Low rate turbo codes based on nonlinear cyclic codes

In this paper we describe parallel concatenations of two convolutional encoders based on nonlinear cyclic codes with codewords of length n=2^m, m being a positive integer. The resulting turbo codes have a very low coding rate, which makes them especially suitable for spread spectrum systems where they can be used for achieving simultaneously error correction and bandwidth expansion. Due to the cyclic properties and codeword length of the component codes, branch metrics can be efficiently computed using the Fast Fourier Transform, which enables simple implementation of the encoder and decoder for the component convolutional coding schemes. Among the possible base nonlinear cyclic codes, special attention is given to the TCH (Tomlinson-Cercas-Hughes) codes family due to their good autocorrelation properties, which enables the resulting turbo codes to achieve good BER performance. These schemes, similarly to the superorthogonal turbo codes, usually perform better than the traditional turbocodes at the cost of bandwidth expansion. Simulation results are presented both for the AWGN and for the uncorrelated Rayleigh fading channels. One of the advantages of the presented solution over the traditional turbo superorthogonal codes is its ability to improve the synchronization process at the receiver due to the good autocorrelation properties of the available nonlinear codes (specially TCH codes).