Equivalence of decipherable and prefix code lengths
= Equivalence of decipherable and prefix code lengths
Prescribed positive word lengths admit a <decipherable code> if and only if they admit a <prefix code>. Counting length-$L$ concatenations of $m$ words proves the <Kraft inequality> for any <decipherable code>; choosing free vertices of the ordered $D$-ary <tree> constructs a <prefix code> whenever this inequality holds. Each <prefix code> has <unique decodability>.