Improving 3-dimensional turbo codes using 3GPP2 interleavers

Abstract

Abstract-This paper deals with the performance improvement of a 3-dimensional turbo code based on the partial concatenation of the 3GPP2 code with a rate-1 post-encoder. First, we optimize the distance spectrum of the 3-dimensional 3GPP2 turbo code by means of the adoption of a non regular post-encoding pattern. This allows us to increase the minimum Hamming distance and thereby to improve the performance at very low error rates. Then, we propose a time varying construction of the postencoded parity in order to reduce the observable loss of convergence at high error rates. The different improvement stages are illustrated with simulation results, asymptotical bounds and EXIT charts.

A survey of three-dimensional turbo codes and recent performance enhancements

“…Then, the first step involves eliminating these codewords by means of the adoption of a non-regular post-encoding pattern. This optimization method is detailed in [6], and different results show that modifying a few addresses in the pattern of post-encoding produces an improvement in the distance properties.…”

“…The next subsections deal with the improvement of the convergence threshold of 3D TCs for transmissions over Rayleigh fading channels. More details are available in [6][7][8] where transmissions over Gaussian channels were considered.…”

“…The choice of the post-encoder influences also the performance in both the waterfall and error floor regions. It has to meet different requirements already detailed in [2,3,6]. In [7], we justified the choice of the post-encoder by means of EXIT analysis.…”

“…Then, the two constituent encoders are eight-state recursive systematic convolutional (RSC) encoders with feedback polynomial 1 + D 2 + D 3 and parity generator polynomial 1 + D + D 3 . This paper is a review paper that enriches our survey on 3D TCs reported in [6][7][8][9][10] and brings new results. In particular, transmissions over independent and identically distributed Rayleigh fast-fading channels are investigated, whereas transmissions over Gaussian channels were mainly considered in [6][7][8].…”

“…This paper is a review paper that enriches our survey on 3D TCs reported in [6][7][8][9][10] and brings new results. In particular, transmissions over independent and identically distributed Rayleigh fast-fading channels are investigated, whereas transmissions over Gaussian channels were mainly considered in [6][7][8]. Furthermore, several examples of MHD values obtained with this code for different block sizes and coding rates are newly presented in Table 1.…”