Distance Bounds for an Ensemble of LDPC Convolutional Codes

Kurzfassung

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.