Four different ways of obtaining low-density parity-check codes
from expander graphs are considered. For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived. These bounds are compared with the known eigenvalue-based lower bounds on the minimum distance of expander codes. Furthermore, Tanner's parity-oriented eigenvalue lower bound on the minimum
distance is generalized to yield a new lower bound on the minimum pseudocodeword weight. These bounds are useful in predicting the performance of LDPC codes under graph-based iterative decoding and linear programming decoding.
Mathematics Subject Classification:
Primary: 58F15, 58F17; Secondary: 53C3.
Christine A. Kelley, Deepak Sridhara. Eigenvalue bounds on the pseudocodeword weight of expander codes. Advances in Mathematics of Communications,
Agnaldo José Ferrari, Tatiana Miguel Rodrigues de Souza.
Rotated $ A_n $-lattice codes of full diversity.
Advances in Mathematics of Communications,