3,408 research outputs found
Analysis of the Second Moment of the LT Decoder
We analyze the second moment of the ripple size during the LT decoding
process and prove that the standard deviation of the ripple size for an LT-code
with length is of the order of Together with a result by Karp
et. al stating that the expectation of the ripple size is of the order of
[3], this gives bounds on the error probability of the LT decoder. We also give
an analytic expression for the variance of the ripple size up to terms of
constant order, and refine the expression in [3] for the expectation of the
ripple size up to terms of the order of , thus providing a first step
towards an analytic finite-length analysis of LT decoding.Comment: 5 pages, 1 figure; submitted to ISIT 200
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
Stabilization of Linear Systems Over Gaussian Networks
The problem of remotely stabilizing a noisy linear time invariant plant over
a Gaussian relay network is addressed. The network is comprised of a sensor
node, a group of relay nodes and a remote controller. The sensor and the relay
nodes operate subject to an average transmit power constraint and they can
cooperate to communicate the observations of the plant's state to the remote
controller. The communication links between all nodes are modeled as Gaussian
channels. Necessary as well as sufficient conditions for mean-square
stabilization over various network topologies are derived. The sufficient
conditions are in general obtained using delay-free linear policies and the
necessary conditions are obtained using information theoretic tools. Different
settings where linear policies are optimal, asymptotically optimal (in certain
parameters of the system) and suboptimal have been identified. For the case
with noisy multi-dimensional sources controlled over scalar channels, it is
shown that linear time varying policies lead to minimum capacity requirements,
meeting the fundamental lower bound. For the case with noiseless sources and
parallel channels, non-linear policies which meet the lower bound have been
identified
Broadcasting a Common Message with Variable-Length Stop-Feedback Codes
We investigate the maximum coding rate achievable over a two-user broadcast
channel for the scenario where a common message is transmitted using
variable-length stop-feedback codes. Specifically, upon decoding the common
message, each decoder sends a stop signal to the encoder, which transmits
continuously until it receives both stop signals. For the point-to-point case,
Polyanskiy, Poor, and Verd\'u (2011) recently demonstrated that variable-length
coding combined with stop feedback significantly increases the speed at which
the maximum coding rate converges to capacity. This speed-up manifests itself
in the absence of a square-root penalty in the asymptotic expansion of the
maximum coding rate for large blocklengths, a result a.k.a. zero dispersion. In
this paper, we show that this speed-up does not necessarily occur for the
broadcast channel with common message. Specifically, there exist scenarios for
which variable-length stop-feedback codes yield a positive dispersion.Comment: Extended version of a paper submitted to ISIT 201
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
Cyclone Codes
We introduce Cyclone codes which are rateless erasure resilient codes. They
combine Pair codes with Luby Transform (LT) codes by computing a code symbol
from a random set of data symbols using bitwise XOR and cyclic shift
operations. The number of data symbols is chosen according to the Robust
Soliton distribution. XOR and cyclic shift operations establish a unitary
commutative ring if data symbols have a length of bits, for some prime
number . We consider the graph given by code symbols combining two data
symbols. If such random pairs are given for data symbols, then a
giant component appears, which can be resolved in linear time. We can extend
Cyclone codes to data symbols of arbitrary even length, provided the Goldbach
conjecture holds.
Applying results for this giant component, it follows that Cyclone codes have
the same encoding and decoding time complexity as LT codes, while the overhead
is upper-bounded by those of LT codes. Simulations indicate that Cyclone codes
significantly decreases the overhead of extra coding symbols
On the Energy Efficiency of LT Codes in Proactive Wireless Sensor Networks
This paper presents an in-depth analysis on the energy efficiency of Luby
Transform (LT) codes with Frequency Shift Keying (FSK) modulation in a Wireless
Sensor Network (WSN) over Rayleigh fading channels with pathloss. We describe a
proactive system model according to a flexible duty-cycling mechanism utilized
in practical sensor apparatus. The present analysis is based on realistic
parameters including the effect of channel bandwidth used in the IEEE 802.15.4
standard, active mode duration and computation energy. A comprehensive
analysis, supported by some simulation studies on the probability mass function
of the LT code rate and coding gain, shows that among uncoded FSK and various
classical channel coding schemes, the optimized LT coded FSK is the most
energy-efficient scheme for distance d greater than the pre-determined
threshold level d_T , where the optimization is performed over coding and
modulation parameters. In addition, although the optimized uncoded FSK
outperforms coded schemes for d < d_T , the energy gap between LT coded and
uncoded FSK is negligible for d < d_T compared to the other coded schemes.
These results come from the flexibility of the LT code to adjust its rate to
suit instantaneous channel conditions, and suggest that LT codes are beneficial
in practical low-power WSNs with dynamic position sensor nodes.Comment: accepted for publication in IEEE Transactions on Signal Processin
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