Even-Rodeh coding
Even-Rodeh code is a universal code encoding the non-negative integers developed by Shimon Even and Michael Rodeh.[1]
Encoding
To code a non-negative integer N in Even-Rodeh coding:
- If N is not less than 4 then set the coded value to a single
0
bit. Otherwise the coded value is empty. - If N is less than 4 then prepend the coded value with 3 bits containing the value of N and stop.
- Prepend the coded value with the binary representation of N.
- Store the number of bits prepended in step 3 as the new value of N.
- Go back to step 2.
To decode an Even-Rodeh-coded integer:
- Read 3 bits and store the value into N.
- If the first bit read was
0
then stop. The decoded number is N. - If the first bit read was
1
then continue to step 2.
- If the first bit read was
- Examine the next bit.
- If the bit is
0
then read 1 bit and stop. The decoded number is N. - If the bit is
1
then read N bits, store the value as the new value of N, and go back to step 2.
- If the bit is
Examples
Number | Encoding | Implied probability |
---|---|---|
0 | 000 | 1/8 |
1 | 001 | 1/8 |
2 | 010 | 1/8 |
3 | 011 | 1/8 |
4 | 100 0 | 1/16 |
︙ | ||
7 | 111 0 | 1/16 |
8 | 100 1000 0 | 1/256 |
︙ | ||
15 | 100 1111 0 | 1/256 |
16 | 101 10000 0 | 1/512 |
︙ | ||
2761 | 100 1100 101011001001 0 | 1/1,048,576 |
︙ |
See also
References
- ↑ Even, Shimon; Rodeh, Michael (April 1978). "Economical encoding of commas between strings". Communications of the ACM. 21 (4): 315–317. doi:10.1145/359460.359480.
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