Distance Bounds for an Ensemble of LDPC Convolutional Codes

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
$\nu$
, the distances are shown to grow linearly with
$\nu$
and the ratio
$d_ {\rm L}/\nu$
approaches the ratio
$d _{ {\rm free}}/\nu$
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.