This is a repost, with a minor correction. I have not coded this
but it is clearly evident that it works, although I intend to code
this shortly. I have also done some independent thinking on hashing
where some methods yield compression but seem to require massive
computation on large numbers. I have another simpler idea but am
not sure whether it yields compression. It is clear that both the
theoretical and practical limit of compression is pretty much
limitless, and entropy must be determined as a lower bound and not
as an upper bound.

This is for coding a binary sequence. Let n be the length of the 
sequence and r the number of 1's in it. 

In regular binary encoding, the individual bit positions are assigned 
fixed weights. Since compression is desired therefore

1) The weights assigned must be variable , and

2) The weight of any position must only be dependent on the number of 
   one's so far or r.

Clearly if there are r 1's in a sequence of length n, the weight of
the n+1'th position will be

w = (2^(r-1))(n - r), where ^ is exponentiation. 


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Posted using www.webuse.net 

daydreamer wrote:
> I have not coded this but it is clearly evident
 > that it works, although I intend to code
> this shortly.

I think at least half of the threads to
comp.compression start like this.

daydreamer wrote:
) This is for coding a binary sequence. Let n be the length of the 
) sequence and r the number of 1's in it. 
)
) In regular binary encoding, the individual bit positions are assigned 
) fixed weights. Since compression is desired therefore
)
) 1) The weights assigned must be variable , and
)
) 2) The weight of any position must only be dependent on the number of 
)    one's so far or r.

3) Therefore, you have to send the value of r beforehand, which takes more
   bits than what you'll save with the subsequent compression.


SaSW, Willem
-- 
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 or something..
            No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

Willem <willem@turtle.stack.nl> wrote:

> daydreamer wrote:
> ) This is for coding a binary sequence. Let n be the length of the 
> ) sequence and r the number of 1's in it. 
> )
> ) In regular binary encoding, the individual bit positions are assigned 
> ) fixed weights. Since compression is desired therefore
> )
> ) 1) The weights assigned must be variable , and
> )
> ) 2) The weight of any position must only be dependent on the number of 
> )    one's so far or r.
> 
> 3) Therefore, you have to send the value of r beforehand, which takes more
>    bits than what you'll save with the subsequent compression.
> 
> 
> SaSW, Willem

Hello,
    The value of r is at most 32 bits for a sequence of length 2^32
bits, and r is always <= n /2. No offence to the mad hatter.
It is rudimentary mathematics. Kindly stop misguiding and misleading
people. Have you even tried it. The idea is phenomenal, so please
stop the misinformation.



Posted using www.webuse.net 

daydreamer wrote:
) Willem <willem@turtle.stack.nl> wrote:
)
)> daydreamer wrote:
)> ) This is for coding a binary sequence. Let n be the length of the 
)> ) sequence and r the number of 1's in it. 
)> )
)> ) In regular binary encoding, the individual bit positions are assigned 
)> ) fixed weights. Since compression is desired therefore
)> )
)> ) 1) The weights assigned must be variable , and
)> )
)> ) 2) The weight of any position must only be dependent on the number of 
)> )    one's so far or r.
)> 
)> 3) Therefore, you have to send the value of r beforehand, which takes more
)>    bits than what you'll save with the subsequent compression.
)> 
)> 
)> SaSW, Willem
)
) Hello,
)     The value of r is at most 32 bits for a sequence of length 2^32
) bits, and r is always <= n /2. No offence to the mad hatter.

Which is roughly the number of bits you can save on average with your
method.  Do the maths and stop handwaving about 'rudimentary mathematics'.


SaSW, Willem
-- 
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 or something..
            No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

On Mar 4, 12:01=A0am, Willem <wil...@turtle.stack.nl> wrote:
> daydreamer wrote:
> ) Hello,
> ) =A0 =A0 The value of r is at most 32 bits for a sequence of length 2^32
> ) bits, and r is always <=3D n /2. No offence to the mad hatter.
>
> Which is roughly the number of bits you can save on average with your
> method. =A0Do the maths and stop handwaving about 'rudimentary mathematic=
s'.

2^n =3D sum C(n,k)
          -- Omar Khayy=E1m

Up from Earth's Centre through the seventh Gate
I rose, and on the Throne of Saturn sate,
And many Knots unravel'd by the Road;
But not the Knot of Human Death and Fate.
          -- Omar Khayy=E1m

HTH.
James Dow Allen