An algorithm for optimal prefix parsing of a noiseless and memoryless channel

We discuss the prefix encoding of a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -ary source <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(Q ≥ 2)</tex> into an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> -symbol channel alphabet with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L ≥ Q</tex> . We present an optimal encoding scheme that minimizes the expected cost per symbol in the case of equally probable source symbols and arbitrary channel symbol costs.