Upper bounds on the rate of LDPC codes
David Burshtein, Michael Krivelevich, Simon N. Litsyn, G. Miller · IEEE Transactions on Information Theory · 2002
We derive upper bounds on the rate of low-density parity-check (LDPC) codes for which reliable communication is achievable. We first generalize Gallager's (1963) bound to a general binary-input symmetric-output channel. We then proceed to derive tighter bounds. We also derive upper bounds on the rate as a function of the minimum distance of the code. We consider both individual codes and ensembles of codes.