123 research outputs found
Erasure Codes with a Banded Structure for Hybrid Iterative-ML Decoding
This paper presents new FEC codes for the erasure channel, LDPC-Band, that
have been designed so as to optimize a hybrid iterative-Maximum Likelihood (ML)
decoding. Indeed, these codes feature simultaneously a sparse parity check
matrix, which allows an efficient use of iterative LDPC decoding, and a
generator matrix with a band structure, which allows fast ML decoding on the
erasure channel. The combination of these two decoding algorithms leads to
erasure codes achieving a very good trade-off between complexity and erasure
correction capability.Comment: 5 page
Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design
In this paper we analyze LT and Raptor codes under inactivation decoding. A
first order analysis is introduced, which provides the expected number of
inactivations for an LT code, as a function of the output distribution, the
number of input symbols and the decoding overhead. The analysis is then
extended to the calculation of the distribution of the number of inactivations.
In both cases, random inactivation is assumed. The developed analytical tools
are then exploited to design LT and Raptor codes, enabling a tight control on
the decoding complexity vs. failure probability trade-off. The accuracy of the
approach is confirmed by numerical simulations.Comment: Accepted for publication in IEEE Transactions on Communication
Bounds on the Error Probability of Raptor Codes under Maximum Likelihood Decoding
In this paper upper and lower bounds on the probability of decoding failure
under maximum likelihood decoding are derived for different (nonbinary) Raptor
code constructions. In particular four different constructions are considered;
(i) the standard Raptor code construction, (ii) a multi-edge type construction,
(iii) a construction where the Raptor code is nonbinary but the generator
matrix of the LT code has only binary entries, (iv) a combination of (ii) and
(iii). The latter construction resembles the one employed by RaptorQ codes,
which at the time of writing this article represents the state of the art in
fountain codes. The bounds are shown to be tight, and provide an important aid
for the design of Raptor codes.Comment: Submitted for revie
RS + LDPC-Staircase Codes for the Erasure Channel: Standards, Usage and Performance
Application-Level Forward Erasure Correction (AL-FEC) codes are a key element of telecommunication systems. They are used to recover from packet losses when retransmission are not feasible and to optimize the large scale distribution of contents. In this paper we introduce Reed-Solomon/LDPCStaircase codes, two complementary AL-FEC codes that have recently been recognized as superior to Raptor codes in the context of the 3GPP-eMBMS call for technology [1]. After a brief introduction to the codes, we explain how to design high performance codecs which is a key aspect when targeting embedded systems with limited CPU/battery capacity. Finally we present the performances of these codes in terms of erasure correction capabilities and encoding/decoding speed, taking advantage of the 3GPP-eMBMS results where they have been ranked first
Fountain Codes under Maximum Likelihood Decoding
This dissertation focuses on fountain codes under maximum likelihood (ML)
decoding. First LT codes are considered under a practical and widely used ML
decoding algorithm known as inactivation decoding. Different analysis
techniques are presented to characterize the decoding complexity. Next an upper
bound to the probability of decoding failure of Raptor codes under ML decoding
is provided. Then, the distance properties of an ensemble of fixed-rate Raptor
codes with linear random outer codes are analyzed. Finally, a novel class of
fountain codes is presented, which consists of a parallel concatenation of a
block code with a linear random fountain code.Comment: PhD Thesi
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