Column operations in LDPC generator matrix

1. How do you find the parity matrix of a generator matrix?
2. How does LDPC work?

How do you find the parity matrix of a generator matrix?

Definition. Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C^⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc^⊤ = 0 (some authors would write this in an equivalent form, cH^⊤ = 0.) to be a codeword of C.

How does LDPC work?

LDPC Decoding Algorithm

The decoding algorithms work by exchanging messages between the check and variable nodes. These messages contain a value that is proportional to the probability or the “belief” in the “correctness” of the received bit.