On 2015-08-05 17:06, Glen Hermannsfeldt (Contractor) wrote:
> 8 bits per byte, all ones.
>     ...
> (and the third compression increased the original from 90 to 110 bytes.)
> 
That's typical.  If each compression reduced the size of the file, every
file could be compressed with enough iterations to a single byte.

A colleague has proposed this as a compression technique: Regard any file
as a stream of ones and zeroes representing a binary number.  Iteratively
subtract 1 from the number.  Most of the time its length doesn't change;
some small fraction of the time a borrow ripples all the way to the left
and it gets one bit shorter.  With sufficient iterations the file is reduced
to a single bit.

The algorithm is reversible; no information is lost.  Simply add 1 as many
times as you subtracted 1 and the original file is restored perfectly.

(Leading zeroes spoil the technique.  Devising a repair is left as an
exercise for the student.)

-- gil

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