irregular ldpc codes - uc3m：非规则ldpc码- uc3m.pdf

Irregular LDPC Codes Irregular LDPC Left (variable) node distribution: Right (check) node distribution: 50% of variable nodes: degree 3 50% of variable nodes: degree 4 All check nodes: degree 7 The Message Flow V i → j 6 edges 2 edges 50% of variable nodes: degree 3 50% of variable nodes: degree 4 All check nodes: degree 7 V i → j Sometimes… At other times… 6 edges 3 edges The Message Flow V i → j 6 edges 2 edges V i → j Sometimes… At other times… 6 edges 3 edges R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 2 = δδδδ·(1–(1 – R 0) 6) 2 R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 3 = δδδδ·(1–(1 – R 0) 6) 3 The Message Flow V i → j 6 edges 2 edges V i → j Sometimes… At other times… 6 edges 3 edges So what is R 1 ??? R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 2 = δδδδ·(1–(1 – R 0) 6) 2 R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 3 = δδδδ·(1–(1 – R 0) 6) 3 The Message Flow Sometimes… At other times… V i → j 6 edges 3 edges 6 edges V i → j 2 edges R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 2 = δδδδ·(1–(1 – R 0) 6) 2 R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 3 = δδδδ·(1–(1 – R 0) 6) 3 Maybe: R 1 = · δδδδ·L 1 2 + · δδδδ·L 1 3 = · δδδδ·(1–(1 – R 0) 6) 2 + · δδδδ·(1–(1 – R 0) 6) 3 Irregular LDPC 50% of variable nodes: degree 3 50% of variable nodes: degree 4 % of edges are connected to variable nodes of degree 4 The Message Flow % of the time … % of the time … V i → j 6 edges 3 edges 6 edges V i → j 2 edges R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 2 = δδδδ·(1–(1 – R 0) 6) 2 R 0 = δδδδ L 1 = 1 –(1 – R 0) 6 R 1 = δδδδ· L 1 3 = δδδδ·(1–(1 – R 0) 6) 3 R 1 = · δδδδ·L 1 2 + · δδδδ·L 1 3 = · δδδδ·(1–(1 – R 0) 6) 2 + · δδδδ·(1–(1 – R 0) 6) 3 Further Iterations V i → j 6 edges 3 edges 6 edges V i → j 2 edges L t+1 = 1 –(1 – R t) 6 R t+1 = δδδδ· L t+1 2 = δδδδ·(1–(1 – R t) 6) 2 L t+1 = 1 –(1 – R t)