.Abstract:
It is shown that lattice codes can achieve capacity on the additive white Gaussian noise channel. More precisely, for any rate R less than capacity and e>0, there exists a lattice code with rate no less than R and average error probability upper-bounded by e. These lattice codes include all points of the (translated) lattice within the spherical bounding region (not just the ones inside a thin spherical shell).read more
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Journal ArticleDOI
Multilevel codes: theoretical concepts and practical design rules
TL;DR: This paper deals with 2/sup l/-ary transmission using multilevel coding (MLC) and multistage decoding (MSD) and shows that capacity can in fact be closely approached at high bandwidth efficiencies.
Journal ArticleDOI
Nested linear/lattice codes for structured multiterminal binning
Ram Zamir,Shlomo Shamai,Uri Erez +2 more
TL;DR: Nested codes are proposed, or more specifically, nested parity-check codes for the binary case and nested lattices in the continuous case, which connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications.
Journal ArticleDOI
Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding
TL;DR: In this article, a lattice code with lattice decoding was proposed to achieve the additive white Gaussian noise (AWGN) channel capacity, whose effective noise is reduced by a factor of /spl radic/(1+SNR/SNR) for any desired nesting ratio.
References
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Sphere packings, lattices, and groups
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Journal ArticleDOI
Probability of error for optimal codes in a Gaussian channel
TL;DR: Upper and lower bounds are found for the error probability in decoding with optimal codes and decoding systems for a continuous channel with an additive gaussian noise and subject to an average power limitation at the transmitter.
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CRC standard mathematical tables and formulae
TL;DR: In this article, the authors present a taxonomy of conversion factors for probability and statistics financial tables, including conversion factors and conversion factors in the context of taxonomic analysis of financial transactions.
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