Lee distance

From Wikipedia, the free encyclopedia

Jump to: navigation, search

In coding theory, the Lee distance is a distance between two strings $x 1 x 2 ... x n$ and $y 1 y 2 ... y n$ of equal length n over the q-ary alphabet {0,1,…,q-1} of size $q\geq 2$ . It is metric, defined as

$\sum_{i=1}^n \mbox{min}(|x_i-y_i|,q-|x_i-y_i|).$

If $q = 2$ or $q = 3$ the Lee distance coincides with the Hamming distance.

The metric space induced by the Lee distance is a discrete analog of the elliptic space.

Example

If $q = 6$ , then the Lee distance between 3340 and 2543 is 1+2+0+3=6.

History and application

The Lee distance is named after C.Y. Lee. It is applied for phase modulation while the Hamming distance is used in case of orthogonal modulation.

References

Lee, C. Y. (1958), "Some properties of nonbinary error-correcting codes", IRE Transactions on Information Theory 4 (2): 77–82, doi:10.1109/TIT.1958.1057446 .
Berlekamp, E. R. (1968), Algebraic Coding Theory, McGraw-Hill .
Deza, E.; Deza, M. (2006), Dictionary of Distances, Elsevier, ISBN 0444520872 .

Return to Fuhz Home - This article covering Lee distance is enhanced for the visually impaired.

Article from Wikipedia. All text is available under the terms of the GNU Free Documentation License - Our Privacy Policy - Thanks Auto Blog Commenter