Distance Spectrum of Fixed-Rate Raptor Codes With Linear Random Precoders

A Lattice-Theoretic Characterization of Optimal Minimum-Distance Linear Precoders

This work investigates linear precoding over non-singular linear channels with additive white Gaussian noise, with lattice-type inputs.The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver...

Summary of Raptor Codes

A fountain code produces for given set of k input symbols (x1, . . . , xk) a potentially limitless stream of output symbols z1, z2, . . .. The input and output symbols can be binary vectors of arbitrary length. Each output symbol is the sum of a randomly and independently chosen subset of the input symbols. Information describing the relations between input and output symbols is obtained at the...

Raptor codes pdf

Linear Locally Repairable Codes with Random Matrices

In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the locality property, is a generator matrix for a locally repairable code with a good minimum distance. The proof of this gives also a constructive method to find...

Random Generation of Linear Codes

Isometry classes of linear codes can be expressed as orbits under the group action of a wreath product. Some combinatorial and algebraic methods are discussed which can be applied for generating linear codes distributed uniformly at random over all isometry classes.