9,621 research outputs found
A New Construction Scheme of Convolutional Codes
Abstract-A new class of (2k, k, 1) convolutional codes is proposed based on the method that creating long codes by short ones in this paper, by embedding (2k, k) double loop cyclic codes in (2, 1, 1) convolutional codes. The structural mechanism of the codes is revealed by defining a state transition matrix and using algebraic method. It is then shown that the code structure is excellent in both proportionality and diversity, so a superior code is easy to be obtained. Simulation results show that, the new convolutional codes present advantages over the traditional (2, 1, l) codes in the errorcorrecting capability and decoding speed
Windowed Decoding of Protograph-based LDPC Convolutional Codes over Erasure Channels
We consider a windowed decoding scheme for LDPC convolutional codes that is
based on the belief-propagation (BP) algorithm. We discuss the advantages of
this decoding scheme and identify certain characteristics of LDPC convolutional
code ensembles that exhibit good performance with the windowed decoder. We will
consider the performance of these ensembles and codes over erasure channels
with and without memory. We show that the structure of LDPC convolutional code
ensembles is suitable to obtain performance close to the theoretical limits
over the memoryless erasure channel, both for the BP decoder and windowed
decoding. However, the same structure imposes limitations on the performance
over erasure channels with memory.Comment: 18 pages, 9 figures, accepted for publication in the IEEE
Transactions on Information Theor
Universal and Robust Distributed Network Codes
Random linear network codes can be designed and implemented in a distributed
manner, with low computational complexity. However, these codes are classically
implemented over finite fields whose size depends on some global network
parameters (size of the network, the number of sinks) that may not be known
prior to code design. Also, if new nodes join the entire network code may have
to be redesigned.
In this work, we present the first universal and robust distributed linear
network coding schemes. Our schemes are universal since they are independent of
all network parameters. They are robust since if nodes join or leave, the
remaining nodes do not need to change their coding operations and the receivers
can still decode. They are distributed since nodes need only have topological
information about the part of the network upstream of them, which can be
naturally streamed as part of the communication protocol.
We present both probabilistic and deterministic schemes that are all
asymptotically rate-optimal in the coding block-length, and have guarantees of
correctness. Our probabilistic designs are computationally efficient, with
order-optimal complexity. Our deterministic designs guarantee zero error
decoding, albeit via codes with high computational complexity in general. Our
coding schemes are based on network codes over ``scalable fields". Instead of
choosing coding coefficients from one field at every node, each node uses
linear coding operations over an ``effective field-size" that depends on the
node's distance from the source node. The analysis of our schemes requires
technical tools that may be of independent interest. In particular, we
generalize the Schwartz-Zippel lemma by proving a non-uniform version, wherein
variables are chosen from sets of possibly different sizes. We also provide a
novel robust distributed algorithm to assign unique IDs to network nodes.Comment: 12 pages, 7 figures, 1 table, under submission to INFOCOM 201
Quantum Convolutional Error Correcting Codes
I report two general methods to construct quantum convolutional codes for
-state quantum systems. Using these general methods, I construct a quantum
convolutional code of rate 1/4, which can correct one quantum error for every
eight consecutive quantum registers.Comment: Minor revisions and clarifications. To appear in Phys. Rev.
Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes
Foliated quantum codes are a resource for fault-tolerant measurement-based
quantum error correction for quantum repeaters and for quantum computation.
They represent a general approach to integrating a range of possible quantum
error correcting codes into larger fault-tolerant networks. Here we present an
efficient heuristic decoding scheme for foliated quantum codes, based on
message passing between primal and dual code 'sheets'. We test this decoder on
two different families of sparse quantum error correcting code: turbo codes and
bicycle codes, and show reasonably high numerical performance thresholds. We
also present a construction schedule for building such code states.Comment: 23 pages, 15 figures, accepted for publication in Phys. Rev.
Spatially-Coupled Random Access on Graphs
In this paper we investigate the effect of spatial coupling applied to the
recently-proposed coded slotted ALOHA (CSA) random access protocol. Thanks to
the bridge between the graphical model describing the iterative interference
cancelation process of CSA over the random access frame and the erasure
recovery process of low-density parity-check (LDPC) codes over the binary
erasure channel (BEC), we propose an access protocol which is inspired by the
convolutional LDPC code construction. The proposed protocol exploits the
terminations of its graphical model to achieve the spatial coupling effect,
attaining performance close to the theoretical limits of CSA. As for the
convolutional LDPC code case, large iterative decoding thresholds are obtained
by simply increasing the density of the graph. We show that the threshold
saturation effect takes place by defining a suitable counterpart of the
maximum-a-posteriori decoding threshold of spatially-coupled LDPC code
ensembles. In the asymptotic setting, the proposed scheme allows sustaining a
traffic close to 1 [packets/slot].Comment: To be presented at IEEE ISIT 2012, Bosto
Error-Correcting Codes for Automatic Control
Systems with automatic feedback control may consist of several remote devices, connected only by unreliable communication channels. It is necessary in these conditions to have a method for accurate, real-time state estimation in the presence of channel noise. This problem is addressed, for the case of polynomial-growth-rate state spaces, through a new type of error-correcting code that is online and computationally efficient. This solution establishes a constructive analog, for some applications in estimation and control, of the Shannon coding theorem
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