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Elias delta coding : ウィキペディア英語版
Elias delta coding
Elias delta code is a universal code encoding the positive integers developed by Peter Elias.
== Encoding ==
To code a number ''X''≥1:
# Let ''N''=⌊log2 ''X''⌋ be the highest power of 2 in ''X'', so 2''N'' ≤ ''X'' < 2''N''+1.
# Let ''L''=⌊log2 ''N''+1⌋ be the highest power of 2 in ''N''+1, so 2''L'' ≤ ''N''+1 < 2''L''+1.
# Write ''L'' zeros, followed by
# the ''L''+1-bit binary representation of ''N''+1, followed by
# all but the leading bit (i.e. the last ''N'' bits) of ''X''.
An equivalent way to express the same process:
#Separate ''X'' into the highest power of 2 it contains (2''N'') and the remaining ''N'' binary digits.
#Encode ''N''+1 with Elias gamma coding.
#Append the remaining ''N'' binary digits to this representation of ''N''+1.
To represent a number x, Elias delta uses \lfloor \log_2(x) \rfloor + 2 \lfloor \log_2 (\lfloor \log_2(x) \rfloor +1) \rfloor + 1 bits.〔
The code begins, using \gamma' instead of \gamma:
To decode an Elias delta-coded integer:
#Read and count zeros from the stream until you reach the first one. Call this count of zeros ''L''.
#Considering the one that was reached to be the first digit of an integer, with a value of 2''L'', read the remaining ''L'' digits of the integer. Call this integer ''N''+1, and subtract one to get ''N''.
#Put a one in the first place of our final output, representing the value 2''N''.
#Read and append the following ''N'' digits.
Example:
001010011
1. 2 leading zeros in 001
2. read 2 more bits i.e. 00101
3. decode N+1 = 00101 = 5
4. get N = 5 − 1 = 4 remaining bits for the complete code i.e. '0011'
5. encoded number = 24 + 3 = 19
This code can be generalized to zero or negative integers in the same ways described in Elias gamma coding.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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