4,817 research outputs found
Convolutional Codes in Rank Metric with Application to Random Network Coding
Random network coding recently attracts attention as a technique to
disseminate information in a network. This paper considers a non-coherent
multi-shot network, where the unknown and time-variant network is used several
times. In order to create dependencies between the different shots, particular
convolutional codes in rank metric are used. These codes are so-called
(partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one.
First, distance measures for convolutional codes in rank metric are shown and
two constructions of (P)UM codes in rank metric based on the generator matrices
of maximum rank distance codes are presented. Second, an efficient
error-erasure decoding algorithm for these codes is presented. Its guaranteed
decoding radius is derived and its complexity is bounded. Finally, it is shown
how to apply these codes for error correction in random linear and affine
network coding.Comment: presented in part at Netcod 2012, submitted to IEEE Transactions on
Information Theor
Block Network Error Control Codes and Syndrome-based Complete Maximum Likelihood Decoding
In this paper, network error control coding is studied for robust and
efficient multicast in a directed acyclic network with imperfect links. The
block network error control coding framework, BNEC, is presented and the
capability of the scheme to correct a mixture of symbol errors and packet
erasures and to detect symbol errors is studied. The idea of syndrome-based
decoding and error detection is introduced for BNEC, which removes the effect
of input data and hence decreases the complexity. Next, an efficient
three-stage syndrome-based BNEC decoding scheme for network error correction is
proposed, in which prior to finding the error values, the position of the edge
errors are identified based on the error spaces at the receivers. In addition
to bounded-distance decoding schemes for error correction up to the refined
Singleton bound, a complete decoding scheme for BNEC is also introduced.
Specifically, it is shown that using the proposed syndrome-based complete
decoding, a network error correcting code with redundancy order d for receiver
t, can correct d-1 random additive errors with a probability sufficiently close
to 1, if the field size is sufficiently large. Also, a complete maximum
likelihood decoding scheme for BNEC is proposed. As the probability of error in
different network edges is not equal in general, and given the equivalency of
certain edge errors within the network at a particular receiver, the number of
edge errors, assessed in the refined Singleton bound, is not a sufficient
statistic for ML decoding
On The Performance of Random Block Codes over Finite-State Fading Channels
As the mobile application landscape expands, wireless networks are tasked
with supporting various connection profiles, including real-time communications
and delay-sensitive traffic. Among many ensuing engineering challenges is the
need to better understand the fundamental limits of forward error correction in
non-asymptotic regimes. This article seeks to characterize the performance of
block codes over finite-state channels with memory. In particular, classical
results from information theory are revisited in the context of channels with
rate transitions, and bounds on the probabilities of decoding failure are
derived for random codes. This study offers new insights about the potential
impact of channel correlation over time on overall performance
Short, unit-memory, Byte-oriented, binary convolutional codes having maximal free distance
It is shown that (n sub 0, k sub 0) convolutional codes with unit memory always achieve the largest free distance among all codes of the same rate k sub 0/n sub 0 and same number 2MK sub 0 of encoder states, where M is the encoder memory. A unit-memory code with maximal free distance is given at each place where this free distance exceeds that of the best code with k sub 0 and n sub 0 relatively prime, for all Mk sub 0 less than or equal to 6 and for R = 1/2, 1/3, 1/4, 2/3. It is shown that the unit-memory codes are byte-oriented in such a way as to be attractive for use in concatenated coding systems
Renormalization group decoder for a four-dimensional toric code
We describe a computationally-efficient heuristic algorithm based on a
renormalization-group procedure which aims at solving the problem of finding
minimal surface given its boundary (curve) in any hypercubic lattice of
dimension . We use this algorithm to correct errors occurring in a
four-dimensional variant of the toric code, having open as opposed to periodic
boundaries. For a phenomenological error model which includes measurement
errors we use a five-dimensional version of our algorithm, achieving a
threshold of . For this error model, this is the highest known
threshold of any topological code. Without measurement errors, a
four-dimensional version of our algorithm can be used and we find a threshold
of . For the gate-based depolarizing error model we find a
threshold of which is below the threshold found for the
two-dimensional toric code.Comment: 18 pages, 12 figures, 3 tables. Comments are welcom
Concatenation of convolutional and block codes Final report
Comparison of concatenated and sequential decoding systems and convolutional code structural propertie
Inter-Block Permuted Turbo Codes
The structure and size of the interleaver used in a turbo code critically
affect the distance spectrum and the covariance property of a component
decoder's information input and soft output. This paper introduces a new class
of interleavers, the inter-block permutation (IBP) interleavers, that can be
build on any existing "good" block-wise interleaver by simply adding an IBP
stage. The IBP interleavers reduce the above-mentioned correlation and increase
the effective interleaving size. The increased effective interleaving size
improves the distance spectrum while the reduced covariance enhances the
iterative decoder's performance. Moreover, the structure of the
IBP(-interleaved) turbo codes (IBPTC) is naturally fit for high rate
applications that necessitate parallel decoding.
We present some useful bounds and constraints associated with the IBPTC that
can be used as design guidelines. The corresponding codeword weight upper
bounds for weight-2 and weight-4 input sequences are derived. Based on some of
the design guidelines, we propose a simple IBP algorithm and show that the
associated IBPTC yields 0.3 to 1.2 dB performance gain, or equivalently, an
IBPTC renders the same performance with a much reduced interleaving delay. The
EXIT and covariance behaviors provide another numerical proof of the
superiority of the proposed IBPTC.Comment: 44 pages, 17 figure
Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes
In this paper, we present an iterative soft-decision decoding algorithm for
Reed-Solomon codes offering both complexity and performance advantages over
previously known decoding algorithms. Our algorithm is a list decoding
algorithm which combines two powerful soft decision decoding techniques which
were previously regarded in the literature as competitive, namely, the
Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation
based on adaptive parity check matrices, recently proposed by Jiang and
Narayanan. Building on the Jiang-Narayanan algorithm, we present a
belief-propagation based algorithm with a significant reduction in
computational complexity. We introduce the concept of using a
belief-propagation based decoder to enhance the soft-input information prior to
decoding with an algebraic soft-decision decoder. Our algorithm can also be
viewed as an interpolation multiplicity assignment scheme for algebraic
soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200
On Scaling Rules for Energy of VLSI Polar Encoders and Decoders
It is shown that all polar encoding schemes of rate of block
length implemented according to the Thompson VLSI model must take energy
. This lower bound is achievable up to
polylogarithmic factors using a mesh network topology defined by Thompson and
the encoding algorithm defined by Arikan. A general class of circuits that
compute successive cancellation decoding adapted from Arikan's butterfly
network algorithm is defined. It is shown that such decoders implemented on a
rectangle grid for codes of rate must take energy
, and this can also be reached up to polylogarithmic
factors using a mesh network. Capacity approaching sequences of energy optimal
polar encoders and decoders, as a function of reciprocal gap to capacity , have energy that scales as
Computing coset leaders and leader codewords of binary codes
In this paper we use the Gr\"obner representation of a binary linear code
to give efficient algorithms for computing the whole set of coset
leaders, denoted by and the set of leader codewords,
denoted by . The first algorithm could be adapted to
provide not only the Newton and the covering radius of but also to
determine the coset leader weight distribution. Moreover, providing the set of
leader codewords we have a test-set for decoding by a gradient-like decoding
algorithm. Another contribution of this article is the relation stablished
between zero neighbours and leader codewords
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