1,840 research outputs found
On the Weight Distribution of Fixed-Rate Raptor Codes
In this paper Raptor code ensembles with linear random precodes 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
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
Expanding window fountain codes for unequal error protection
A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally. © 2009 IEEE
Expanding window fountain codes for unequal error protection
A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally. © 2009 IEEE
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
Reconfigurable rateless codes
We propose novel reconfigurable rateless codes, that are capable of not only varying the block length but also adaptively modify their encoding strategy by incrementally adjusting their degree distribution according to the prevalent channel conditions without the availability of the channel state information at the transmitter. In particular, we characterize a reconfigurable ratelesscode designed for the transmission of 9,500 information bits that achieves a performance, which is approximately 1 dB away from the discrete-input continuous-output memoryless channel’s (DCMC) capacity over a diverse range of channel signal-to-noise (SNR) ratios
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
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