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- Agrell, Erik, 1965, et al.
(författare)
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Gray coding for multilevel constellations in Gaussian noise
- 2007
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 53:1, s. 224-235
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Tidskriftsartikel (refereegranskat)abstract
- The problem of finding the optimal labeling (bit-to-symbol mapping) of multilevel coherent phase shift keying (PSK), pulse amplitude modulation (PAM), and quadrature amplitude modulation (QAM) constellations with respect to minimizing the bit-error probability (BEP) over a Gaussian channel is addressed. We show that using the binary reflected Gray code (BRGC) to label the signal constellation results in the lowest possible BEP for high enough signal energy-to-noise ratios and analyze what is "high enough"in this sense. It turns out that the BRGC is optimal for PSK and PAM systems whenever the target BEP is at most a few percent, which covers most systems of practical interest. New and simple closed-form expressions are presented for the BEP of PSK, PAM, and QAM using the BRGC. © 2007 IEEE.
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- Agrell, Erik, 1965, et al.
(författare)
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On the optimality of the binary reflected Gray code
- 2004
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 50:12, s. 3170-3182
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns the problem of selecting a binary labeling for the signal constellation in M-PSK, M-PAM, and M-QAM communication systems. Gray labelings are discussed and the original work by Frank Gray is analyzed. As is noted, the number of distinct Gray labelings that result in different bit-error probability grows rapidly with increasing constellation size. By introducing a recursive Gray labeling construction method called expansion, the paper answers the natural question of what labeling, among all possible constellation labelings, will give the lowest possible average probability of bit errors for the considered constellations. Under certain assumptions on the channel, the answer is that the labeling proposed by Gray, the binary reflected Gray code, is the optimal labeling for all three constellations, which has, surprisingly, never been proved before.
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- Agrell, Erik, 1965, et al.
(författare)
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The binary reflected Gray code is optimal for M-PSK
- 2004
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Ingår i: Proc. IEEE International Symposium on Information Theory, Chicago, Illinois, USA. - 0780382803 ; , s. 164-
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Konferensbidrag (refereegranskat)abstract
- This paper is concerned with the problem of selecting a binary labeling for the signal constellation in an M-PSK communication system. A good starting point is labelings having the Gray property, but this is not altogether enough, since the number of distinct Gray labelings that result in different bit error probability grows rapidly with increasing constellation size. By introducing a recursive Gray labeling construction method called expansion, the paper answers the natural question of what labeling, among all possible constellation labelings (not only Gray), that will give the lowest possible average probability of bit errors. Under certain assumptions on the channel, the answer is that the labeling originally proposed by Gray, the binary reflected Gray code, is the optimal labeling for M-PSK systems, which has, surprisingly, never been proved before.
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- Bombarda, F., et al.
(författare)
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Runaway electron beam control
- 2019
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Ingår i: Plasma Physics and Controlled Fusion. - : IOP Publishing. - 1361-6587 .- 0741-3335. ; 61:1
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Tidskriftsartikel (refereegranskat)
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