Showing papers by "Johannes B. Huber published in 2009"

LDPC codes and convolutional codes with equal structural delay: a comparison

Abstract: We compare convolutional codes and LDPC codes with respect to their decoding performance and their structural delay, which is the inevitable delay solely depending on the structural properties of the coding scheme. Besides the decoding performance, the data delay caused by the channel code is of great importance as this is a crucial factor for many applications. Convolutional codes are known to show a good performance while imposing only a very low latency on the data. LDPC codes yield superior decoding performance but impose a larger delay due to the block structure. The results obtained by comparison will also be related to theoretical limits obtained from random coding and the sphere packing bound. It will be shown that convolutional codes are still the first choice for applications for which a very low data delay is required and the bit error rate is the considered performance criterion. However, if one focuses on a low signal-to-noise ratio or if the obtained frame error rate is the base for comparison, LDPC codes compare favorably.

The Trapping Redundancy of Linear Block Codes

Abstract: We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which quantifies the relationship between the number of redundant rows in any parity-check matrix of a given code and the size of its smallest trapping set. Trapping sets with certain parameter sizes are known to cause error-floors in the performance curves of iterative belief propagation (BP) decoders, and it is therefore important to identify decoding matrices that avoid such sets. Bounds on the trapping redundancy are obtained using probabilistic and constructive methods, and the analysis covers both general and elementary trapping sets. Numerical values for these bounds are computed for the [2640, 1320] Margulis code and the class of projective geometry codes, and compared with some new code-specific trapping set size estimates.

Signal combining for relay transmission with rateless codes

Abstract: The invention of practical rateless codes in the form of Luby transform and Raptor codes has facilitated the implementation of decode-and-forward relaying schemes which permit the relay to autonomously switch between listening and collaboration phase. Considering the classical three-node relay network employing such a flexible decode-and-forward mechanism, in this paper we investigate signal combining strategies for the destination node. In particular, we compare information and energy combining considered previously in the literature and introduce a new, so-called mixed combining scheme, which is a hybrid of the two former strategies. Assuming general finite-size signal constellations we show that mixed combining is advantageous over the pure combining schemes in terms of achievable rate given the same total transmit energy. A comparison of the associated constellation-constrained capacities with simulated rates achieved for relay transmission with moderate-length Raptor codes underscores (i) the relevance of the capacity-based analysis and (ii) the suitability of rateless codes for relay transmission.

Causal discrete-time system approximation of non-bandlimited continuous-time systems by means of discrete prolate spheroidal wave functions

Abstract: SUMMARY In general, linear time-invariant (LTI) continuous-time (CT) systems can be implemented by means of LTI discrete-time (DT) systems, at least for a certain frequency band. If a causal CT system is not bandlimited, the equivalent DT system may has be to non-causal for perfectly implementing the CT system within a certain frequency band. This paper studies the question to which degree a causal DT system can approximate the CT system. By reducing the approximation frequency band, the approximation accuracy can be increased—at the expense of a higher energy of the impulse response of the DT system. It turns out, that there exists a strict trade-off between approximation accuracy, measured in the squared integral error, and energy of the impulse response of the DT system. The theoretically optimal trade-off can be achieved by approximations based on a weighted linear combination of the discrete prolate spheroidal wave functions (DPSWFs). The results are not limited to the case of approximating a CT system by means of a causal DT system, but they generally hold for the approximation of an arbitrary spectrum by means of a spectrum of an indexlimited time sequence. Copyright © 2008 John Wiley & Sons, Ltd.

The lowest-possible BER and FER for any discrete memoryless channel with given capacity

Abstract: We investigate properties of a channel coding scheme leading to the minimum-possible frame error ratio when transmitting over a memoryless channel with rate R > C. The results are compared to the well-known properties of a channel coding scheme leading to minimum bit error ratio. It is concluded that these two optimization requests are contradicting. A valuable application of the derived results is presented.

Decision-Feedback Subset Multiple-Symbol Differential Detection for Unitary Space-Time Modulation

Abstract: In this paper, a novel noncoherent detection algorithm for differential space-time modulation (DSTM) over flat-fading multiple-input-multiple-output channels is presented. This algorithm, which is referred to as decision-feedback subset multiple-symbol differential detection (DF-S-MSDD), combines ideas from decision-feedback differential detection (DFDD) and subset multiple-symbol differential detection (S-MSDD). More specifically, the DF-S-MSDD decision metric includes a number of previous decisions (i.e., decision feedback), and the optimization over the remaining hypothetical symbols returns decisions only on a subset of these symbols (i.e., S-MSDD). Furthermore, an implementation of DF-S-MSDD based on tree-search (TS) methods is devised. Due to the concept of subset detection, DF-S-MSDD outperforms MSDD in terms of error-rate performance. At the same time, due to the use of decision feedback, it also requires lower computational complexity than the TS-based MSDD schemes for the DSTM recently proposed in the literature.