Extended Non-Binary Low-Density Parity-Check Codes over Erasure Channels

Based on the extended binary image of non-binary LDPC codes, we propose a method for generating extra redundant bits, such as to decreases the coding rate of a mother code. The proposed method allows for using the same decoder, regardless of how many extra redundant bits have been produced, which considerably increases the flexibility of the system without significantly increasing its complexity. Extended codes are also optimized for the binary erasure channel, by using density evolution methods. Nevertheless, the results presented in this paper can easily be extrapolated to more general channel models.Comment: ISIT 2011, submitte

On the beta-drift of an initially circular vortex patch

The nonlinear inviscid evolution of a vortex patch in a single-layer quasi-geostrophic fluid and within a background planetary vorticity gradient is examined numerically at unprecedented spatial resolution. The evolution is governed by two dimensionless parameters: the initial size (radius) of the vortex compared to the Rossby deformation radius, and the initial strength of the vortex compared to the variation of the planetary vorticity across the vortex. It is found that the zonal speed of a vortex increases with its strength. However, the meridional speed reaches a maximum at intermediate vortex strengths. Both large and weak vortices are readily deformed, often into elliptical and tripolar shapes. This deformation is shown to be related to an instability of the instantaneous vorticity distribution in the absence of the planetary vorticity gradient β. The extremely high numerical resolution employed reveals a striking feature of the flow evolution, namely the generation of very sharp vorticity gradients surrounding the vortex and extending downstream of it in time. These gradients form as the vortex forces background planetary vorticity contours out of its way as it propagates. The contours close to the vortex swirl rapidly around the vortex and homogenize, but at some critical distance the swirl is not strong enough and, instead, a sharp vorticity gradient forms. The region inside this sharp gradient is called the ‘trapped zone’, though it shrinks slowly in time and leaks. This leaking occurs in a narrow wake called the ‘trailing front’, another zone of sharp vorticity gradients, extending behind the vortex

Near-optimal Assembly for Shotgun Sequencing with Noisy Reads

Recent work identified the fundamental limits on the information requirements in terms of read length and coverage depth required for successful de novo genome reconstruction from shotgun sequencing data, based on the idealistic assumption of no errors in the reads (noiseless reads). In this work, we show that even when there is noise in the reads, one can successfully reconstruct with information requirements close to the noiseless fundamental limit. A new assembly algorithm, X-phased Multibridging, is designed based on a probabilistic model of the genome. It is shown through analysis to perform well on the model, and through simulations to perform well on real genomes

Education and Youth Unemployment in South Africa

The problem of high youth unemployment is a global phenomenon. According to an International Labour Office study in 2004, youth (15-24) make up nearly half (47%) of the world's unemployed, 88 million out of 186 million, even though youth are only 25% of the world's working age population. Of the world's 550 million working poor who cannot lift themselves above US $1 per day poverty measure, 150 million are youth. The ILO estimated in 2004 that halving global youth unemployment would increase global GDP by US$2.2 trillion, 4% of global GDP. These statistics lend weight to the notion that youth unemployment is a problem worthy of attention. In addition, one may argue that addressing unemployment in general would also lower poverty levels and add to GDP (World Bank 2006).

Schooling as a Lottery: Racial Differences in School Advancement in Urban South Africa

This paper develops a stochastic model of grade repetition to analyze the large racial differences in progress through secondary school in South Africa. The model predicts that a larger stochastic component in the link between learning and measured performance will generate higher enrollment, higher failure rates, and a weaker link between ability and grade progression. Using recently collected longitudinal data we find that progress through secondary school is strongly associated with scores on a baseline literacy and numeracy test. In grades 8-11 the effect of these scores on grade progression is much stronger for white and coloured students than for African students, while there is no racial difference in the impact of the scores on passing the nationally standardized grade 12 matriculation exam. The results provide strong support for our model, suggesting that grade progression in African schools is poorly linked to actual ability and learning. The results point to the importance of considering the stochastic component of grade repetition in analyzing school systems with high failure rates.

Schooling as a Lottery: Racial Differences in School Advancement in Urban South Africa

This paper develops a stochastic model of grade repetition to analyze the large racial differences in progress through secondary school in South Africa. The model predicts that a larger stochastic component in the link between learning and measured performance will generate higher enrollment, higher failure rates, and a weaker link between ability and grade progression. Using recently collected longitudinal data we find that progress through secondary school is strongly associated with scores on a baseline literacy and numeracy test. In grades 8-11 the effect of these scores on grade progression is much stronger for white and coloured students than for African students, while there is no racial difference in the impact of the scores on passing the nationally standardized grade 12 matriculation exam. The results provide strong support for our model, suggesting that grade progression in African schools is poorly linked to actual ability and learning. The results point to the importance of considering the stochastic component of grade repetition in analyzing school systems with high failure rates.