Asymptotic trapping set analysis of regular protograph-based LDPC convolutional code ensembles

It has been suggested that ldquonear-codewordsrdquo may be a significant factor affecting decoding failures of LDPC codes over the AWGN channel. A near-codeword is a sequence that satisfies almost all of the check equations. These near-codewords can be associated with so-called dasiatrapping setspsila that exist in the Tanner graph of a code. In this paper, we analyse the trapping sets of protograph-based LDPC convolutional codes. LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. Further, it has been shown that some ensembles of LDPC convolutional codes are asymptotically good, in the sense that the average free distance grows linearly with constraint length. Here, asymptotic methods are used to calculate a lower bound on the trapping set growth rates for several ensembles of regular asymptotically good protograph-based LDPC convolutional codes. This provides us with an estimate of where the error floor will occur for these codes under iterative message-passing decoding.