Francisco Lázaro

Inactivation decoding analysis for LT codes

We provide two analytical tools to model the inactivation decoding process of LT codes. First, a model is presented which derives the expected number of inactivations occurring in the decoding process of an LT code. This analysis is then extended allowing the derivation of the distribution of the number of inactivations. The accuracy of the method is verified by Monte Carlo simulations. The proposed analysis opens the door to the design of LT codes optimized for inactivation decoding.

Bounds on the Error Probability of Raptor Codes

In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn randomly from some ensemble of codes. The bound is shown to be tight by means of simulations. This bound provides a new insight into Raptor codes since it shows how Raptor codes can be analyzed similarly to a classical fixed rate serial concatenation.

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

Raptor code ensembles with linear random outer codes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight distribution. The asymptotic growth rate analysis is then exploited to develop a necessary and sufficient condition under which the fixed-rate Raptor code ensemble exhibits a strictly positive typical minimum distance. The condition involves the rate of the outer code, the rate of the inner fixed-rate Luby Transform (LT) code and the LT code degree distribution. Additionally, it is shown that for ensembles fulfilling this condition, the minimum distance of a code randomly drawn from the ensemble has a linear growth with the block length. The analytical results can be used to make accurate predictions of the performance of finite length Raptor codes. These results are particularly useful for fixed-rate Raptor codes under maximum likelihood erasure decoding, whose performance is driven by their weight distribution.

Finite-Length Analysis of Frameless ALOHA With Multi-User Detection

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On the weight distribution of fixed-rate Raptor codes

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Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design

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Frameless ALOHA with Reliability-Latency Guarantees

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An advanced AIS receiver using a priori information

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Enhanced AIS receiver design for satellite reception

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Fountain Codes under Maximum Likelihood Decoding.

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