Low complexity decoding of low density parity check codes

A decoder for a low density parity check code having a processor providing a method comprising:

• a) defining a set of variable nodes indexed by an integer n and a set of check nodes indexed by an integer m, wherein each variable node n is associated with a set of check nodes M(n) and each check node m is associated with a set of variable nodes N(m);
• b) predetermining a neutral check message magnitude CKn, a weak check message magnitude CKw, a medium check message magnitude CKm and a strong check message magnitude CKs;
• c) initializing all of the variable nodes to have values Wn equal to initial values Ln(0) computed from received symbols;
• d) quantizing each variable node value Wn with respect to a decision threshold X and weight thresholds T1 and T2 to provide a quantized value Qn and a weight Rn, wherein Qn is selected from predetermined values Q0 and Q1, wherein Qn=Q0 if Wn<X and Qn=Q1 if Wn≧X, and wherein Rn is weak if |Wn−X|≦T1, Rn is medium if T1<|Wn−X|≦T2, and Rn is strong if T2<|Wn−X|;
• e) providing a variable message Zn from each variable node n to each of the corresponding set of check nodes M(n), wherein the variable message Zn includes the quantized value Qn and the weight Rn;
• f) calculating a check node output message Lmn from each check node m to each of the corresponding set of variable nodes N(m), wherein Lmn is determined by a parity check function fmn[{Zn:nεN(m)}] of the variable messages provided to check node m and wherein Lmn depends partly on the predetermined check message magnitudes CKn, CKw, CKm and CKs;
• g) updating the variable node values Wn based on the check node output messages Lmn;
• h) repeating steps (d) through (g) above in sequence until a termination condition is satisfied.