Marco Breiling

A logarithmic upper bound on the minimum distance of turbo codes

We derive new upper bounds on the minimum distance, which turbo codes can maximally attain with the optimum interleaver of a given length. The new bounds grow approximately logarithmically with the interleaver length, and they are tighter than all previously derived bounds for medium-length and long interleavers. An extensive discussion highlights the impacts of the new bounds in the context of interleaver design and provides some new design guidelines.

The super-trellis structure of turbo codes

In this contribution we derive the super-trellis structure of turbo codes. We show that this structure and its associated decoding complexity depend strongly on the interleaver applied in the turbo encoder. We provide upper bounds for the super-trellis complexity. Turbo codes are usually decoded by an iterative decoding algorithm, which is suboptimum. Applying the super-trellis structure, we can optimally decode simple turbo codes and compare the associated bit-error rate results to those of iterative algorithms.

Upper bound on the minimum distance of turbo codes

An upper bound on the minimum distance of turbo codes is derived, which depends only on the interleaver length and the component scramblers employed. The derivation of this bound considers exclusively turbo encoder input words of weight 2. The bound does not only hold for a particular interleaver but for all possible interleavers including the best. It is shown that in contrast to general linear binary codes the minimum distance of turbo codes cannot grow stronger than the square root of the block length. This implies that turbo codes are asymptotically bad. A rigorous proof for the bound is provided, which is based on a geometric approach.

Combinatorial analysis of the minimum distance of turbo codes

In this paper, new upper bounds on the maximum attainable minimum Hamming distance of turbo codes with arbitrary-including the best-interleavers are established using a combinatorial approach. These upper bounds depend on the interleaver length, the code rate, and the scramblers employed in the encoder. Examples of the new bounds for particular turbo codes are given and discussed. The new bounds are tighter than all existing ones and prove that the minimum Hamming distance of turbo codes cannot asymptotically grow at a rate more than the third root of the codeword length.

Non-iterative joint channel equalisation and channel decoding

A non-iterative turbo equaliser scheme is proposed, which outperforms the iterative turbo equaliser by about 0.7 dB at a BER of 10/sup -3/ over a symbol-spaced two-path channel and by about 3.4 dB at a BER of 10/sup -3/ over a five-path Gaussian channel.

Optimum non-iterative turbo-decoding

By observing the structure of the decoders trellis a new, non-iterative turbo-decoder based on a super-trellis structure is proposed, which exhibits the same decoding complexity as a conventional convolutional decoder possessing an identical number of trellis states. For the investigated half-rate, memory-length two code the proposed algorithm requires about 0.5 dB lower Gaussian channel signal-to-noise ratio (SNR) than the maximum a posteriori (MAP) algorithm using 16 iterations.

Choice of Physical Layer Parameters for Satellite Broadcast

This chapter assesses the choice of the physical layer parameters (code rate, modulation, time interleaving) that are best suited for satellite broadcast. The optimum choice depends on the system’s envisaged spectral efficiency or available signal-to-noise ratio, and the target usage environment, like rural or sub-urban reception. The analysis is carried out by means of information theory and evaluation of satellite field measurements.