83,922 research outputs found
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
Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers
We propose two coded schemes for the distributed computing problem of
multiplying a matrix by a set of vectors. The first scheme is based on
partitioning the matrix into submatrices and applying maximum distance
separable (MDS) codes to each submatrix. For this scheme, we prove that up to a
given number of partitions the communication load and the computational delay
(not including the encoding and decoding delay) are identical to those of the
scheme recently proposed by Li et al., based on a single, long MDS code.
However, due to the use of shorter MDS codes, our scheme yields a significantly
lower overall computational delay when the delay incurred by encoding and
decoding is also considered. We further propose a second coded scheme based on
Luby Transform (LT) codes under inactivation decoding. Interestingly, LT codes
may reduce the delay over the partitioned scheme at the expense of an increased
communication load. We also consider distributed computing under a deadline and
show numerically that the proposed schemes outperform other schemes in the
literature, with the LT code-based scheme yielding the best performance for the
scenarios considered.Comment: To appear in IEEE Transactions on Communication
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
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