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Universal coding From Wikipedia, the free encyclopedia
Levenshtein coding is a universal code encoding the non-negative integers developed by Vladimir Levenshtein.[1][2]
The code of zero is "0"; to code a positive number:
The code begins:
Number | Encoding | Implied probability | |
---|---|---|---|
0 | 0 | 1/2 | |
1 | 10 | 1/4 | |
2 | 110 0 | 1/16 | |
3 | 110 1 | 1/16 | |
4 | 1110 0 00 | 1/128 | |
5 | 1110 0 01 | 1/128 | |
6 | 1110 0 10 | 1/128 | |
7 | 1110 0 11 | 1/128 | |
8 | 1110 1 000 | 1/256 | |
9 | 1110 1 001 | 1/256 | |
10 | 1110 1 010 | 1/256 | |
11 | 1110 1 011 | 1/256 | |
12 | 1110 1 100 | 1/256 | |
13 | 1110 1 101 | 1/256 | |
14 | 1110 1 110 | 1/256 | |
15 | 1110 1 111 | 1/256 | |
16 | 11110 0 00 0000 | 1/4096 | |
17 | 11110 0 00 0001 | 1/4096 |
To decode a Levenshtein-coded integer:
The Levenshtein code of a positive integer is always one bit longer than the Elias omega code of that integer. However, there is a Levenshtein code for zero, whereas Elias omega coding would require the numbers to be shifted so that a zero is represented by the code for one instead.
void levenshteinEncode(char* source, char* dest)
{
IntReader intreader(source);
BitWriter bitwriter(dest);
while (intreader.hasLeft())
{
int num = intreader.getInt();
if (num == 0)
bitwriter.outputBit(0);
else
{
int c = 0;
BitStack bits;
do {
int m = 0;
for (int temp = num; temp > 1; temp>>=1) // calculate floor(log2(num))
++m;
for (int i=0; i < m; ++i)
bits.pushBit((num >> i) & 1);
num = m;
++c;
} while (num > 0);
for (int i=0; i < c; ++i)
bitwriter.outputBit(1);
bitwriter.outputBit(0);
while (bits.length() > 0)
bitwriter.outputBit(bits.popBit());
}
}
}
void levenshteinDecode(char* source, char* dest)
{
BitReader bitreader(source);
IntWriter intwriter(dest);
while (bitreader.hasLeft())
{
int n = 0;
while (bitreader.inputBit()) // potentially dangerous with malformed files.
++n;
int num;
if (n == 0)
num = 0;
else
{
num = 1;
for (int i = 0; i < n-1; ++i)
{
int val = 1;
for (int j = 0; j < num; ++j)
val = (val << 1) | bitreader.inputBit();
num = val;
}
}
intwriter.putInt(num); // write out the value
}
bitreader.close();
intwriter.close();
}
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