Cheap Transmission

Let $A$ and $B$ be bit strings (sequences of $0$'s and $1$'s). If $A$ is equal to the leftmost $length(A)$ bits of $B$, then $A$ is said to be a prefix of $B$. For example, $00110$ is a prefix of $001101001$, but not of $00111$ or $100110$. A prefix-free code of size $n$ is a collection of $n$ distinct bit strings such that no string is a prefix of any other. For example, this is a prefix-f