814 research outputs found
On the Computing of the Minimum Distance of Linear Block Codes by Heuristic Methods
The evaluation of the minimum distance of linear block codes remains an open
problem in coding theory, and it is not easy to determine its true value by
classical methods, for this reason the problem has been solved in the
literature with heuristic techniques such as genetic algorithms and local
search algorithms. In this paper we propose two approaches to attack the
hardness of this problem. The first approach is based on genetic algorithms and
it yield to good results comparing to another work based also on genetic
algorithms. The second approach is based on a new randomized algorithm which we
call Multiple Impulse Method MIM, where the principle is to search codewords
locally around the all-zero codeword perturbed by a minimum level of noise,
anticipating that the resultant nearest nonzero codewords will most likely
contain the minimum Hamming-weight codeword whose Hamming weight is equal to
the minimum distance of the linear code
Efficient Maximum-Likelihood Soft-Decision Decoding of Linear Block Codes Using Algorithm A
In this report we present a novel and efficient maximum-likelihood soft-decision decoding algorithm for linear block codes. The approach used here is to convert the decoding problem into a search problem through a graph which is a trellis for an equivalent code of the transmitted code. Algorithm A*, which uses a priority-first search strategy, is employed to search through this graph. This search is guided by an evaluation function f defined to take advantage of the information provided by the received vector and the inherent properties of the transmitted code. This function f is used to drastically reduce the search space and to make the decoding efforts of this decoding algorithm adaptable to the noise level. Simulation results for the ( 48, 24) and the (72, 36) binary extended quadratic residue codes and the (128, 64) binary extended BCH code are given to substantiate the above claim
Constructions of Rank Modulation Codes
Rank modulation is a way of encoding information to correct errors in flash
memory devices as well as impulse noise in transmission lines. Modeling rank
modulation involves construction of packings of the space of permutations
equipped with the Kendall tau distance.
We present several general constructions of codes in permutations that cover
a broad range of code parameters. In particular, we show a number of ways in
which conventional error-correcting codes can be modified to correct errors in
the Kendall space. Codes that we construct afford simple encoding and decoding
algorithms of essentially the same complexity as required to correct errors in
the Hamming metric. For instance, from binary BCH codes we obtain codes
correcting Kendall errors in memory cells that support the order of
messages, for any constant We also construct
families of codes that correct a number of errors that grows with at
varying rates, from to . One of our constructions
gives rise to a family of rank modulation codes for which the trade-off between
the number of messages and the number of correctable Kendall errors approaches
the optimal scaling rate. Finally, we list a number of possibilities for
constructing codes of finite length, and give examples of rank modulation codes
with specific parameters.Comment: Submitted to IEEE Transactions on Information Theor
Design of tch-type sequences for communications
This thesis deals with the design of a class of cyclic codes inspired by TCH codewords.
Since TCH codes are linked to finite fields the fundamental concepts and facts about abstract
algebra, namely group theory and number theory, constitute the first part of the thesis.
By exploring group geometric properties and identifying an equivalence between some operations
on codes and the symmetries of the dihedral group we were able to simplify the generation
of codewords thus saving on the necessary number of computations. Moreover, we
also presented an algebraic method to obtain binary generalized TCH codewords of length
N = 2k, k = 1,2, . . . , 16. By exploring Zech logarithm’s properties as well as a group theoretic
isomorphism we developed a method that is both faster and less complex than what was
proposed before. In addition, it is valid for all relevant cases relating the codeword length N
and not only those resulting from N = p
Loss-resilient Coding of Texture and Depth for Free-viewpoint Video Conferencing
Free-viewpoint video conferencing allows a participant to observe the remote
3D scene from any freely chosen viewpoint. An intermediate virtual viewpoint
image is commonly synthesized using two pairs of transmitted texture and depth
maps from two neighboring captured viewpoints via depth-image-based rendering
(DIBR). To maintain high quality of synthesized images, it is imperative to
contain the adverse effects of network packet losses that may arise during
texture and depth video transmission. Towards this end, we develop an
integrated approach that exploits the representation redundancy inherent in the
multiple streamed videos a voxel in the 3D scene visible to two captured views
is sampled and coded twice in the two views. In particular, at the receiver we
first develop an error concealment strategy that adaptively blends
corresponding pixels in the two captured views during DIBR, so that pixels from
the more reliable transmitted view are weighted more heavily. We then couple it
with a sender-side optimization of reference picture selection (RPS) during
real-time video coding, so that blocks containing samples of voxels that are
visible in both views are more error-resiliently coded in one view only, given
adaptive blending will erase errors in the other view. Further, synthesized
view distortion sensitivities to texture versus depth errors are analyzed, so
that relative importance of texture and depth code blocks can be computed for
system-wide RPS optimization. Experimental results show that the proposed
scheme can outperform the use of a traditional feedback channel by up to 0.82
dB on average at 8% packet loss rate, and by as much as 3 dB for particular
frames
A STUDY OF LINEAR ERROR CORRECTING CODES
Since Shannon's ground-breaking work in 1948, there have been two main development streams
of channel coding in approaching the limit of communication channels, namely classical coding
theory which aims at designing codes with large minimum Hamming distance and probabilistic
coding which places the emphasis on low complexity probabilistic decoding using long codes built
from simple constituent codes. This work presents some further investigations in these two channel
coding development streams.
Low-density parity-check (LDPC) codes form a class of capacity-approaching codes with sparse
parity-check matrix and low-complexity decoder Two novel methods of constructing algebraic binary
LDPC codes are presented. These methods are based on the theory of cyclotomic cosets, idempotents
and Mattson-Solomon polynomials, and are complementary to each other. The two methods
generate in addition to some new cyclic iteratively decodable codes, the well-known Euclidean and
projective geometry codes. Their extension to non binary fields is shown to be straightforward.
These algebraic cyclic LDPC codes, for short block lengths, converge considerably well under iterative
decoding. It is also shown that for some of these codes, maximum likelihood performance may
be achieved by a modified belief propagation decoder which uses a different subset of 7^ codewords
of the dual code for each iteration.
Following a property of the revolving-door combination generator, multi-threaded minimum
Hamming distance computation algorithms are developed. Using these algorithms, the previously
unknown, minimum Hamming distance of the quadratic residue code for prime 199 has been evaluated.
In addition, the highest minimum Hamming distance attainable by all binary cyclic codes
of odd lengths from 129 to 189 has been determined, and as many as 901 new binary linear codes
which have higher minimum Hamming distance than the previously considered best known linear
code have been found.
It is shown that by exploiting the structure of circulant matrices, the number of codewords
required, to compute the minimum Hamming distance and the number of codewords of a given
Hamming weight of binary double-circulant codes based on primes, may be reduced. A means
of independently verifying the exhaustively computed number of codewords of a given Hamming
weight of these double-circulant codes is developed and in coiyunction with this, it is proved that
some published results are incorrect and the correct weight spectra are presented. Moreover, it is
shown that it is possible to estimate the minimum Hamming distance of this family of prime-based
double-circulant codes.
It is shown that linear codes may be efficiently decoded using the incremental correlation Dorsch
algorithm. By extending this algorithm, a list decoder is derived and a novel, CRC-less error detection
mechanism that offers much better throughput and performance than the conventional ORG
scheme is described. Using the same method it is shown that the performance of conventional CRC
scheme may be considerably enhanced. Error detection is an integral part of an incremental redundancy
communications system and it is shown that sequences of good error correction codes,
suitable for use in incremental redundancy communications systems may be obtained using the
Constructions X and XX. Examples are given and their performances presented in comparison to
conventional CRC schemes
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm
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