1 research outputs found
A Branch-and-Cut Algorithm to Design LDPC Codes without Small Cycles in Communication Systems
In a digital communication system, information is sent from one place to
another over a noisy communication channel using binary symbols (bits).
Original information is encoded by adding redundant bits, which are then used
by low--density parity--check (LDPC) codes to detect and correct errors that
may have been introduced during transmission. Error correction capability of an
LDPC code is severely degraded due to harmful structures such as small cycles
in its bipartite graph representation known as Tanner graph (TG). We introduce
an integer programming formulation to generate a TG for a given smallest cycle
length. We propose a branch-and-cut algorithm for its solution and investigate
structural properties of the problem to derive valid inequalities and variable
fixing rules. We introduce a heuristic to obtain feasible solutions of the
problem. Our computational experiments show that our algorithm can generate
LDPC codes without small cycles in acceptable amount of time for practically
relevant code lengths.Comment: 31 pages, 18 figures, 7 table