2,498 research outputs found
Design and Analysis of LT Codes with Decreasing Ripple Size
In this paper we propose a new design of LT codes, which decreases the amount
of necessary overhead in comparison to existing designs. The design focuses on
a parameter of the LT decoding process called the ripple size. This parameter
was also a key element in the design proposed in the original work by Luby.
Specifically, Luby argued that an LT code should provide a constant ripple size
during decoding. In this work we show that the ripple size should decrease
during decoding, in order to reduce the necessary overhead. Initially we
motivate this claim by analytical results related to the redundancy within an
LT code. We then propose a new design procedure, which can provide any desired
achievable decreasing ripple size. The new design procedure is evaluated and
compared to the current state of the art through simulations. This reveals a
significant increase in performance with respect to both average overhead and
error probability at any fixed overhead
Doped Fountain Coding for Minimum Delay Data Collection in Circular Networks
This paper studies decentralized, Fountain and network-coding based
strategies for facilitating data collection in circular wireless sensor
networks, which rely on the stochastic diversity of data storage. The goal is
to allow for a reduced delay collection by a data collector who accesses the
network at a random position and random time. Data dissemination is performed
by a set of relays which form a circular route to exchange source packets. The
storage nodes within the transmission range of the route's relays linearly
combine and store overheard relay transmissions using random decentralized
strategies. An intelligent data collector first collects a minimum set of coded
packets from a subset of storage nodes in its proximity, which might be
sufficient for recovering the original packets and, by using a message-passing
decoder, attempts recovering all original source packets from this set.
Whenever the decoder stalls, the source packet which restarts decoding is
polled/doped from its original source node. The random-walk-based analysis of
the decoding/doping process furnishes the collection delay analysis with a
prediction on the number of required doped packets. The number of doped packets
can be surprisingly small when employed with an Ideal Soliton code degree
distribution and, hence, the doping strategy may have the least collection
delay when the density of source nodes is sufficiently large. Furthermore, we
demonstrate that network coding makes dissemination more efficient at the
expense of a larger collection delay. Not surprisingly, a circular network
allows for a significantly more (analytically and otherwise) tractable
strategies relative to a network whose model is a random geometric graph
Rateless Codes with Progressive Recovery for Layered Multimedia Delivery
This paper proposes a novel approach, based on unequal error protection, to
enhance rateless codes with progressive recovery for layered multimedia
delivery. With a parallel encoding structure, the proposed Progressive Rateless
codes (PRC) assign unequal redundancy to each layer in accordance with their
importance. Each output symbol contains information from all layers, and thus
the stream layers can be recovered progressively at the expected received
ratios of output symbols. Furthermore, the dependency between layers is
naturally considered. The performance of the PRC is evaluated and compared with
some related UEP approaches. Results show that our PRC approach provides better
recovery performance with lower overhead both theoretically and numerically
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
Rotation and Neoclassical Ripple Transport in ITER
Neoclassical transport in the presence of non-axisymmetric magnetic fields
causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The
toroidal symmetry of ITER will be broken by the finite number of toroidal field
coils and by test blanket modules (TBMs). The addition of ferritic inserts
(FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic
equilibria with toroidal field ripple and ferromagnetic structures are
calculated for an ITER steady-state scenario using the Variational Moments
Equilibrium Code (VMEC). Neoclassical transport quantities in the presence of
these error fields are calculated using the Stellarator Fokker-Planck Iterative
Neoclassical Conservative Solver (SFINCS). These calculations fully account for
, flux surface shaping, multiple species, magnitude of ripple, and
collisionality rather than applying approximate analytic NTV formulae. As NTV
is a complicated nonlinear function of , we study its behavior over a
plausible range of . We estimate the toroidal flow, and hence , using
a semi-analytic turbulent intrinsic rotation model and NUBEAM calculations of
neutral beam torque. The NTV from the ripple dominates
that from lower perturbations of the TBMs. With the inclusion of FIs, the
magnitude of NTV torque is reduced by about 75% near the edge. We present
comparisons of several models of tangential magnetic drifts, finding
appreciable differences only for superbanana-plateau transport at small .
We find the scaling of calculated NTV torque with ripple magnitude to indicate
that ripple-trapping may be a significant mechanism for NTV in ITER. The
computed NTV torque without ferritic components is comparable in magnitude to
the NBI and intrinsic turbulent torques and will likely damp rotation, but the
NTV torque is significantly reduced by the planned ferritic inserts
LT Code Equations
The LT Code equations describe the process of encoding input symbols into an error correcting code that requires no feedback from the receiver. The mathematical process involved the development of LT Codes is important. This thesis address the issue of improving the understanding of the LT Code equations presented in the original paper. This task is accomplished by inserting the mathematical details when possible, providing graphical results to the equations, and comparing the equations results against random computer generated simulations results. This thesis will improve the understanding of how LT Codes equations related to actual results
Raptor Codes in the Low SNR Regime
In this paper, we revisit the design of Raptor codes for binary input
additive white Gaussian noise (BIAWGN) channels, where we are interested in
very low signal to noise ratios (SNRs). A linear programming degree
distribution optimization problem is defined for Raptor codes in the low SNR
regime through several approximations. We also provide an exact expression for
the polynomial representation of the degree distribution with infinite maximum
degree in the low SNR regime, which enables us to calculate the exact value of
the fractions of output nodes of small degrees. A more practical degree
distribution design is also proposed for Raptor codes in the low SNR regime,
where we include the rate efficiency and the decoding complexity in the
optimization problem, and an upper bound on the maximum rate efficiency is
derived for given design parameters. Simulation results show that the Raptor
code with the designed degree distributions can approach rate efficiencies
larger than 0.95 in the low SNR regime.Comment: Submitted to the IEEE Transactions on Communications. arXiv admin
note: text overlap with arXiv:1510.0772
Unequal Error Protection Raptor Codes
We design Unequal Error Protection (UEP) Raptor codes with the UEP property provided by the precode part of Raptor codes which is usually a Low Density Parity Check (LDPC) code. Existing UEP Raptor codes apply the UEP property on the Luby transform (LT) code part of Raptor codes. This approach lowers the bit erasure rate (BER) of the more important bits (MIB) of the data decoded by the LT part of the decoder of Raptor code at the expense of degrading the BER performance of Less Important Bits (LIB), and hence the overall BER of the data passed from the LT part to the LDPC part of the decoder is higher compared to the case of using an Equal Error Protection (EEP) LT code. The proposed UEP Raptor code design has the structure of UEP LDPC code and EEP LT code so that it has the advantage of passing data blocks with lower BER from the LT code part to the LDPC code part of the decoder. This advantage is translated into improved performance in terms of required overhead and achieved BER on both the MIB bits and LIB bits of the decoded data compared to UEP Raptor codes applying the UEP property on the LT part. We propose two design schemes. The first combines a partially regular LDPC code which has UEP properties with an EEP LT code, and the second scheme uses two LDPC codes with different code rates in the precode part such that the MIB bits are encoded using the LDPC code with lower rate and the LT part is EEP. Simulations of both designs exhibit improved BER performance on both the MIB bits and LIB bits while consuming smaller overheads. The second design can be used to provide unequal protection for cases where the MIB bits comprise a fraction of more than 0.4 of the source data which is a case where UEP Raptor codes with UEP LT codes perform poorly
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