Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design

In this paper we analyze LT and Raptor codes under inactivation decoding. A first order analysis is introduced, which provides the expected number of inactivations for an LT code, as a function of the output distribution, the number of input symbols and the decoding overhead. The analysis is then extended to the calculation of the distribution of the number of inactivations. In both cases, random inactivation is assumed. The developed analytical tools are then exploited to design LT and Raptor codes, enabling a tight control on the decoding complexity vs. failure probability trade-off. The accuracy of the approach is confirmed by numerical simulations.Comment: Accepted for publication in IEEE Transactions on Communication

RAPTOR I: Time-dependent radiative transfer in arbitrary spacetimes

Observational efforts to image the immediate environment of a black hole at the scale of the event horizon benefit from the development of efficient imaging codes that are capable of producing synthetic data, which may be compared with observational data. We aim to present RAPTOR, a new public code that produces accurate images, animations, and spectra of relativistic plasmas in strong gravity by numerically integrating the equations of motion of light rays and performing time-dependent radiative transfer calculations along the rays. The code is compatible with any analytical or numerical spacetime. It is hardware-agnostic and may be compiled and run both on GPUs and CPUs. We describe the algorithms used in RAPTOR and test the code's performance. We have performed a detailed comparison of RAPTOR output with that of other radiative-transfer codes and demonstrate convergence of the results. We then applied RAPTOR to study accretion models of supermassive black holes, performing time-dependent radiative transfer through general relativistic magneto-hydrodynamical (GRMHD) simulations and investigating the expected observational differences between the so-called fast-light and slow-light paradigms. Using RAPTOR to produce synthetic images and light curves of a GRMHD model of an accreting black hole, we find that the relative difference between fast-light and slow-light light curves is less than 5%. Using two distinct radiative-transfer codes to process the same data, we find integrated flux densities with a relative difference less than 0.01%. For two-dimensional GRMHD models, such as those examined in this paper, the fast-light approximation suffices as long as errors of a few percent are acceptable. The convergence of the results of two different codes demonstrates that they are, at a minimum, consistent.Comment: 18 pages, 14 figures, 5 table

Rateless Coding for Gaussian Channels

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.Comment: 18 page

Low Density Generator Matrix (LDGM)-based Raptor Codes for Broadband Internet of Things (IoT)

This thesis proposes a new coding technique supporting Internet-of-Things (IoT) communications between devices and relay stations or base stations (BS). The new coding scheme is based on Raptor codes ensemble with Low Density Generator Matrix (LDGM) codes as the precode, called LDGM-Raptor codes, which is expected to be suitable for future IoT systems. This is possible because the proposed coding scheme requires low computational complexity with high reliability. The utilization of LDGM as the precode is because of its property on low encoding/ decoding complexity leading to its potential applications, e.g., (i) for the error correction in each device called channel coding, and (ii) for the error correction in the networks, which is called network coding. This thesis considers LDGM-Raptor codes for channel coding for IoT devices with broadband communications that requires very low latency and good performances supported by optimal degree distributions. The degree distributions of LDGM-Raptor codes are designed optimally using Extrinsic Information Transfer (EXIT) chart in order to meet requirements of wireless broadband IoT communications. Since LDGM-Raptor codes are constructed from two basic coding schemes having four degree distributions, the optimization on four degree distributions is then required. Furthermore, to minimize the outage probability over broadband wireless channels, this thesis considers the design of LDGM-Raptor codes having degree distributions suitable for multipath Rayleigh fading channels. The design of LDGM-Raptor codes is also analyzed using EXIT chart to predict its theoretical bit-error rate (BER) performances. A series of computer simulation is conducted to validate the theoretical performances predicted by EXIT chart. We use soft decoding algorithm in order to obtain high performances compared to the hard decoding scheme. To evaluate the performances of broadband channel, we use Indonesia channel model developed for the fifth telecommunication generation (5G) system having rich number of paths. The results show that excellent performances are provided by the proposed LDGM-Raptor codes as predicted by the EXIT charts. The computational complexity of the proposed codes is also evaluated for practical purposes. The results of this thesis are expected to contribute the development of future massive wireless IoT networks. Keywords: Internet of Things, Massive connections, Raptor Codes, LDGM, Low Computational Complexit

Extending DIRAC File Management with Erasure-Coding for efficient storage

The state of the art in Grid style data management is to achieve increased resilience of data via multiple complete replicas of data files across multiple storage endpoints. While this is effective, it is not the most space-efficient approach to resilience, especially when the reliability of individual storage endpoints is sufficiently high that only a few will be inactive at any point in time. We report on work performed as part of GridPP\cite{GridPP}, extending the Dirac File Catalogue and file management interface to allow the placement of erasure-coded files: each file distributed as N identically-sized chunks of data striped across a vector of storage endpoints, encoded such that any M chunks can be lost and the original file can be reconstructed. The tools developed are transparent to the user, and, as well as allowing up and downloading of data to Grid storage, also provide the possibility of parallelising access across all of the distributed chunks at once, improving data transfer and IO performance. We expect this approach to be of most interest to smaller VOs, who have tighter bounds on the storage available to them, but larger (WLCG) VOs may be interested as their total data increases during Run 2. We provide an analysis of the costs and benefits of the approach, along with future development and implementation plans in this area. In general, overheads for multiple file transfers provide the largest issue for competitiveness of this approach at present.Comment: 21st International Conference on Computing for High Energy and Nuclear Physics (CHEP2015

Bilayer Low-Density Parity-Check Codes for Decode-and-Forward in Relay Channels

This paper describes an efficient implementation of binning for the relay channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated information bits in specially designed bilayer graphical code structures. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC codes are capable of working at two different channel parameters and two different rates: that at the relay and at the destination. To analyze the performance of bilayer LDPC codes, bilayer density evolution is devised as an extension of the standard density evolution algorithm. Based on bilayer density evolution, a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming. Further, in order to approach the theoretical decode-and-forward rate for a wide range of channel parameters, this paper proposes two different forms bilayer codes, the bilayer-expurgated and bilayer-lengthened codes. It is demonstrated that a properly designed bilayer LDPC code can achieve an asymptotic infinite-length threshold within 0.24 dB gap to the Shannon limits of two different channels simultaneously for a wide range of channel parameters. By practical code construction, finite-length bilayer codes are shown to be able to approach within a 0.6 dB gap to the theoretical decode-and-forward rate of the relay channel at a block length of $10^5$ and a bit-error probability (BER) of $10^{-4}$. Finally, it is demonstrated that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays.Comment: Submitted to IEEE Trans. Info. Theor

Time-dependent excitation and ionization modelling of absorption-line variability due to GRB 080310

We model the time-variable absorption of FeII, FeIII, SiII, CII and CrII detected in UVES spectra of GRB 080310, with the afterglow radiation exciting and ionizing the interstellar medium in the host galaxy at a redshift of z=2.42743. To estimate the rest-frame afterglow brightness as a function of time, we use a combination of the optical VRI photometry obtained by the RAPTOR-T telescope array -- which are presented in this paper -- and Swift's X-Ray Telescope observations. Excitation alone, which has been successfully applied for a handful of other GRBs, fails to describe the observed column-density evolution in the case of GRB 080310. Inclusion of ionization is required to explain the column-density decrease of all observed FeII levels (including the ground state 6D9/2) and increase of the FeIII 7S3 level. The large population of ions in this latter level (up to 10% of all FeIII) can only be explained through ionization of FeII, whereby a large fraction of the ionized FeII ions -- we calculate 31% using the Flexible Atomic (FAC) and Cowan codes -- initially populate the 7S3 level of FeIII rather than the ground state. This channel for producing a significant FeIII 7S3 level population may be relevant for other objects in which absorption lines from this level -- the UV34 triplet -- are observed, such as BAL quasars and Eta Carinae. This provides conclusive evidence for time-variable ionization in the circumburst medium, which to date has not been convincingly detected. However, the best-fit distance of the neutral absorbing cloud to the GRB is 200--400 pc, i.e. similar to GRB-absorber distance estimates for GRBs without any evidence for ionization. We find that the presence of time-varying ionization in GRB 080310 is likely due to a combination of the super-solar iron abundance ([Fe/H]=+0.2) and the low HI column density (log N(HI)=18.7). [abridged]Comment: 14 pages, 6 figures; accepted for publication in A&A (on August 8, 2012