Abstract—In this paper, we discuss the rate splitting issue for the design of finite length Raptor codes, in a joint decoding framework. We show that the choice of a rate lower than usually proposed for the precode enables to design Raptor codes that perform well at small lengths, with almost

, and the original symbols are recovered from the collected ones with O(k log(1/ε)) operations. We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions

Abstract-Let {(X,, Y,J}r = 1 be a sequence of independent drawings of a pair of dependent random variables X, Y. Let us say that X takes values in the finite set 6. It is desired to encode the sequence {X,} in blocks of length n into a binary stream*of rate R, which can in turn be decoded as a

symbols are recovered from the collected ones with operations. symbols We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which

“bandlimited and sinc kernel ” case. In particular, we show how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinite-length signals with finite local rate of innovation, we show local sampling

in any material form whatsoever without the author’s prior written permission. To my family. In this dissertation we present new methods for designing efficient Raptor codes in finite and practical block lengths. First we propose an extension of Raptor codes which keeps all the desirable properties

Abstract-In this paper, performance of finite-length batched sparse (BATS) codes with belief propagation (BP) decoding is analyzed. For fixed number of input symbols and fixed number of batches, a recursive formula is obtained to calculate the exact probability distribution of the stopping time

having continuous search space, binary-coded GAs discretize the search space by using a coding of the problem variables in binary strings. However, the coding of real-valued variables in finite-length strings causes a number of difficulties---inability to achieve arbitrary precision in the obtained

The goal of the present paper is the derivation of a framework for the finite-length analysis of message-passing iterative decoding of low-density parity-check codes. To this end we introduce the concept of graph-cover decoding. Whereas in maximum-likelihood decoding all codewords in a code

Codewords in finite covers of a Tanner graph G are characterized. Since iterative, locally operating decoding algorithms cannot distinguish the underlying graph G from any covering graph, these codewords, dubbed pseudo-codewords are directly responible for sub-optimal behavior of iterative decoding