On Deriving Good LDPC Convolutional Codes from QC LDPC Block Codes

In this paper we study the iterative decoding behavior of time-invariant and time-varying LDPC convolutional codes derived by unwrapping QC LDPC block codes. In particular, for a time-varying LDPC convolutional code, we show that the minimum pseudo-weight of the convolutional code is at least as large as the minimum pseudo-weight of the underlying QC code. We also prove that the unwrapped convolutional codes have fewer short cycles than the QC codes. These results taken together lead to improved BER performance in the low-to-moderate SNR region, where the decoding behavior is influenced by the complete pseudo-codeword spectra and by the Tanner graph cycle histogram, with the time-varying convolutional codes outperforming both the underlying QC block codes and their time-invariant convolutional counterparts.