The decoder logic behind this repo is built based on H. Wymeersch, H. Steendam, and M. Moeneclaey "Log-domain decoding of LDPC codes over GF(q)"
Decoder in NBLdpcDecoder::Decode
Every message passed on the Tanner graph is a length-q vector of LLRs, relative to symbol value 0:
L(a) = ln P(a) - ln P(0), a = 0, 1, 2, 3
L(0) = 0 if fixed. A positive L(a) means a is more likely than 0, negative L(a) means a is less likely than 0, and magnitude of L(a) is the confidence of this estimation w.r.t. 0.
Substitution channel model. The channel is defined by a substitution probability matrix
Q[i][j] = P(received = j | sent = i) where i, j = 0, 1, 2, 3
read from file and stored as log-probabilities:
M[i][j] = ln(Q[i][j])
Channel input LLR (m_ppInputLLRs[i], filled by DnaChannel::ComputeLLRs): given observed symbol y_i and substitution probability matrix,
L_i(a) = ln P(y_i | c_i=a) - ln P(y_i | c_i=0) = ln Q[a][y_i] - ln Q[0][y_i]
For a given variable node i, it receives an observed symbol y_i from the channel. Then for every candidate symbol a in GF(4), apply this formula to build the LLR vector message initialized at that VN.