Active distances for convolutional codes

Rolf Johannesson, Kamil Sh. Zigangirov

Stephan Ludwig

Dmitri V. Truhachev, Kamil Sh. Zigangirov, Daniel J. Costello

Existence type lower bounds on the free distance of periodically time-varying LDPC convolutional codes and on the minimum distance of tail-biting LDPC convolutional codes are derived. It is demonstrated that the bound on free distance of periodically time-varying LDPC convolutional codes approaches the bound on free distance of general (nonperiodic) time-varying LDPC convolutional codes as the period increases. The proof of the bound is based on lower bounding the minimum distance of corresponding tail-biting LDPC convolutional codes, which is of interest in its own right.

Marcos B. S. Tavares, Michael Lentmaier, Gerhard Paul Fettweis +1 more

We analyze a class of LDPC convolutional codes that are constructed from tightly braided convolutional base codes by a lifting procedure. For these braided protograph convolutional codes, we show that the distances grow linearly with the constraint length, and we present lower bounds on their asymptotic segment distance and free distance as well as on the asymptotic minimum distance of their tail-biting versions. With some constraints imposed on the lifting permutations, braided protograph convolutional codes can also be decoded as turbo-like codes by iterative application of the BCJR algorithm. For this case, we derive an explicit upper-bound on the asymptotic decoding error probability as a function of the number of iterations.

Karin Engdahl, Michael Lentmaier, Kamil Sh. Zigangirov

Patrick Guy Farrell