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Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!sarah!bingnews!kym
From: kym@bingvaxu.cc.binghamton.edu (R. Kym Horsell)
Subject: Re: theoretical compression factor
Message-ID: <1991Mar25.054838.15588@bingvaxu.cc.binghamton.edu>
Keywords: random
Organization: State University of New York at Binghamton
References: <1991Mar25.031214.25696@bingvaxu.cc.binghamton.edu>
Date: Mon, 25 Mar 1991 05:48:38 GMT


I found one little problem with my algebra & understanding.
Delta modulation takes N bits into O(N) bits, NOT less. 

The theoretical compression factor for my binary strings example
would therefore be

	2p(1-p)

where p is the proportion of 0's (or 1's -- it doesn't matter).

For /usr/dict/words the proportion of 1's is about 56% (only
considering the lsb 7 bits of each char). This should give
a compression factor of about 49% with the method outlined.

Tables of random ascii digits contain about .38 1's (taking only lsb 7
bits) which leads to a similar .47 compression factor. If we massage
digit strings to 4-bit groups (by subtracting the '0') we find only
about 6% 1's and therefore the compression factor would be .1 (i.e. a 1Mb 
file of random digits -> 100Kb).

Again, if there are any glaring errors, please comment.

-kym