Regular binary Tanner code[1] 

A binary Tanner code defined on a regular bipartite graph, with the inner code being the same for all vertices.

An alternative definition maps the variable nodes of the generalized Tanner graph to edges of a regular graph \(G\) and the constraint nodes to vertices of \(G\). Bits are placed on edges of \(G\) such that each subsequence of bits corresponding to edges in the neighborhood any vertex belong to some short binary linear code \(C_0\).

More technically, let \(G(V,E)\) be a \(\Delta\)-regular (not necessarily bipartite) graph with number of vertices \(|V| = n \) and number of edges \(|E| = N = n\Delta/2\). Let \(C_0\) be a linear binary code of length \(\Delta\) and rate \(R_0\). The Tanner code \(T(G,C_0)\), whose bits are placed on edges of the graph, consists of the following codewords: \begin{align} \left\{ c \in GF(2)^{n}\,\text{s.t. }\forall v\in V,\left.c\right|_{N(v)}\in C_{0}\right\} ~, \tag*{(1)}\end{align} where \(\left.c\right|_{N(v)}\) is the subsequence formed by the \(\Delta\) bits located on the neighbors \(N(v)\) of the vertex \(v\). The dimension of \(T\) is at least \(N -n(\Delta -\Delta R_0) = N(2R_0-1)\geq 0\) whenever \(R_0 \geq \frac{1}{2}\).