Optimal regular LDPC codes for the binary erasure channel
Mahmoud Rashidpour, Amin Shokrollahi, S. Hamidreza Jamali · IEEE Communications Letters · 2005
We prove that for any given R between 0 and 1 the best threshold value for a regular LDPC code of rate R with common variable degree v and common check degree c occurs when v is at least 3 and is minimal subject to the condition R=1-v/c.