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