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:

  1. If N is not less than 4 then set the coded value to a single 0 bit. Otherwise the coded value is empty.
  2. If N is less than 8 then prepend the coded value with 3 bits containing the value of N and stop.
  3. Prepend the coded value with the binary representation of N.
  4. Store the number of bits prepended in step 3 as the new value of N.
  5. Go back to step 2.

To decode an Even–Rodeh-coded integer:

  1. 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.
  2. 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.

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
5 101 0 1/16
6 110 0 1/16
7 111 0 1/16
8 100 1000 0 1/256
9 100 1001 0 1/256
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15 100 1111 0 1/256
16 101 10000 0 1/512
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2761 100 1100 101011001001 0 1/1,048,576
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See also

References

  1. ^ 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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