As the error clearly states, the sizes of variables H1 and extra_cols are not compatible for horizontal concatenation.
What exactly do you want to do with that particular operations of horizontal and vertical concatenation? What is the expected output from that step?
Also, note that m=1 and m=2 will lead to an error in the 3rd and 5th lines of the function get_random_index(), respecitvely.
m=4;%input('Enter the number of elements m = ');
Hb=hankel(1:m,m:-1:1); % Hankel matrix
%% Initialization of the sub-matrices with dimensions (m-1 x m-1)
a=zeros(m-1,m-1,m-2);
a(:,:,1)=eye(m-1); % the identity sub-matrix with index = 1
for k=2:m-1
a(:,:,k)=circshift(a(:,:,k-1),1,2); % Sub-matrix with indexes = 2 to m-1
end
a(:,:,m) = zeros(m-1); % Sub-matrix with index = m
%% Choice of indexes x and y where (x + y = m)
idx = get_random_index(m);
%% Replacement of the sub-matrices with indexes 1,2,...m in Hb
H1 = zeros(m*(m-1));
a = num2cell(a,[1 2]);
for ii = 1:m
for jj = 1:m
if ismember(Hb(ii,jj),idx)
H1((m-1)*(ii-1)+1:(m-1)*ii,(m-1)*(jj-1)+1:(m-1)*jj) = a{Hb(ii,jj)};
end
end
end
% Desired code rate
code_rate = 3/4;
% Determine the number of extra rows and columns needed
num_extra_rows = round((1/code_rate - 1) * m);
num_extra_cols = num_extra_rows;
% Create the extra rows and columns
extra_rows = repmat(eye(m), num_extra_rows, 1);
extra_cols = repmat(eye(m), 1, num_extra_cols);
% Add the extra rows and columns to H1
H1
extra_cols
%% Function
function idx = get_random_index(m)
if mod(m,2)
idx = randi([1 m-1]);
else
idx = randi([1 m-2]);
if idx >= m/2
idx = idx+1;
end
end
idx = [idx m-idx];
end
