Towards ideal codes: looking for new turbo code schemes

Kbaier Ben Ismail, Dhouha (2011). Towards ideal codes: looking for new turbo code schemes. PhD thesis Telecom Bretagne, Brest, France.



While turbo codes (TCs) offer performance very close to the Shannon limit in the so-called waterfall region, they suffer from a flattening effect due to a poor minimum distance. In future system generations, low error rates will be required to open the way to real-time and demanding applications, such as TV broadcasting or videoconferencing. Therefore, state-of-the-art TCs are no longer suitable for these kinds of applications and more powerful coding schemes are required. At the same time, a reasonable complexity should be preserved. The first part of this thesis is dedicated to explore a new hybrid concatenation structure combining both parallel and serial concatenation based on a 3-dimensional (3D) code, simply derived from the classical TC by concatenating a rate-1 post-encoder at its output. First, we search for effcient post-encoder structures by means of EXtrinsic Information Transfer (EXIT) charts, especially when transmissions over non Gaussian channels (fading channels, erasure channels) are considered. Other key parameters of the 3D TC are sensibly selected. Various simulations show that 3D TCs have a better asymptotical behaviour with respect to classical TCs. An optimization method, in the case of the 3GPP2 code, allows the minimum distance of the 3D TC to be even more increased. On the other hand, a loss in the convergence threshold and an increase in complexity are observed. In order to reduce the observable loss of convergence, a time varying post-encoder is proposed. The time-varying technique reduces the loss of convergence by 10% to 50% of its value expressed in dB. However, there is no need to use this technique, when the 3D TC is associated with a high order modulation such as M-PSK or M-QAM. Indeed, a specific Gray mapping where the systematic bits and the post-encoded parity bits are placed in the best protected binary positions of the modulation scheme, allows the loss in convergence to be transformed into a gain at low signal to noise ratios (SNRs). Thus, we obtain 3D TCs which perform better than the classical TCs in both the waterfall and the error floor regions. The second part of this study deals with irregular TCs. Here, the problem is the opposite of the precedent. Although irregular TCs can achieve performance closer to capacity, their asymptotic performance is very poor. First of all, the degree profile is selected by means of EXIT diagrams. Then, the design of powerful permutations suited for such code structures is considered. Graph-based permutations using the Dijkstra's algorithm and an estimation of the minimum distance, improve the distance properties of these codes. Nevertheless, this task takes a lot of time for the large blocks, and a memory is required to store the interleaved addresses. To take advantage of the results in the first part of the thesis, and in order to combine both studies, a new modified structure is proposed. The association of irregular TCs with the same post-encoder used for 3D TCs results in irregular turbo coding schemes which perform better than regular TCs at low and high SNRs at the same time. Keywords: turbo code, 3-dimensional turbo code, 3GPP2 code, minimum distance, convergence threshold, EXIT chart, time-varying trellis, modulation, decoding complexity, irregular turbo code, degree profile, Dijkstra's algorithm, correlation graph.

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