In coding theory, a Tanner graph, named after Michael Tanner, is a bipartite graph used to state constraints or equations which specify error correcting codes. In coding theory, Tanner graphs are used to construct longer codes from smaller ones. Both encoders and decoders employ these graphs extensively.
Tanner graphs were proposed by Michael Tanner[1] as a means to create larger error correcting codes from smaller ones using recursive techniques. He generalized the techniques of Elias for product codes.
Tanner discussed lower bounds on the codes obtained from these graphs irrespective of the specific characteristics of the codes which were being used to construct larger codes.
Tanner graphs are partitioned into subcode nodes and digit nodes. For linear block codes, the subcode nodes denote rows of the parity-check matrix H. The digit nodes represent the columns of the matrix H. An edge connects a subcode node to a digit node if a nonzero entry exists in the intersection of the corresponding row and column.
Tanner proved the following bounds
Let
R
m
n
R\geq1-(1-r)m
The advantage of these recursive techniques is that they are computationally tractable. The codingalgorithm for Tanner graphs is extremely efficient in practice, although it is notguaranteed to converge except for cycle-free graphs, which are known not to admit asymptoticallygood codes.[2]
Zemor's decoding algorithm, which is a recursive low-complexity approach to code construction, is based on Tanner graphs.