Generalization of Tanner´s minimum distance bounds for LDPC codes

Tanner derived minimum distance bounds of regular codes in terms of the eigenvalues of the adjacency matrix by using some graphical analysis on the associated graph of the code. In this letter, we generalize Tanner´s results by deriving a bit-oriented bound and a parity-oriented bound on the minimum distances of both regular and block-wise irregular LDPC codes.