Low-Density Parity Check (LDPC) codes can be defined by a parity check matrix $\boldsymbol{H}$, it holds for each code word $\boldsymbol{v}$ that $$\boldsymbol{H\cdot v^{\mathsf{T}}}=\boldsymbol{0}$$ A regular block $\left(\mathit{d_{v},d_{c}}\right)$ LDPC code has variable node degree $d_{v}$ and check node degree $d_{c}$, which equals the column (row)-weight of $\boldsymbol{H}$.

Example and Tanner Graph

${k=4}$ information bits and ${m=4}$ parity bits $$\mathbf{H=(P\mid I)=\left[\mathrm{\begin{array}{cccccccc} 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0\\ 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0\\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \end{array}}\right]}$$ $\mathbf{H}$ can be represented by a bipartite graph, so-called Tanner graph [1]