Let X and Y be the binary random numbers. e.g. {0,1}^n. Assume that X and Y strings length 100 bits with an error probability of 1% (10 error bits). To correct the errors in Y string, X and Y agree to divide their strings into blocks. Each block size 20 bits overall they have 5 blocks. Now both X and Y apply binary search algorithm to detect the error block by exchanging the parity information of the block.
E.g. The first block of Y contained a one-bit error (assume that 18th position of Y is an error)
X={10110000010010110100};
Y={10110000010010110000};
To correct that bit they divide the block into subblocks and exchange the parity bits. The first 20 bits divided into 1-10 bits and 11-20 bits and then they compute the parity of those subblocks. Now 2 bits of information need to be exchanged with Y to identify the error block.
e.g X_1={1011000001}; mod(sum(X_1),2)=0;
Y_1={1011000001};mod(sum(Y_1),2)=0;
X_2={0010110100}; mod(sum(X_2),2)=0;
Y_2={0010110000}; mod(sum(Y_2),2)=1;
The mod (X1)+ mod (X_2)= mod(X). Suppose if I exchange the one parity bit instead of two parity bits, how can I extract that in Y side and distinguish which parity bits coresponding to which subblock?.
I knew this is going to minimise the number of parity bits exchanged.
At the moment, I couldn't implement it. Can anyone help me with this?.
