Channel Coding: Theory, Algorithms, and Applications

Example 12

The unstructured irregular ensemble with design rate $R=1/2$ and degree distribution pair

$\begin{array}{cc}\hfill \lambda (x)=& 0.062498x+0.479743x^2+0.049808x^5+0.117758x^8+0.290192x^{29}\hfill \\ \hfill \rho (x)=& x^8\hfill \end{array}$

is characterized by a threshold ${(E_b/N_0)}^{\ast }=0.559022\text{dB}$ (evaluated by EXIT chart). The degree distribution pair has been obtained via threshold optimization constrained to maximum variable node degree equal to 30, concentrated check node degree equal to 9, design rate 1/2, and ${\lambda }_2{\rho }^{\prime }$