Upper bounds on the rate of LDPC codes as a function of minimum distance

Abstract

New upper bounds on the rate of low-density parity-check (LDPC) codes as a function of the minimum distance of the code are derived. These bounds are based on combinatorial arguments and linear programming. They improve on the previous bounds due to Burshtein et al. It is proved that at least for high rate LDPC codes have worse relative minimum distance than the one guaranteed by the Gilbert-Varshamov bound