15 research outputs found
Band Codes for Energy-Efficient Network Coding with Application to P2P Mobile Streaming
A key problem in random network coding (NC) lies in the complexity and energy
consumption associated with the packet decoding processes, which hinder its
application in mobile environments. Controlling and hence limiting such factors
has always been an important but elusive research goal, since the packet degree
distribution, which is the main factor driving the complexity, is altered in a
non-deterministic way by the random recombinations at the network nodes. In
this paper we tackle this problem proposing Band Codes (BC), a novel class of
network codes specifically designed to preserve the packet degree distribution
during packet encoding, ecombination and decoding. BC are random codes over
GF(2) that exhibit low decoding complexity, feature limited and controlled
degree distribution by construction, and hence allow to effectively apply NC
even in energy-constrained scenarios. In particular, in this paper we motivate
and describe our new design and provide a thorough analysis of its performance.
We provide numerical simulations of the performance of BC in order to validate
the analysis and assess the overhead of BC with respect to a onventional NC
scheme. Moreover, peer-to-peer media streaming experiments with a random-push
protocol show that BC reduce the decoding complexity by a factor of two, to a
point where NC-based mobile streaming to mobile devices becomes practically
feasible.Comment: To be published in IEEE Transacions on Multimedi
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
Degree Distribution Optimization in Raptor Network Coding
We consider a multi-source delivery system, where Raptor coding at sources and linear network coding in overlay nodes work in concert for efficient data delivery in networks with diversity. Such a combination permits to increase throughput and loss resiliency in multicast scenarios with possibly multiple sources. The network coding operations however change the degree distribution in the set of packets that reach the receivers, so that the low complexity decoding benefits of Raptor codes are unfortunately diminished. We propose in this paper to change the degree distribution at encoder, in such a way that the degree distribution after network coding operations recovers a form that leads to low complexity decoding. We first analyze how the degree distribution of the encoded symbols is altered by network coding operations and losses in a regular network. Then we formulate a geometric optimization problem in order to compute the best degree distribution for encoding at sources, such that the decoding complexity is low and close to Raptor decoders' performance. Simulations show that it is possible to maintain the low complexity decoding performance of Raptor codes even after linear network coding operations, as long as the coding at sources is adapted to the network characteristics
Buffer-Based Distributed LT Codes
We focus on the design of distributed Luby transform (DLT) codes for erasure
networks with multiple sources and multiple relays, communicating to a single
destination. The erasure-floor performance of DLT codes improves with the
maximum degree of the relay-degree distribution. However, for conventional DLT
codes, the maximum degree is upper-bounded by the number of sources. An
additional constraint is that the sources are required to have the same
information block length. We introduce a -bit buffer for each source-relay
link, which allows the relay to select multiple encoded bits from the same
source for the relay-encoding process; thus, the number of sources no longer
limits the maximum degree at the relay. Furthermore, the introduction of
buffers facilitates the use of different information block sizes across
sources. Based on density evolution we develop an asymptotic analytical
framework for optimization of the relay-degree distribution. We further
integrate techniques for unequal erasure protection into the optimization
framework. The proposed codes are considered for both lossless and lossy
source-relay links. Numerical examples show that there is no loss in erasure
performance for transmission over lossy source-relay links as compared to
lossless links. Additional delays, however, may occur. The design framework and
our contributions are demonstrated by a number of illustrative examples,
showing the improvements obtained by the proposed buffer-based DLT codes.Comment: 14 pages, 17 figures, submitte
AND-OR tree analysis of distributed LT codes
In this contribution, we consider design of distributed LT codes, i.e., independent rateless encodings of multiple sources which communicate to a common relay, where relay is able to combine incoming packets from the sources and forwards them to receivers. We provide density evolution formulae for distributed LT codes, which allow us to formulate distributed LT code design problem and prove the equivalence of performance of distributed LT codes and LT codes with related parameters in the asymptotic regime. Furthermore, we demonstrate that allowing LT coding apparatus at both the sources and the relay may prove advantageous to coding only at the sources and coding only at the relay
Design Of Fountain Codes With Error Control
This thesis is focused on providing unequal error protection (uep) to two disjoint sources which are communicating to a comdestination via a comrelay by using distributed lt codes over a binary erasure channel (bec), and designing fountain codes with error control property by integrating lt codes with turbo codes over a binary input additive white gaussian noise (bi-awgn) channel. A simple yet efficient technique for decomposing the rsd into two entirely different degree distributions is developed and presented in this thesis. These two distributions are used to encode data symbols at the sources and the encoded symbols from the sources are selectively xored at the relay based on a suitable relay operation before the combined codeword is transmitted to the destination. By doing so, it is shown that the uep can be provided to these sources. The performance of lt codes over the awgn channel is well studied and presented in this thesis which indicates that these codes have weak error correction ability over the channel. But, errors introduced into individual symbols during the transmission of information over noisy channels need correction by some error correcting codes. Since it is found that lt codes alone are weak at correcting those errors, lt codes are integrated with turbo codes which are good error correcting codes. Therefore, the source data (symbols) are at first turbo encoded and then lt encoded and transmitted over the awgn channel. When the corrupted encoded symbols are received at receiver, lt decoding is conducted folloby turbo decoding. The overall performance of the integrated system is studied and presented in this thesis, which suggests that the errors left after lt decoding can be corrected to some extent by turbo decoder