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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 an alphabet with total size of number n. It is a slightly more general form of binary encoding when n is not a power of two.
If n is a power of two, then the coded value for 0 ≤ x < n is the simple binary code for x of length log2(n).
Otherwise let k = floor(log2(n)), such that 2k < n < 2k+1
and let u = 2k+1 − n.
Truncated binary encoding assigns the first u symbols codewords of length k and then assigns the remaining n − u symbols the last n − u codewords of length k + 1. Because all the codewords of length k + 1 consist of an unassigned codeword of length k with a "0" or "1" appended, the resulting code is a prefix code.
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