Random substitution for QAM symbols

Hi everyone, I want to do a random substitution for QAM symbols based on secret key or random vector.

For example, suppose 4-QAM modulation with the following substitution:

(00) is substituated to (10) ,

(01) is substituated to (00),

(10) is substituated to (11), and

(11) is substituated to (01).

Based on a secret key, the subsituation box is changed.

May you guide me how to do that in matlab with any M-ary QAM?

Thanks in advance.

Answer 1

[Walter Roberson]

lookup = [1 0; 0 0; 1 1; 0 1];   %must be in numeric order

output = reshape(lookup([2 1] * reshape(VectorOfBits, 2, []) + 1, :).', 1, []);

The [2 1]* is converting from 2 bit binary into decimal. Then +1 to get a 1-based index, that is used to index into the lookup table of replacements. The rest has to do with arranging bits in the right order for processing.

There are other ways, such as

output = reshape(lookup(VectorOfBits(1:2:end)*2 + VectorOfBits(2:2:end) + 1,:).', 1, []);

and some of the work can be made easier if you make the lookup table column-oriented instead of row oriented.

[YAHYA AL-MOLIKI]

Thank you Mr. Walter. Unfortuently, your code doesn't implement a corect subsistution.

[Walter Roberson]

I tested the code before I posted. Both versions work according to the requirements that were given.

Answer 2

[YAHYA AL-MOLIKI]

I suggest the following code to implement substituation.

function y=substit(x,k)

y=zeros(length(x),2);

Rl=[0 0; 0 1; 1 0; 1 1];

Rm=randintrlv(Rl,k); %k is the secret key that is used to produce the substituation table.

for i=1:length(x)

switch binaryVectorToDecimal(x(i,:))

case 0

y(i,:)=Rm(1,:);

case 1

y(i,:)=Rm(2,:);

case 2

y(i,:)=Rm(3,:);

case 3

y(i,:)=Rm(4,:);

end

end

end

If there is another suggestion, you may share your codes.

[YAHYA AL-MOLIKI]

I suggest also the following code to implement inverse substituation as follows:

function y=invsubstit(x,k)

y=zeros(length(x),2);

Rl=[0 0; 0 1; 1 0; 1 1];

Rm=randintrlv(Rl,k);

Rmd=binaryVectorToDecimal(Rm);

for i=1:length(x)

switch binaryVectorToDecimal(x(i,:))

case 0

m=find(Rmd==0);

y(i,:)=Rl(m,:);

case 1

m=find(Rmd==1);

y(i,:)=Rl(m,:);

case 2

m=find(Rmd==2);

y(i,:)=Rl(m,:);

case 3

m=find(Rmd==3);

y(i,:)=Rl(m,:);

end

end

end