Chaotic Digital Encoding for 2D Trellis-Coded Modulation

Abstract

In this paper, nonlinear digital filters with finite precision are analyzed as recursive systematic convolutional (RSC) encoders. An infinite impulse response (IIR) digital filter with finite precision (wordlength of N bits) is a rate 1 RSC encoder over a Galois field GF(2N). The Frey chaotic filter is analyzed for two different wordlengths N, and it is demonstrated that this encoder can be used for trellis-coded modulation (TCM) schemes. A definition for the encoding rate is provided in the context of the new structure. The Frey encoder scheme is modified in order to reduce the encoding rate from 1 to 1/2. In fact, this modification consists in increasing the number of encoder outputs, using the same wordlength as for the input. The resulted encoders are used for two-dimensional (2D) TCM schemes. Also, the signal sets are partitioned following the Ungerboeck’s rules. The symbol error rate (SER) is estimated for all proposed structures and the results show the expected coding gains as compared to their equivalent non-encoded and linear versions.