53 research outputs found
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
Cooperative Local Repair in Distributed Storage
Erasure-correcting codes, that support local repair of codeword symbols, have
attracted substantial attention recently for their application in distributed
storage systems. This paper investigates a generalization of the usual locally
repairable codes. In particular, this paper studies a class of codes with the
following property: any small set of codeword symbols can be reconstructed
(repaired) from a small number of other symbols. This is referred to as
cooperative local repair. The main contribution of this paper is bounds on the
trade-off of the minimum distance and the dimension of such codes, as well as
explicit constructions of families of codes that enable cooperative local
repair. Some other results regarding cooperative local repair are also
presented, including an analysis for the well-known Hadamard/Simplex codes.Comment: Fixed some minor issues in Theorem 1, EURASIP Journal on Advances in
Signal Processing, December 201
On a Low-Rate TLDPC Code Ensemble and the Necessary Condition on the Linear Minimum Distance for Sparse-Graph Codes
This paper addresses the issue of design of low-rate sparse-graph codes with
linear minimum distance in the blocklength. First, we define a necessary
condition which needs to be satisfied when the linear minimum distance is to be
ensured. The condition is formulated in terms of degree-1 and degree-2 variable
nodes and of low-weight codewords of the underlying code, and it generalizies
results known for turbo codes [8] and LDPC codes. Then, we present a new
ensemble of low-rate codes, which itself is a subclass of TLDPC codes [4], [5],
and which is designed under this necessary condition. The asymptotic analysis
of the ensemble shows that its iterative threshold is situated close to the
Shannon limit. In addition to the linear minimum distance property, it has a
simple structure and enjoys a low decoding complexity and a fast convergence.Comment: submitted to IEEE Trans. on Communication
Error Resilience in Distributed Storage via Rank-Metric Codes
This paper presents a novel coding scheme for distributed storage systems
containing nodes with adversarial errors. The key challenge in such systems is
the propagation of erroneous data from a single corrupted node to the rest of
the system during a node repair process. This paper presents a concatenated
coding scheme which is based on two types of codes: maximum rank distance (MRD)
code as an outer code and optimal repair maximal distance separable (MDS) array
code as an inner code. Given this, two different types of adversarial errors
are considered: the first type considers an adversary that can replace the
content of an affected node only once; while the second attack-type considers
an adversary that can pollute data an unbounded number of times. This paper
proves that the proposed coding scheme attains a suitable upper bound on
resilience capacity for the first type of error. Further, the paper presents
mechanisms that combine this code with subspace signatures to achieve error
resilience for the second type of errors. Finally, the paper concludes by
presenting a construction based on MRD codes for optimal locally repairable
scalar codes that can tolerate adversarial errors
Coding schemes for multicode CDMA systems.
Zhao Fei.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 87-89).Abstracts in English and Chinese.Chapter 1. --- Introduction --- p.1Chapter 1.1 --- Multirate Scheme --- p.2Chapter 1.1.1 --- VSF Scheme --- p.3Chapter 1.1.2 --- Multicode Scheme --- p.5Chapter 1.2 --- Multicode CDMA System --- p.7Chapter 1.2.1 --- System Model --- p.7Chapter 1.2.2 --- Envelope Variation of Multicode Signal --- p.9Chapter 1.2.3 --- Drawback of Multicode Scheme --- p.11Chapter 1.3 --- Organization of the Thesis --- p.13Chapter 2. --- Related Work on Minimization of PAP of Multicode CDMA --- p.15Chapter 2.1 --- Constant Amplitude Coding --- p.16Chapter 2.2 --- Multidimensional Multicode Scheme --- p.22Chapter 2.3 --- Precoding for Multicode Scheme --- p.25Chapter 2.4 --- Summary --- p.26Chapter 3. --- Multicode CDMA System with Constant Amplitude Transmission --- p.27Chapter 3.1 --- System Model --- p.28Chapter 3.2 --- Selection of Hadamard Code Sequences --- p.31Chapter 3.3 --- The Optimal Receiver for the Multicode System --- p.37Chapter 3.3.1 --- The Maximum-Likelihood Sequence Detector --- p.38Chapter 3.3.2 --- Maximum A Posteriori Probability Detector --- p.41Chapter 4. --- Multicode CDMA System Combined with Error-Correcting Codes --- p.45Chapter 4.1 --- Hamming Codes --- p.46Chapter 4.2 --- Gallager's Codes --- p.48Chapter 4.2.1 --- Encoding of Gallager's Codes --- p.48Chapter 4.2.2 --- Multicode Scheme combined with Gallager's Code --- p.52Chapter 4.2.3 --- Iterative Decoding of the Multicode Scheme --- p.55Chapter 4.3 --- Zigzag Codes --- p.59Chapter 4.4 --- Simulation Results and Discussion --- p.62Chapter 5. --- Multicode CDMA System with Bounded PAP Transmission --- p.68Chapter 5.1 --- Quantized Multicode Scheme --- p.69Chapter 5.1.1 --- System Model --- p.69Chapter 5.1.2 --- Interference of Code Channels --- p.71Chapter 5.2 --- Parallel Multicode Scheme --- p.74Chapter 5.2.1 --- System Model --- p.74Chapter 5.2.2 --- Selection of Hadamard Code Sequences --- p.75Chapter 6. --- Conclusions and Future Work --- p.82Chapter 6.1 --- Conclusions --- p.82Chapter 6.2 --- Future Work --- p.84Bibliography --- p.8
Efficient fault-tolerant quantum computing
Fault tolerant quantum computing methods which work with efficient quantum
error correcting codes are discussed. Several new techniques are introduced to
restrict accumulation of errors before or during the recovery. Classes of
eligible quantum codes are obtained, and good candidates exhibited. This
permits a new analysis of the permissible error rates and minimum overheads for
robust quantum computing. It is found that, under the standard noise model of
ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an
order of magnitude larger than the logical machine contained within it in order
to be reliable. For example, a scale-up by a factor of 22, with gate error rate
of order , is sufficient to permit large quantum algorithms such as
factorization of thousand-digit numbers.Comment: 21 pages plus 5 figures. Replaced with figures in new format to avoid
problem
High-Rate Regenerating Codes Through Layering
In this paper, we provide explicit constructions for a class of exact-repair
regenerating codes that possess a layered structure. These regenerating codes
correspond to interior points on the storage-repair-bandwidth tradeoff, and
compare very well in comparison to scheme that employs space-sharing between
MSR and MBR codes. For the parameter set with , we
construct a class of codes with an auxiliary parameter , referred to as
canonical codes. With in the range , these codes operate in
the region between the MSR point and the MBR point, and perform significantly
better than the space-sharing line. They only require a field size greater than
. For the case of , canonical codes can also be shown to
achieve an interior point on the line-segment joining the MSR point and the
next point of slope-discontinuity on the storage-repair-bandwidth tradeoff.
Thus we establish the existence of exact-repair codes on a point other than the
MSR and the MBR point on the storage-repair-bandwidth tradeoff. We also
construct layered regenerating codes for general parameter set ,
which we refer to as non-canonical codes. These codes also perform
significantly better than the space-sharing line, though they require a
significantly higher field size. All the codes constructed in this paper are
high-rate, can repair multiple node-failures and do not require any computation
at the helper nodes. We also construct optimal codes with locality in which the
local codes are layered regenerating codes.Comment: 20 pages, 9 figure
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