Truncated binary encoding
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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 |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| UNUSED | 101 |
| UNUSED | 110 |
| UNUSED | 111 |
Instead, truncated binary allocates:
| Number | Encoding |
|---|---|
| 0 | 00 |
| 1 | 01 |
| 2 | 10 |
| 3 | 110 |
| 4 | 111 |
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.