| biject 2007-12-13, 6:56 pm |
| On Dec 13, 5:35 am, Mark Nelson <snorkel...@gmail.com> wrote:
> On Dec 12, 10:00 pm, biject <davvid_a_sc...@email.com> wrote:
>
>
> David,
>
> The reversible transform permutes all the data in a message. The
> standard procedure for inverting the transform requires that you know
> in advance the position of the final character.
>
> It sounds like you are saying that you can permute a message of N
> symbols into another message of N symbols, and can then perform the
> inverse without knowing the position of the final character.
>
> Do I misunderstand your claim?
>
> |
> | Mark Nelson -http://marknelson.us
> |
Yes its what I call a Scottification of the BWT it gets rid of the
index
you have the code test it. N symbols to N symbols its what the BWT
should have been in first place to allow for bijective compression.
But llike any compressor sometimes you end up with a smaller file
sometimes not. Its like bijective arithmetic versus bijective huffman
sometime one better sometimes the other. Though for most useful
the bijective arithmetic better.
For an example take bananas
old way it bwt tranforms to BNNSAAA
one way to get reverse is to list transform then sort single charter
string
this gets AAABNNS then create an array of two elements each you get
BA NA NA SB AN AN AS sort these then repeat eventually you get
a table of with word BANANAS each with rotation possible you need an
index to pick which rotation thats the old way.
In my way you end up using the .top row for the inverse BTWS no index
each single cycle maps to one unique file.
In my case when I BWTS BANANAS I get SNNBAAA it looks as nice
as old way but no index. There is no reverse of this string regardless
of
index with old BWT method since this is not a single cycle string.
if you apply the method of about you end up with 2 differeents cyles
usinga above method first row is
ANANAS you can repeat if needed
ANASAN is second row
ASANAN is thrid row
BBBBBB is forth row
NANASA is next
NASANA is next
SANANA is last
now first cycle is ANANAS if it was a single cycle it would have all
7 letters and reverse done
this does not so look for next cycle its B know combine the 2 in
reverse order
you get BANANAS so new way
BANANAS transforms to SNNBAAA while old way
BANABAS transforms to BNNSAAA with an index
 ly there is no revere transform old way to SNNBAAA
but n new way
ANANASB transform to BNNSAAA
BWTS is the reverse of above. Look at it this way when you sort lets
say the word THE apears
many times in the single cycle method they woul sort together. If
there are many cyles in new
way that contain the word THE in each cycle, The BWT still sorts them
together.
David A. Scott
--
My Crypto code
http://bijective.dogma.net/crypto/scott19u.zip
http://www.jim.com/jamesd/Kong/scott19u.zip old version
My Compression code http://bijective.dogma.net/
**TO EMAIL ME drop the roman "five" **
Disclaimer:I am in no way responsible for any of the statements
made in the above text. For all I know I might be drugged.
As a famous person once said "any cryptograhic
system is only as strong as its weakest link"
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