Bounds for codes over the unit circle
- 1 November 1986
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 32 (6) , 760-767
- https://doi.org/10.1109/tit.1986.1057230
Abstract
Let be a code of length and rate over the alphabet , and let be the minimum Euclidean distance of . For large , the lower and upper bounds are obtained in parametric form on the achievable pairs , where holds. To obtain these bounds, the arguments leading to the Gilbert bound and the Elias bound, respectively, are applied to the alphabet . For , they are shown to be expressible in terms of the modified Bessel function of the first kind. The Elias type bound is compared with the Kabatyanskii-Levenshtein (K-L) bound that holds for less restrictive alphabets. It turns out that our upper bound improves the K-L bound for .Keywords
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