I have two binary vectors x1 and x2 of length n=100 bits, with Hamming distance d(x1,x2)≤10. I want to compress x1 with rate H(x1|x2) and transmitting the compressed version of x1 to decoder while putting x2 as the side information at the decoder. Finally, I want to decompress x1 by considering x2 as the side information.
If I want to do this process by utilizing LDPC codes. How should I design the LDPC code to make sure that it has the capability of correcting t=10 bits at the decoder? Generally, I need to know the steps of designing LDPC codes with the capability of correcting t bits?