arXiv subjects

Abdelaziz Amraoui

Publications and source records attributed to Abdelaziz Amraoui.

3 recordsLinked to original sources

arXiv2006

How to Find Good Finite-Length Codes: From Art Towards Science

We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn based on a finite-length scaling result to model large scale erasures and a union bound involving minimal stopping sets to take into account small error events. We show that the performances of optimized ensembles as observed in simulations are well described by our approximation. Although we only address the case of transmission over the binary erasure channel, our method should be applicable to a more general setting.

cs.IT↗

arXiv2004

Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes

Consider communication over the binary erasure channel BEC using random low-density parity-check codes with finite-blocklength n from `standard' ensembles. We show that large error events is conveniently described within a scaling theory, and explain how to estimate heuristically their effect. Among other quantities, we consider the finite length threshold e(n), defined by requiring a block error probability P_B = 1/2. For ensembles with minimum variable degree larger than two, the following expression is argued to hold e(n) = e -e_1 n^{-2/3} +Θ(n^{-1}) with a calculable shift} parameter e_1>0.

cs.IT↗

arXiv2004

Finite-Length Scaling for Iteratively Decoded LDPC Ensembles

In this paper we investigate the behavior of iteratively decoded low-density parity-check codes over the binary erasure channel in the so-called ``waterfall region." We show that the performance curves in this region follow a very basic scaling law. We conjecture that essentially the same scaling behavior applies in a much more general setting and we provide some empirical evidence to support this conjecture. The scaling law, together with the error floor expressions developed previously, can be used for fast finite-length optimization.

cs.IT↗