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Table 1 LDPC decoding based on log likelihood ratio (LLR) belief propagation (BP) algorithm

From: Dynamic voltage and frequency scaling scheme for an adaptive LDPC decoder using SNR estimation

Definition LDPC decoding
H mn the value at row m and col n of H-matrix
N(m) the set of bit nodes including the check node m
M(n) the set of check nodes including the bit node n
Algorithm  
Initialization set F n  = LLR for bit nodes (n = 1,2,…,N)
  set Z mn  = F n if H mn is 1 for each (m,n)
  while (i ≤ imax)
Check node for each check node
Processing where each (m,n) if H mn is 1
  T mn = n N m \ n 1 - e Z m n 1 + e Z m n
  L mn = ln 1 - T mn 1 + T mn
  end for
Bit node for each bit node
Processing where each (m,n) if Hmn is 1
  Z mn = F n + m M n \ m L m n
  Z n = F n + m M n L mn
  end for
Tentative for each n (n = 1,2,…,N)
Decision C ^ = C ^ 1 C ^ N , C ^ n = 0 , Z n 0 1 , Z n < 0
  end for
Parity check if H 2 C ^ 1 C ^ N T is 0
  return success
  i ++
  end while