29,015 research outputs found
Trellis decoding complexity of linear block codes
In this partially tutorial paper, we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity: maximum state and edge dimensions, total span length, and total vertices, edges and mergers. We obtain bounds on these complexities as extensions of well-known dimension/length profile (DLP) bounds. Codes meeting these bounds minimize all the complexity measures simultaneously; conversely, a code attaining the bound for total span length, vertices, or edges, must likewise attain it for all the others. We define a notion of âuniformâ optimality that embraces different domains of optimization, such as different permutations of a code or different codes with the same parameters, and we give examples of uniformly optimal codes and permutations. We also give some conditions that identify certain cases when no code or permutation can meet the bounds. In addition to DLP-based bounds, we derive new inequalities relating one complexity measure to another, which can be used in conjunction with known bounds on one measure to imply bounds on the others. As an application, we infer new bounds on maximum state and edge complexity and on total vertices and edges from bounds on span lengths
Constructions of Generalized Concatenated Codes and Their Trellis-Based Decoding Complexity
In this correspondence, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis omplexity than Euclidean geometry (EG), ReedâMuller (RM), or BoseâChaudhuriâHocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to their minimum distances. Several codes of the same length, dimension, and minimum distance as the best linear codes known are constructed
PyMorph: Automated Galaxy Structural Parameter Estimation using Python
We present a new software pipeline -- PyMorph -- for automated estimation of
structural parameters of galaxies. Both parametric fits through a two
dimensional bulge disk decomposition as well as structural parameter
measurements like concentration, asymmetry etc. are supported. The pipeline is
designed to be easy to use yet flexible; individual software modules can be
replaced with ease. A find-and-fit mode is available so that all galaxies in a
image can be measured with a simple command. A parallel version of the Pymorph
pipeline runs on computer clusters and a Virtual Observatory compatible web
enabled interface is under development.Comment: 15 pages, 12 figures, 1 table, accepted for publication in MNRA
Precoding for Outage Probability Minimization on Block Fading Channels
The outage probability limit is a fundamental and achievable lower bound on
the word error rate of coded communication systems affected by fading. This
limit is mainly determined by two parameters: the diversity order and the
coding gain. With linear precoding, full diversity on a block fading channel
can be achieved without error-correcting code. However, the effect of precoding
on the coding gain is not well known, mainly due to the complicated expression
of the outage probability. Using a geometric approach, this paper establishes
simple upper bounds on the outage probability, the minimization of which yields
to precoding matrices that achieve very good performance. For discrete
alphabets, it is shown that the combination of constellation expansion and
precoding is sufficient to closely approach the minimum possible outage
achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing
the coding gain.Comment: Submitted to Transactions on Information Theory on March 23, 201
Higher Hamming weights for locally recoverable codes on algebraic curves
We study the locally recoverable codes on algebraic curves. In the first part
of this article, we provide a bound of generalized Hamming weight of these
codes. Whereas in the second part, we propose a new family of algebraic
geometric LRC codes, that are LRC codes from Norm-Trace curve. Finally, using
some properties of Hermitian codes, we improve the bounds of distance proposed
in [1] for some Hermitian LRC codes.
[1] A. Barg, I. Tamo, and S. Vlladut. Locally recoverable codes on algebraic
curves. arXiv preprint arXiv:1501.04904, 2015
Self-dual codes, subcode structures, and applications.
The classification of self-dual codes has been an extremely active area in coding theory since 1972 [33]. A particularly interesting class of self-dual codes is those of Type II which have high minimum distance (called extremal or near-extremal). It is notable that this class of codes contains famous unique codes: the extended Hamming [8,4,4] code, the extended Golay [24,12,8] code, and the extended quadratic residue [48,24,12] code. We examine the subcode structures of Type II codes for lengths up to 24, extremal Type II codes of length 32, and give partial results on the extended quadratic residue [48,24,12] code. We also develop a generalization of self-dual codes to Network Coding Theory and give some results on existence of self-dual network codes with largest minimum distance for lengths up to 10. Complementary Information Set (CIS for short) codes, a class of classical codes recently developed in [7], have important applications to Cryptography. CIS codes contain self-dual codes as a subclass. We give a new classification result for CIS codes of length 14 and a partial result for length 16
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