Low-density parity-check codes for nonergodic block-fading channels

We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not performwell under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

Coded slotted aloha with multipacket reception over block fading channels (for satellite networks)

Random access (RA) protocols are normally used in a satellite networks for initial terminal access and are particularly effective since no coordination is required. On the other hand, contention resolution diversity slotted Aloha (CRDSA), irregular repetition slotted Aloha (IRSA) and coded slotted Aloha (CSA) has shown to be more efficient than classic RA schemes as slotted Aloha, and can be exploited also when short packets transmissions are done over a shared medium. In particular, they relies on burst repetition and on successive interference cancellation (SIC) applied at the receiver. The SIC process can be well described using a bipartite graph representation and exploiting tools used for analyze iterative decoding. The scope of my Master Thesis has been to described the performance of such RA protocols when the Rayleigh fading is taken into account. In this context, each user has the ability to correctly decode a packet also in presence of collision and when SIC is considered this may result in multi-packet reception. Analysis of the SIC procedure under Rayleigh fading has been analytically derived for the asymptotic case (infinite frame length), helping the analysis of both throughput and packet loss rates. An upper bound of the achievable performance has been analytically obtained. It can be show that in particular channel conditions the throughput of the system can be greater than one packets per slot which is the theoretical limit of the Collision Channel case.

A denoising approach for iterative side information creation in distributed video coding

In distributed video coding, motion estimation is typically performed at the decoder to generate the side information, increasing the decoder complexity while providing low complexity encoding in comparison with predictive video coding. Motion estimation can be performed once to create the side information or several times to refine the side information quality along the decoding process. In this paper, motion estimation is performed at the decoder side to generate multiple side information hypotheses which are adaptively and dynamically combined, whenever additional decoded information is available. The proposed iterative side information creation algorithm is inspired in video denoising filters and requires some statistics of the virtual channel between each side information hypothesis and the original data. With the proposed denoising algorithm for side information creation, a RD performance gain up to 1.2 dB is obtained for the same bitrate.

Systematic analysis of the decoding delay in multiview video

We present a framework for the analysis of the decoding delay in multiview video coding (MVC). We show that in real-time applications, an accurate estimation of the decoding delay is essential to achieve a minimum communication latency. As opposed to single-view codecs, the complexity of the multiview prediction structure and the parallel decoding of several views requires a systematic analysis of this decoding delay, which we solve using graph theory and a model of the decoder hardware architecture. Our framework assumes a decoder implementation in general purpose multi-core processors with multi-threading capabilities. For this hardware model, we show that frame processing times depend on the computational load of the decoder and we provide an iterative algorithm to compute jointly frame processing times and decoding delay. Finally, we show that decoding delay analysis can be applied to design decoders with the objective of minimizing the communication latency of the MVC system.

Belief propagation vs. TAP for decoding corrupted messages

We employ two different methods, based on belief propagation and TAP,for decoding corrupted messages encoded by employing Sourlas's method, where the code word comprises products of K bits selected randomly from the original message. We show that the equations obtained by the two approaches are similar and provide the same solution as the one obtained by the replica approach in some cases K=2. However, we also show that for K>=3 and unbiased messages the iterative solution is sensitive to the initial conditions and is likely to provide erroneous solutions; and that it is generally beneficial to use Nishimori's temperature, especially in the case of biased messages.

Density evolution and power profile optimization for iterative multiuser decoders based on individually optimum multiuser detectors

Iterative multiuser joint decoding based on exact Belief Propagation (BP) is analyzed in the large system limit by means of the replica method. It is shown that performance can be improved by appropriate power assignment to the users. The optimum power assignment can be found by linear programming in most technically relevant cases. The performance of BP iterative multiuser joint decoding is compared to suboptimum approximations based on Interference Cancellation (IC). While IC receivers show a significant loss for equal-power users, they yield performance close to BP under optimum power assignment.

One-time signature scheme from syndrome decoding over generic error-correcting codes

We describe a one-time signature scheme based on the hardness of the syndrome decoding problem, and prove it secure in the random oracle model. Our proposal can be instantiated on general linear error correcting codes, rather than restricted families like alternant codes for which a decoding trapdoor is known to exist. (C) 2010 Elsevier Inc. All rights reserved,

A Geometric Approach for Turbo Decoding of Reed-Solomon Codes in QAM Modulation Schemes

This work studies the turbo decoding of Reed-Solomon codes in QAM modulation schemes for additive white Gaussian noise channels (AWGN) by using a geometric approach. Considering the relations between the Galois field elements of the Reed-Solomon code and the symbols combined with their geometric dispositions in the QAM constellation, a turbo decoding algorithm, based on the work of Chase and Pyndiah, is developed. Simulation results show that the performance achieved is similar to the one obtained with the pragmatic approach with binary decomposition and analysis.

Fast-convergent iterative scheme for filtering velocity signals and finding Kolmogorov scales

The present fundamental knowledge of fluid turbulence has been established primarily from hot- and cold-wire measurements. Unfortunately, however, these measurements necessarily suffer from contamination by noise since no certain method has previously been available to optimally filter noise from the measured signals. This limitation has impeded our progress of understanding turbulence profoundly. We address this limitation by presenting a simple, fast-convergent iterative scheme to digitally filter signals optimally and find Kolmogorov scales definitely. The great efficacy of the scheme is demonstrated by its application to the instantaneous velocity measured in a turbulent jet.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Resolution of natural groups using iterative assignment tests: an example from two species of Australian native rats (Rattus)

Sympatric individuals of Rattus fuscipes and Rattus leucopus, two Australian native rats from the tropical wet forests of north Queensland, are difficult to distinguish morphologically and are often confused in the field. When we started a study on fine-scale movements of these species, using microsatellite markers, we found that the species as identified in the field did not form coherent genetic groups. In this study, we examined the potential of an iterative process of genetic assignment to separate specimens from distinct (e.g. species, populations) natural groups. Five loci with extensive overlap in allele distributions between species were used for the iterative process. Samples were randomly distributed into two starting groups of equal size and then subjected to the test. At each iteration, misassigned samples switched groups, and the output groups from a given round of assignment formed the input groups for the next round. All samples were assigned correctly on the 10th iteration, in which two genetic groups were clearly separated. Mitochondrial DNA sequences were obtained from samples from each genetic group identified by assignment, together with those of museum voucher specimens, to assess which species corresponded to which genetic group. The iterative procedure was also used to resolve groups within species, adequately separating the genetically identified R. leucopus from our two sampling sites. These results show that the iterative assignment process can correctly differentiate samples into their appropriate natural groups when diagnostic genetic markers are not available, which allowed us to resolve accurately the two R. leucopus and R. fuscipes species. Our approach provides an analytical tool that may be applicable to a broad variety of situations where genetic groups need to be resolved.