A small demo which performs a greedy “lower triangulation” on the adjacency matrix of a random code instance of a given LDPC ensemble. The encoding complexity is proportional to the square of the “gap.” In the depicted figure the gap is the height at which the “diagonal” hits the vertical axis of the matrix.

You should enter the degree distribution as polynomials. There are three different ways of doing it.

• Edge perspective: In this case enter the polynomials as ∑_i λ_i x^i-1, where λ_i is the fraction of edges connected to a variable(check) node of degree i. Notice that the power to x is i-1.
• Node perspective: In this case enter the polynomials as ∑_i ∧_i xⁱ, where ∧_i is the fraction of variable (check) nodes of degree i.
• Number of nodes: This is the same as node perspective except that instead of the fraction of nodes, ∧_i denotes the number of nodes.

Block length is the number of variable nodes.

• T. Richardson and R. Urbanke, "Efficient encoding of low-density parity-check codes,” IEEE Trans. Inform. Theory, vol. 47, pp. 638–656, Feb. 2000. Download in .ps