Performance of A Nonlinear Dynamical System of Two-Dimensional TPC Decoder

The nonlinear dynamical system of turbo code decoders and LDPC code decoders has been analyzed in detail by a lot of researchers. But the dynamical behaviours of turbo product code (TPC) decoders have not been reported so far. In this paper, we model a discrete dynamical system of two-dimensional (2-D) TPC decoders using one input parameter (corresponding to the SNR) and one output parameter (corresponding to E(l)-the mean square value of the posterior probabilities of all the zero code words at the lth iteration), and apply E(l) measures to study their dynamical behaviours. Typical periodic and chaotic behaviours at low SNRs, periodic behaviours at waterfall region and two types of fixed points are discovered and systematically analyzed.