Cyclic spot-error-correcting codes.

Vita.

(v, k, λ) Configurations and self-dual codes

The incidence matrix of a (v, k, λ) configuration is used to construct a (2v, v) and a (2v + 2, v + 1) self-dual code. If the incidence matrix is a circulant, the codes obtained are quasi-cyclic and extended quasi-cyclic, respectively. The weight distributions of some codes of this type are obtained.

On the Successive Refinability of MIMO channels: DMT and codes

Diversity embedded space time codes are high rate codes that are designed such that they have a high diversity code embedded within them. A recent work by Diggavi and Tse characterizes the performance limits that can be achieved by diversity embedded space-time codes in terms of the achievable Diversity Multiplexing Tradeoff (DMT). In particular, they have shown that the trade off is successively refinable for rayleigh fading channels with one degree of freedom using superposition coding and Successive Interference Cancellation (SIC). However, for Multiple-Input Multiple-Output (MIMO) channels, the questions of successive refinability remains open. We consider MIMO Channels under superposition coding and SIC. We derive an upper bound on the successive refinement characteristics of the DMT. We then construct explicit space time codes that achieve the derived upper bound. These codes, constructed from cyclic division algebras, have minimal delay. Our results establish that when the channel has more than one degree of freedom, the DMT is not successive refinable using superposition coding and SIC. The channels considered in this work can have arbitrary fading statistics.

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Generalized distributive law for ML decoding of space-time block codes

The problem of designing good space-time block codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well-known technique of decoding STBCs as conditional ML (CML) decoding. In this paper, we introduce a new framework to construct ML decoders for STBCs based on the generalized distributive law (GDL) and the factor-graph-based sum-product algorithm. We say that an STBC is fast GDL decodable if the order of GDL decoding complexity of the code, with respect to the constellation size, is strictly less than M-lambda, where lambda is the number of independent symbols in the STBC. We give sufficient conditions for an STBC to admit fast GDL decoding, and show that both multigroup and conditionally multigroup decodable codes are fast GDL decodable. For any STBC, whether fast GDL decodable or not, we show that the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable, the GDL decoder provides about 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only half as complex as the CML decoder.

Characterisation of the cyclic behaviour of reinforced concrete elements with plain bars

Sismos recentes comprovam a elevada vulnerabilidade dos edifícios existentes de betão armado. A resposta das estruturas aos sismos é fortemente condicionada pelas características da aderência aço-betão, que exibe degradação das propriedades iniciais quando sujeitas a carregamentos cíclicos e alternados. Este fenómeno é ainda mais gravoso para elementos com armadura lisa, predominantes na maioria das estruturas construídas até à década de 70 nos países do sul da Europa. A prática corrente de conceção, dimensionamento e pormenorização das estruturas antigas leva a que tenham características de comportamento e níveis de segurança associados não compatíveis com as exigências atuais. Os estudos realizados sobre o comportamento cíclico de elementos estruturais de betão armado com armadura lisa são ainda insuficientes para a completa caracterização deste tipo de elementos. Esta tese visou a caraterização da relação tensão de aderência versus escorregamento para elementos estruturais com armadura lisa e o estudo da resposta cíclica de pilares e nós viga-pilar de betão armado com armadura lisa. Foram realizados dez séries de ensaios de arrancamento (nove monotónicos e um cíclico) em provetes com varões lisos. Os resultados destes ensaios permitiram propor novas expressões empíricas para a estimativa dos parâmetros usados num modelo disponível na literatura para representação da relação tensão de aderência versus escorregamento. É ainda proposto um novo modelo monotónico para a relação tensão de aderência versus escorregamento que representa melhor a resposta após a resistência máxima de aderência. Uma campanha de ensaios unidirecionais em pilares e nós viga-pilar foi também realizada com o objetivo principal de caracterizar o comportamento cíclico deste tipo de elementos. No total foram realizados oito ensaios em pilares, sete ensaios em nós viga-pilar interiores e seis ensaios em nós viga-pilar exteriores representativos de estruturas antigas de betão armado com armadura lisa. Os resultados experimentais permitiram avaliar a influência do escorregamento e estudar o mecanismo de corte em nós e a evolução dos danos para elementos com armadura lisa. Com base nos resultados experimentais foi proposta uma adaptação na expressão do Eurocódigo 8-3 para o cálculo da capacidade última de rotação de elementos com armadura lisa. Foi também desenvolvido um estudo paramétrico, com diferentes estratégias de modelação não linear, para a simulação da resposta de pilares considerando o escorregamento da armadura lisa. Por último, foi proposto um novo modelo simplificado trilinear para o aço que contempla o efeito do escorregamento da armadura lisa.

The symmetry group of Z(q)(n) in the Lee space and the Z(qn)-linear codes

The Z(4)-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the Z(4)-linearity to Z(q)n-linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (Z(q)(n), d(L)), as one of the most interesting spaces for coding applications. We establish the symmetry group of Z(q)(n) for any n and q by determining its isometries. We also show that there is no cyclic subgroup of order q(n) in Gamma(Z(q)(n)) acting transitively in Z(q)(n). Therefore, there exists no Z(q)n-linear code with respect to the cyclic subgroup.

On the construction of perfect codes from HEX signal constellations

Recently, minimum and non-minimum delay perfect codes were proposed for any channel of dimension n. Their construction appears in the literature as a subset of cyclic division algebras over Q(zeta(3)) only for the dimension n = 2(s)n(1), where s is an element of {0,1}, n(1) is odd and the signal constellations are isomorphic to Z[zeta(3)](n) In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over Q(zeta(3)), where the signal constellations are isomorphic to the hexagonal A(2)(n)-rotated lattice, for any channel of any dimension n such that gcd(n,3) = 1. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Construction of perfect space-time codes

In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over ℚ(ζ3), where the signal constellations are isomorphic to the hexagonal An 2 -rotated lattice, for any channel of any dimension n such that gcd{n, 3) = 1.

A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Linear codes over finite local rings in a chain

For a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) & \subseteq & (\mathcal{A},\mathcal{M}) \\ \cap & & \cap & & & & \cap & & \cap \\ (\mathcal{R}_{0},\mathcal{M}_{0}^{2}) & & (\mathcal{R}_{1},\mathcal{M}_{1}^{2}) & & & & (\mathcal{R}_{t-1},\mathcal{M}_{t-1}^{2}) & & (\mathcal{R},\mathcal{M}^{2}) \end{array} \end{equation*} be a chain of unitary local commutative rings $(\mathcal{A}_{i},\mathcal{M}_{i})$ with their corresponding Galois ring extensions $(\mathcal{R}_{i},\mathcal{M}_{i}^{2})$, for $i=0,1,\cdots,t$. In this paper, we have given a construction technique of the cyclic, BCH, alternant, Goppa and Srivastava codes over these rings. Though, initially in \cite{AP} it is for local ring $(\mathcal{A},\mathcal{M})$, in this paper, this new approach have given a choice in selection of most suitable code in error corrections and code rate perspectives.

On the Weight Distribution of the Coset Leaders of Constacyclic Codes

Constacyclic codes with one and the same generator polynomial and distinct length are considered. We give a generalization of the previous result of the first author [4] for constacyclic codes. Suitable maps between vector spaces determined by the lengths of the codes are applied. It is proven that the weight distributions of the coset leaders don’t depend on the word length, but on generator polynomials only. In particular, we prove that every constacyclic code has the same weight distribution of the coset leaders as a suitable cyclic code.

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.

On MDS convolutional codes over Z_p^r

Maximum distance separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in Oued and Sole (IEEE Trans Inf Theory 59(11):7305–7313, 2013) via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Zpr from a new perspective. We introduce the notions of p-standard form and r-optimal parameters to derive a novel upper bound of Singleton type on the free distance. Moreover, we present a constructive method for building general (non necessarily free) MDS convolutional codes over Zpr for any given set of parameters.