On the theory of low-density convolutional codes. II. (English. Russian original) Zbl 1038.94012

Lentmaier, M.; Truhachev, D. V.; Zigangirov, K. Sh.

Probl. Inf. Transm. 37, No. 4, 288-306 (2001); translation from Probl. Peredachi Inf. 37, No. 4, 15-35 (2001).

The paper deals with iterative decoding algorithms of low-density convolutional (LDC) codes. The authors analyse their asymptotic properties, discussing two families of LDC codes, namely homogeneous LDC codes and a convolutional version of turbo codes.
They prove the existence of an upper bound on the decoding bit error probability and bounds on iterative limits for LDC codes and a family of turbo codes. They also discuss a derivation of these bounds. Procedures applied by the authors are analogous to those proposed by Gallager.
Bounds on iterative limits are obtained for two channel models: the additive white Gaussian noise channel and the binary symmetric channel. For the calculation of estimates of log-likelihood ratios – estimates of the Bhattacharyya parameter – a Monte Carlo technique is used.

Reviewer: Jozef Woźniak (Gdańsk)

MSC:

94B10	Convolutional codes
94B65	Bounds on codes
94B70	Error probability in coding theory
94A40	Channel models (including quantum) in information and communication theory

Keywords:

low-density convolutional codes; turbo-codes; asymptotic analysis and properties; channel models; bounds on codes