<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="MSHTML 6.00.2800.1458" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face=Arial size=2>I realized I omitted something important --
sorry.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>This process should not be regarded as lossless;
but lossless compressor's can readily be constructed using this
method.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Here is how:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Be compressing a buffer containing an imperfect
representation of the client data; XOR that imperfect buffer to the actual
client buffer; </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Send the map (compress it first!) of the XOR'ed
differences.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Of course everything you want to send costs (in
space) and the budget cannot exceed the size of the original input
buffer.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=julesg@newebmail.com href="mailto:julesg@newebmail.com">Jules
Gilbert</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=discuss@blu.org
href="mailto:discuss@blu.org">discuss@blu.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Sunday, August 15, 2004 10:52
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> a few facts</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>I did do one demo at MIT in 1996; </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Also while I am not willing to bring floppies in
and do a public demo; I have offered to show certain BLU folks a demo,
off-line from a meeting, to video tape the demo, and then to show the video
tape at a BLU meeting.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I don't know yet whether the people I am talking
to will agree to this -- and won't know until next week or later, (at least
this is my best information at this moment.)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Also, you guys should simply build the model I
described. IT COMPRESS'ES. It's not powerful and it's not
efficient, but it works.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Let me try and show you why, because apparently
some participants here have a little trouble understanding basic vector
algebra.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>First, the client vector (the original buffer) is
random; that won't produce much of value when curve-fit.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Now, building the monotonic vector merely
transforms the X-component (completely random,) to the Y-component, because
now the randomness is tied to the Y attribute. Graph it if you don't get
this. Of course each term used in the curve fit doesn't do much, because
the coefficients 'lock' on the largest non-linearity;</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>This is why, after the subtraction of the
approximation, the residue line has one major discontinuity for
each term. Remember, we are not trying to reduce a 1GB to 1byte here,
each curve fit (and subsequent subtraction) simply reduces the magnitude of
the residue remaining to be compressed.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I am sorry to observe these dynamics; I was
hoping for someone to come forward and say, I built it and I have the
following issues -- or -- I observed ... </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Here's a little more info; maybe this will help
get the right person going...</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The subtractive operation can be replaced by an
XOR; That's less intuitive and doesn't process the left-most three-bit
column field as well, but it does substanially improve the remaining
right-columns; Also, doing this to say 128 cells, each 1 bit
wide;</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>And by applying this process to each vector
concurrently, then making a new vector from the residue of each Y'th row
produces data with much better characteristics;</FONT></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Today my best perpetual compressor's don't use
floating point, but (except for the Y[zero] row of course, where no
improvement can be obtained,) building a "cross-hatch" vector
set has big advantages.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I am pretty busy these days, (and I don't do
compression work any more -- the fighting is just ugly, not why I went into
programming at all) but if someone is interested in this stuff, please email
me.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>--jg</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV> </DIV></BLOCKQUOTE></BODY></HTML>