Distance Bounds for an Ensemble of LDPC Convolutional Codes
Arvind Sridharan, Dmitri V. Truhachev, Michael Lentmaier, Daniel J. Costello, Kamil Sh. Zigangirov · IEEE Transactions on Information Theory · 2007
An ensemble of$(J,K)$-regular low-density parity- check (LDPC) convolutional codes is introduced and existence-type lower bounds on the minimum distance$d _ {\rm L}$of code segments of finite length$L$and on the free distance$d _{\rm free}$are derived. For sufficiently large constraint lengths$ u$, the distances are shown to grow linearly with$ u$and the ratio$d_ {\rm L}/ u$approaches the ratio$d _{ {\rm free}}/ u$for large$L$. Moreover, the ratio of free distance to constraint length is several times larger than the ratio of minimum distance to block length for Gallager's ensemble of (J,K)-regular LDPC block codes.