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 distanced _ Lof code segments of finite lengthLand on the free distanced freeare derived. For sufficiently large constraint lengthsν, the distances are shown to grow linearly withνand the ratiod_ L/νapproaches the ratiod _ free/νfor largeL. 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.