| 1. |
- 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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| 2. |
- 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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| 3. |
- Lassing, Johan, 1973, et al.
(författare)
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Computation of the Exact Bit-Error Rate of Coherent M-ary PSK With Gray Code Bit Mapping
- 2003
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Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; 51:11, s. 1758-1760
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Tidskriftsartikel (refereegranskat)abstract
- The problem of calculating the average bit-error probability (BEP) of coherent M-ary phase-shift keying (PSK) over a Gaussian channel has been studied previously in the literature. A solution to the problem for systems using a binary reflected Gray code (BRGC) to map bits to symbols was first presented by Lee. In this letter, we show that the results obtained by Lee are incorrect for M greater than or equal to 16. We show that the reason for this is an invalid assumption that the bit-error rate (BER) is independent of the transmitted symbols, an assumption which has also propagated to textbooks. We give a new expression for the BER of M-PSK systems using the BRGC and compare this with Lee's results.
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| 4. |
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| 5. |
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| 6. |
- Lassing, Johan, 1973, et al.
(författare)
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Unequal Bit-Error Protection in Coherent M-ary PSK
- 2003
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Ingår i: Proceedings IEEE Vehicular Technology Conference Fall, Orlando, Florida, USA. ; 1, s. 251-256
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Konferensbidrag (refereegranskat)abstract
- This paper addresses the problem of evaluating the bit-error probability of the individual bits of a symbol in a communication system using coherent M-ary phase shift keying. Exact expressions are provided, and these are evaluated for seven different mappings from bits to symbols, including five Gray mappings, for a 32-PSK system. It is shown that the highly varying error performance obtained with a common binary reflected Gray mapping can be restored by using a balanced Gray mapping.
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| 7. |
- Agrell, Erik, 1965, et al.
(författare)
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A table of upper bounds for binary codes
- 2001
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 47:7, s. 3004-3006
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Tidskriftsartikel (refereegranskat)abstract
- Let A(n, d) denote the maximum possible number of codewords in an (n, d) binary code. We establish four new bounds on A(n, d), namely, A(21, 4)⩽43689, A(22, 4)⩽87378, A(22, 6)⩽6941, and A(23, 4)⩽173491. Furthermore, using previous upper bounds on the size of constant-weight binary codes, we reapply known methods to generate a table of bounds on A(n, d) for all n⩽28. This table extends the range of parameters compared with previously known tables.
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| 8. |
- Agrell, Erik, 1965, et al.
(författare)
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Closest point search in lattices
- 2002
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 48:8, s. 2201-2214
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Tidskriftsartikel (refereegranskat)abstract
- In this semitutorial paper, a comprehensive survey of closest point search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closest point search algorithm, based on the Schnorr-Euchner variation of the Pohst method, is implemented. Given an arbitrary point x is an element of R-m and a generator matrix for a lattice A, the algorithm computes the point of A that is closest to x. The algorithm is shown to be substantially faster than other known methods, by means of a theoretical comparison with the Kannan algorithm and an experimental comparison with the Pohst algorithm and its variants, such as the recent Viterbo-Boutros decoder. Modifications of the algorithm are developed to solve a number of related search problems for lattices, such as finding a shortest vector, determining the kissing number, computing the Voronoi-relevant vectors, and finding. a Korkine-Zolotareff reduced basis.
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| 9. |
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| 10. |
- Agrell, Erik, 1965, et al.
(författare)
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Constant-weight code bounds from spherical code bounds
- 2000
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Ingår i: Proc. IEEE International Symposium on Information, Sorrento, Italy. - 0780358570 ; , s. 391-
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Konferensbidrag (refereegranskat)abstract
- We present new upper bounds on the size of constant-weight binary codes, derived from bounds for spherical codes. In particular, we improve upon the 1982 Johnson bound and the linear programming bound for constant-weight codes.
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