Rate distortion plot how?

I need to test my compression program and what I need is to plot a
rate-distortion figure Specifically

my signal is f[n]=1 if n=0,1,.....,12.
and f[n]=0 otherwise. n is from 0 to 255.


My algorithm decompose the signal to 256 coefficients and using M bits
to encode each coefficient. (M can be changed)

Now to plot the rate_distortion, I guess I will:

1. Let M = some various numbers (5, 6, ...,100) and calculate the
corresponding distortions: ie: M1= 5, D1, M2=6, D2, ..... and so on.

Then plot this data (plot (M,D)) one axis is M and the other one is D.
Is this plot a RATE- DISTORTION?
If not please guide me how to do plot it.
Thanks

"A.E lover" <aelover11@gmail.com> writes:

> I need to test my compression program and what I need is to plot a
> rate-distortion figure Specifically
>
> my signal is f[n]=1 if n=0,1,.....,12.
> and f[n]=0 otherwise. n is from 0 to 255.
>
>
> My algorithm decompose the signal to 256 coefficients and using M bits
> to encode each coefficient. (M can be changed)
>
> Now to plot the rate_distortion, I guess I will:
>
> 1. Let M = some various numbers (5, 6, ...,100) and calculate the
> corresponding distortions: ie: M1= 5, D1, M2=6, D2, ..... and so on.
>
> Then plot this data (plot (M,D)) one axis is M and the other one is D.
> Is this plot a RATE- DISTORTION?
> If not please guide me how to do plot it.
> Thanks

Hi,

The rate distortion function first requires three things to be defined:

  1. A distortion measure d(x,y), where d(x,y) \in R and d(x,y) >= 0.

  2. The average distortion over n symbols, D(x^n, y^n) = (1/n) sum_{i=1}^n (d(x_i,y_i)).

  3. An input probability density function p(x).

The rate distortion function r(delta) is then defined as the minimum
rate r such that the average distortion D is less than delta. 

The performance of any encoder/decoder should fall on a point in the
r(delta),delta plane between the delta axis and the r(delta) function.

Do you mean you wish to determine which point your encoder/decoder
falls on this plane? If so, then I would generate a source at the
assumed input distribution and measure the resulting average
distortion and rate. These two parameters define a point on the
r(theta), theta plane, and hopefully it is close to the theoretical
rate limit at the measured distortion.

See [cover] for a reference.

--Randy

@book{cover,
  title = "Elements of Information Theory",
  author = "Thomas M. Cover and Joy A. Thomas",
  publisher = "John Wiley and Sons, Inc.",
  year = "1991"}

-- 
%  Randy Yates                  % "So now it's getting late,
%% Fuquay-Varina, NC            %    and those who hesitate
%%% 919-577-9882                %    got no one..."
%%%% <yates@ieee.org>           % 'Waterfall', *Face The Music*, ELO
http://home.earthlink.net/~yatescr

A.E lover wrote:
> I need to test my compression program and what I need is to plot a
> rate-distortion figure Specifically
> 
> my signal is f[n]=1 if n=0,1,.....,12.
> and f[n]=0 otherwise. n is from 0 to 255.
> 
> 
> My algorithm decompose the signal to 256 coefficients and using M bits
> to encode each coefficient. (M can be changed)
> 
> Now to plot the rate_distortion, I guess I will:
> 
> 1. Let M = some various numbers (5, 6, ...,100) and calculate the
> corresponding distortions: ie: M1= 5, D1, M2=6, D2, ..... and so on.
> 
> Then plot this data (plot (M,D)) one axis is M and the other one is D.
> Is this plot a RATE- DISTORTION?
> If not please guide me how to do plot it.

By what criteria do you assess distortion?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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