Redundancy Allocation of Partitioned Linear Block Codes

Most memories suffer from both permanent defects and intermittent random errors. The partitioned linear block codes (PLBC) were proposed by Heegard to efficiently mask stuck-at defects and correct random errors. The PLBC have two separate redundancy parts for defects and random errors. In this paper, we investigate the allocation of redundancy between these two parts. The optimal redundancy allocation will be investigated using simulations and the simulation results show that the PLBC can significantly reduce the probability of decoding failure in memory with defects. In addition, we will derive the upper bound on the probability of decoding failure of PLBC and estimate the optimal redundancy allocation using this upper bound. The estimated redundancy allocation matches the optimal redundancy allocation well.Comment: 5 pages, 2 figures, to appear in IEEE International Symposium on Information Theory (ISIT), Jul. 201

Approximation of Entropy Numbers

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction works for a very general class of operators between Banach spaces, in particular reflexive spaces. As a consequence of this technique we also obtain that the entropy number of a bounded linear operator T between two separable Hilbert spaces is equal to the entropy number of the adjoint of T. This gives a complete answer to the question posed by B. Carl [4] in the setting of separable Hilbert spaces.Comment: 10 page

Statistical properties of fracture in a random spring model

Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack localization measuring the evolution of damage as the external load is raised. We find that, as in the fuse model, damage is initially uniform and localizes at peak load. Scaling laws for the damage density, fracture strength and avalanche distributions follow with slight variations the behavior observed in the random fuse model. We thus conclude that scalar models provide a faithful representation of the fracture properties of disordered systems.Comment: 12 pages, 17 figures, 1 gif figur