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.     

SLM peak-power reduction without explicit side information

Selected mapping (SLM) peak-power reduction is distortionless as it selects the actual transmit signal from a set of alternative signals, which all represent the same information. The specific signal generation information needs to be transmitted and carefully protected against bit errors. Here, me propose an extension of SLM, which employs scrambling and refrains from the use of explicit side information in the receiver. Some additional complexity and nearly vanishing redundancy is introduced to achieve markedly improved transmit signal statistics. Even though SLM is applicable with any modulation, we concentrate on orthogonal frequency-division multiplexing (OFDM) in this letter     

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     

Non-iterative optimum super-trellis decoding of turbo codes

An optimum non-iterative turbo decoder is proposed that is highly parallelisable and out-performs the maximum a-posteriori decoder     

Procedures and applications to enlarge the level 1+ PSA to internal fires in German nuclear power plants

Investigations have shown that the consequences from fires in nuclear power plants can be significant. Methodologies considering fire in probabilistic safety analyses have been evolving in the last few years. In order to provide a basis for further discussions on benefits and limits of such an analysis in Germany, current methods are investigated. As a result a qualitative screening process is proposed to identify critical fire zones followed by a quantitative event tree analysis in which the fire caused frequency of initiating events and different core damage states will be determined. The models and data proposed for a probabilistic fire risk analysis have been successfully applied in complete and partial fire risk assessments in German nuclear power plants.     

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