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Exp 9 :-To obtain standard Huffman code and code efficency using MATLAB , a DMS generates symbols a,b,c with probability.

%% Huffman Code
clc;
clear all;
close all;

% Inputs
unique_chars = ['a' 'b' 'c' 'd' 'e']
probabilities = [0.2 0.4 0.25 0.1 0.05]

% Initialize cell array for codewords
n = length(probabilities);
codewords = cell(1, n);

% Track matrix relationships
temp_prob = probabilities;
tree = cell(1, n);

for i = 1:n
    tree{i} = i;
end

% Combine nodes until only one tree root remains
while length(temp_prob) > 1

    % Sort probabilities in ascending order
    [temp_prob, idx] = sort(temp_prob);
    tree = tree(idx);

    % Assign binary digits to paths
    left_nodes = tree{1};
    right_nodes = tree{2};

    for idx_l = left_nodes
        codewords{idx_l} = ['0', codewords{idx_l}];
    end

    for idx_r = right_nodes
        codewords{idx_r} = ['1', codewords{idx_r}];
    end

    % Merge the lowest two probabilities
    new_prob = temp_prob(1) + temp_prob(2);
    new_node = [left_nodes, right_nodes];

    % Rebuild arrays
    temp_prob = [new_prob, temp_prob(3:end)];
    tree = [{new_node}, tree(3:end)];

end

% Print results
fprintf('\n--- Huffman Codebook ---\n');

for i = 1:length(unique_chars)
    fprintf("Character: '%c' -> Code: %s\n", ...
        unique_chars(i), codewords{i});
end

exp 10 :- To encode and decode linear block codes using MATLAB.

%% Linear Block Code
clc;
clear all;
close all;

%% Encoder
disp('======= Generator Matrix =======');
disp('Parity Matrix');

P = [1 1 0; 0 1 1; 1 0 1; 1 1 1]

disp('Generator Matrix');
G = [eye(4,4), P]

%% Encoder
disp('======= Encoder =======');
disp('Data');

D = [1 1 0 1];

disp('Code');
C = mod(D*G, 2);

%% Decoder
disp('======= Decoder =======');
disp('Error Pattern');

E = [0 0 0 1 0 0 0];

disp('Received Code');
R = mod((C + E), 2);

disp('H Transpose');
HT = [P; eye(3)];

disp('Syndrome');
S = mod(R*HT, 2);

if all(S == 0)
    disp('=== No Error in received message ===');

    disp('Decoded Data');
    D_received = R(1:4);

else
    disp('=== Error in received message ===');

    disp('Location of error bit');
    [tf, index] = ismember(S, HT, 'rows');
    disp(index);

    disp('Corrected Received Message');
    Error = zeros(1,7);
    Error(index) = 1;

    R_corrected = mod((R + Error), 2);
    disp(R_corrected);

    disp('Decoded Data');
    D_received = R_corrected(1:4);
end