Date: Tue, 25 Jul 2000 23:42:39 -0700 (PDT) From: Kris Kennaway <kris@FreeBSD.org> To: "Jeroen C. van Gelderen" <jeroen@vangelderen.org> Cc: arch@freebsd.org Subject: Re: Quantifying entropy Message-ID: <Pine.BSF.4.21.0007252338370.58758-100000@freefall.freebsd.org> In-Reply-To: <Pine.BSF.4.21.0007222010590.52795-100000@freefall.freebsd.org>
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On Sat, 22 Jul 2000, Kris Kennaway wrote:
> Some interesting numbers:
>
> The shannon entropy of this sample as a pure probability distribution is
> 8.50 bits/sample (they're 16-bit signed values).
>
> Compressing with gzip -9 and comparing the file sizes gives an entropy
> estimate of 10.4 bits/sample.
>
> Compressing with bzip2 -9 gives an estimate of 7.90 bits/sample,
> suggesting there is indeed some time-correlation in the signal noise.
Actually I just worked out why bzip2 gave this result: bzip2 treats the
data as an 8-bit source, and from that perspective my data has 7.92 bits
of entropy per 16-bits :-) (because the spectrum is peaked around 320
(when interpreted as unsigned 16-bit quantities), every second byte is
most likely to be an '00' or '01', thus skewing the 8-bit distribution)
Kris
--
In God we Trust -- all others must submit an X.509 certificate.
-- Charles Forsythe <forsythe@alum.mit.edu>
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