One-to-one source code

A one-to-one source code is an injective function from source symbols to finite codewords. Unlike a prefix code, it need not permit instantaneous decoding of concatenated codewords.

Order source symbols by decreasing probability and assign the $i$th symbol a binary word of length $\lfloor {\log }_{2}i\rfloor$. This minimizes expected length among one-to-one binary codes because the available shortest words are assigned to the most probable symbols.