Levenshtein coding
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Levenshtein coding is a universal code encoding the non-negative integers developed by Vladimir Levenshtein.
The code of zero is "0"; to code a positive number:
- Initialize the step count variable C to 1.
- Write the binary representation of the number without the leading "1" to the beginning of the code.
- Let M be the number of bits written in step 2.
- If M is not 0, increment C, repeat from step 2 with M as the new number.
- Write C "1" bits and a "0" to the beginning of the code.
The code begins:
0 0 1 10 2 110 0 3 110 1 4 1110 0 00 5 1110 0 01 6 1110 0 10 7 1110 0 11 8 1110 1 000 9 1110 1 001 10 1110 1 010 11 1110 1 011 12 1110 1 100 13 1110 1 101 14 1110 1 110 15 1110 1 111 16 11110 0 00 0000 17 11110 0 00 0001
To decode a Levenstein-coded integer:
- Count the number of "1" bits until a "0" is encountered.
- If the count is zero, the value is zero, otherwise
- Start with a variable N, set it to a value of 1 and repeat count minus 1 times:
- Read N bits, prepend "1", assign the resulting value to N
The Levenstein code of a positive integer is always one bit longer than the Elias omega code of that integer.
See also Elias omega coding, Log*
[edit] Sources
- 1968 paper by V. I. Levenshtein (in Russian)
