Low complexity iterative decoding of product codes using a Generalized Array Code form of the Nordstrom-Robinson code

This paper proposes encoding and decoding for nonlinear turbo product codes and investigates the performance of nonlinear turbo product codes. The proposed nonlinear turbo product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes over higher order alphabets, e.g., Preparata or Kerdock codes. The performance and the complexity of the proposed construction are evaluated using the well known nonlinear Nordstrom-Robinson code which is presented in the Generalized Array Code format with a low complexity trellis. The proposed construction shows the additional coding gain, reduced error floor and lower implementation complexity. The (64,24,12) nonlinear turbo product code has about effective 2.5dB gain and 1dB gain at a BER of 10^-6 when compared to the (64,15,16) linear turbo product code and the (64,24,10) linear turbo product code, respectively. The (256,64,36) nonlinear turbo product code composed of two Nordstrom-Robinson codes has about 0.7dB gain at a BER of 10^-5 when compared to the (256,64,25) linear turbo product code composed of two (16,8,5) Quasi-Cyclic codes. These are achieved for codes with relatively short block lengths that make them particularly attractive for new emerging standards that aim at efficient mobile data transmission.