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# about the rate distortion function

Asked by Genus on 15 May 2013

I am having problems with the rate distortion function implemented in matlab. im recieving an error message of

```Error in ==> blahut at 9
m=sum(p.*Y); %mathematical expectation of Y
```
```Error in ==> Rate_distort at 18
[R,SNR] = blahut(p,nl,Y');
```

here is the blahut mfile

```function [R,SNR] = blahut(p,nl,Y)
%This function computes one point of H(D) for given lambda
%D is distortion in dB
%p is probability distribution of input sequence
%nl=-lambda
%Y is approximating set
```
```m=sum(p.*Y); %mathematical expectation of Y
sigma2=sum(p.*(Y-m).^2);%variation of Y
N=length(p);
ry=p; %initialization of distribution r(y)
diff=(diag(Y)*ones(N,N)-ones(N,N)*diag(Y)).^2;
```
```A=2.^(-nl*diff);
D=diff.*A;
flag=1;
%%%%%%%%Iterations%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
while flag==1
v=ry*A'; %sum_y r(y)2^(lambda d(x,y))
P=p./v;%p(x)/sum_y r(y)2^(lambda d(x,y))
c=P*A; %c(y)
ry=ry.*c; %modified distribution
%%%%%%%%Computing thresholds%%%%%%%%%%%%%%%%%%%%
TU=-sum(ry.*log2(c));
TL=-max(log2(c));
error=TU-TL;
%%%%%%%%%%%%%Stopping rule%%%%%%%%%%%%%%%%%%%%%
if error < 10^(-3)
flag=0;
end
d=P*D*ry'; %distortion
rate=-nl*d-log2(v)*p'-TL; %rate;
end
R=rate;
SNR=10*log10(sigma2/d);%distortion in dB
```

Here is my test file with components

N takes in values from 10:10:50

P is the probability distribution in the form of the binomial distribution

theta takes in value in the interval [0 1]

also theta is specified for theta = i/n with i = 0,1,....,n

```%% Values for n
n=50;
%%
theta=0:0.5;
nVec=10:n;
for jdx=1:length(theta)
for kdx=1:length(nVec)
p(jdx,kdx)=nchoosek(n,nVec(kdx))*((theta)^nVec(kdx))*((1-(theta))^(n-nVec(kdx)));
end
end
%% specifications for rate distortion
nl = 0.1;
Y = [0 1; 1  0];
%% Blahut algorithm for rate distortion calculation
[R,SNR] = blahut(p,nl,Y');
```

When I type in my disitortion matrix for Y, this is where Im encountering the error

```Error in ==> blahut at 9
m=sum(p.*Y); %mathematical expectation of Y
```
`    end`

I also need to know how to plot the Distortion vs R(D).

Walter Roberson on 19 May 2013

There would be an error message just before that. For example it might say something like "matrix dimensions must agree". We need to see that message.

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