Tanner graphs

A Tanner graph is a bipartite graph representation of the parity-check equations of a linear code.

Linear Block Codes
The Tanner graph $G$ of a linear block code has the vertex bipartition $V(G) = V_v \cup V_c$. The vertices in $V_v$ are called variable nodes and the ones in $V_c$ are called check nodes. The variable nodes represent the codeword bits and the check nodes represent the parity-check equations. A variable node $v_i$ is connected to a check node $c_j$ if and only if the bit corresponding to $v_i$ is involved in the parity-check equation corresponding to $c_j$.

For example, if the parity-check equation $$v_1 + v_3 + v_7 = 0$$ is represented by the check-node $c_3$, then $c_3$ is connected to $v_1, v_3, v_7$ and no other variable nodes.