LT code encoding with k packet using probability of Ideal Soliton matlab

given data input K-packets and N packets I need to produce N packet codes, where each code is an ex-or combination of the original packet, I define d which is will be a random number that will tell me how many packets I can combine; each package will be generated automatically. Then create a probability of distribution of numbers between 1 and k probability which must be equal to 1: Soliton Distribution and calculate the probability of each value between 2 and k,all by using matlab function

Answer 1

[Gojo]

Hi Wael,

I understand that you have ‘K’ packets using which you wish to create ‘N’ packet codes. The packet code is generated by combining ‘d’ packets using an ex-or combination where ‘d’ is a random number generated using Ideal Soliton Distribution.

The Ideal Soliton distribution is given by:

P(1) =1/K ,

P(i) =1 / ( i * (i-1) ) (for i=2,3,4……K.)

You can refer to the following MATLAB Answer for generating the Ideal Soliton Distribution: https://www.mathworks.com/matlabcentral/answers/644135-ideal-soliton-distribution-code

After generating the probability distribution, you can generate a random number ‘d’ using the “randsample” function. The Soliton distribution can be passed as an argument in “randsample” function. You can refer to the documentation of “randsample” function: https://www.mathworks.com/help/stats/randsample.html

Please refer to the following code snippet:

K = 10;  
N = 5;   

% Randomly generating K-packets (input data) 
K_packets = randi([0, 1], K, 8) 

K_packets = 10×8

1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0

packet_codes = generate_packet_codes(K,K_packets, N) 

packet_codes = 5×8

1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0

function packet_codes = generate_packet_codes(K,K_packets, N) 
    % Calculate Soliton distribution probabilities 
    soliton_probs = zeros(1, K); 
    soliton_probs(1) = 1 / K; 
    for d = 2:K 
        soliton_probs(d) = 1 / (d * (d - 1)); 
    end 

    % Ensure the probability distribution sums to 1 
    soliton_probs = soliton_probs / sum(soliton_probs); 

    % Generating N packet codes 
    packet_codes = zeros(N, 8); 

    for i = 1:N 
        % Generate 'd' using Soliton distribution 
        d = randsample(1:K, 1, true, soliton_probs); 
        
        % Randomly select d packets to XOR 
        packets_to_xor = randsample(1:K, d); 
        for j = 1:d 
            packet_codes(i, :) = bitxor(packet_codes(i, :), K_packets(packets_to_xor(j), :)); 
        end 
    end 
end 

I have generated ‘K’ packets and a vector containing Soliton distribution for ‘K’ integers. I have used “randsample” to generate a random number ‘d’, and then selected ‘d’ random packets and combined them using XOR to generate ‘N’ packet codes.

I hope this helps.