
Numeral systems are optimal for encoding sequences of symbols (digits) that have uniform distribution.
An asymmetric numeral system is a generalization constructed to be optimal for any given probability distribution

of symbols (digits).
With some information stored in a natural number

, to add some information stored in a digit

that all has the same probability (

), take

to place this information in the right-most bits.
In the asymmetric case

should hold asymptotically.
This cannot usually be done exactly, but for asymptotic behavior the symbols only need to be distributed uniformly. A random number generator can be used to choose a specific distribution. If this generator is initialized with a given key, this additionally encrypts the output.
To encode in this way,

would grow to infinity. To prevent that,

is restricted to some range

and some bits are removed in blocks of "width" bits to a bit stream (compressed file).
Basic information about this coding can be found in:
More information about using it in cryptography: