Analytical approach to low-density convolutional codes

A statistical analysis of low-density convolutional (LDC) codes is performed. This analysis is based on the consideration of a special statistical ensemble of Markov scramblers and the solution to a system of recurrent equations describing this ensemble. The results of the analysis are lower bounds for the free distance of the codes and upper bounds for the maximum likelihood decoding error probability. For the case where the size of the scrambler tends to infinity some asymptotic bounds for the free distance and the error probability are derived. Simulation results for iterative decoding of LDC codes are also presented.