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 dL, of code segments of finite length L and on the free distance dfree are derived. For sufficiently large constraint lengths v, the distances are shown to grow linearly with v and the ratio dL/v approaches the ratio dfee/v 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.