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Truncated binary encoding

Truncated binary encoding is an entropy encoding typically used for uniform probability distributions with a finite alphabet. It is parameterized by a maximum number n. It is slightly more general than binary encoding which is only optimal where n is a power of two.

For example, if n is 4, binary encoding allocates these codewords:

Number Encoding
0000
1001
2010
3011
4100
UNUSED101
UNUSED110
UNUSED111

Instead, truncated binary allocates:

Number Encoding
000
101
210
3110
4111

You can think of this as allocating an UNUSED to the first few symbols (until you run out of UNUSEDs), to make the first few symbols' codewords shorter.



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