Fountain coding with decoder side information

In this contribution, we consider the application of Digital Fountain (DF) codes to the problem of data transmission when side information is available at the decoder. The side information is modelled as a "virtual" channel output when original information sequence is the input. For two cases of the system model, which model both the virtual and the actual transmission channel either as a binary erasure channel or as a binary input additive white Gaussian noise (BIAWGN) channel, we propose methods of enhancing the design of standard non-systematic DF codes by optimizing their output degree distribution based oil the side information assumption. In addition, a systematic Raptor design has been employed as a possible solution to the problem

Rate adaptive binary erasure quantization with dual fountain codes

In this contribution, duals of fountain codes are introduced and their use for lossy source compression is investigated. It is shown both theoretically and experimentally that the source coding dual of the binary erasure channel coding problem, binary erasure quantization, is solved at a nearly optimal rate with application of duals of LT and raptor codes by a belief propagation-like algorithm which amounts to a graph pruning procedure. Furthermore, this quantizing scheme is rate adaptive, i.e., its rate can be modified on-the-fly in order to adapt to the source distribution, very much like LT and raptor codes are able to adapt their rate to the erasure probability of a channel

Expanding window fountain codes for unequal error protection

A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally. © 2009 IEEE

Decentralised distributed fountain coding: asymptotic analysis and design

A class of generic decentralised distributed fountain coding schemes is introduced and the tools of analysis of the performance of such schemes are presented. It is demonstrated that the developed approach can be used to formulate a robust code design methodology in a number of instances. We show that two non-standard applications of fountain codes, fountain codes for distributed source coding and fountain codes for unequal error protection lie within this decentralised distributed fountain coding framework

Expanding window fountain codes for unequal error protection

A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally. © 2009 IEEE

Expanding window fountain codes for unequal error protection

A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally

Bayesian approaches to distribution regression

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the groups. This effectively assumes that small and large groups are estimated equally well, and should have equal weight in the final regression. We account for this uncertainty with a Bayesian distribution regression formalism, improving the robustness and performance of the model when group sizes vary. We frame our models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. We demonstrate our approach on illustrative toy datasets, as well as on a challenging problem of predicting age from images

Feature-to-feature regression for a two-step conditional independence test

The algorithms for causal discovery and more broadly for learning the structure of graphical models require well calibrated and consistent conditional independence (CI) tests. We revisit the CI tests which are based on two-step procedures and involve regression with subsequent (unconditional) independence test (RESIT) on regression residuals and investigate the assumptions under which these tests operate. In particular, we demonstrate that when going beyond simple functional relationships with additive noise, such tests can lead to an inflated number of false discoveries. We study the relationship of these tests with those based on dependence measures using reproducing kernel Hilbert spaces (RKHS) and propose an extension of RESIT which uses RKHS-valued regression. The resulting test inherits the simple two-step testing procedure of RESIT, while giving correct Type I control and competitive power. When used as a component of the PC algorithm, the proposed test is more robust to the case where hidden variables induce a switching behaviour in the associations present in the data

Bayesian kernel two-sample testing

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modelling the difference between kernel mean embeddings in the reproducing kernel Hilbert space utilising the framework established by Flaxman et al (2016). The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e. testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach