Un code de permutations G(n,d) un sous-ensemble C de Sym(n) tel que la distance de Hamming D entre deux éléments de C est supérieure ou égale à d. Dans cette thèse, le groupe des isométries de (Sym(n),D) est déterminé et il est prouvé que ces isométries sont des automorphismes du schéma d'association induit sur Sym(n) par ses classes de conjugaison. Ceci mène, par programmation linéaire, à de nouveaux majorants de la taille maximale des G(n,d) pour n et d fixés et n compris entre 11 et 13. Des algorithmes de génération avec rejet d'objets isomorphes sont développés. Pour classer les G(n,d) non isométriques, des invariants ont été construits et leur efficacité étudiée. Tous les G(4,3) et les G(5,4) ont été engendrés à une isométrie près, il y en a respectivement 61 et 9445 (dont 139 sont maximaux et décrits explicitement). D’autres classes de G(n,d) sont étudiées. A permutation code G(n,d) is a subset C of Sym(n) such that the Hamming distance D between two elements of C is larger than or equal to d. In this thesis, we characterize the isometry group of the metric space (Sym(n),D) and we prove that these isometries are automorphisms of the association scheme induced on Sym(n) by the conjugacy classes. This leads, by linear programming, to new upper bounds for the maximal size of G(n,d) codes for n and d fixed and n between 11 and 13. We develop generating algorithms with rejection of isomorphic objects. In order to classify the G(n,d) codes up to isometry, we construct invariants and study their efficiency. We generate all G(4,3) and G(4,5)codes up to isometry; there are respectively 61 and 9445 of them. Precisely 139 out of the latter codes are maximal and explicitly described. We also study other classes of G(n,d)codes.

<p>The aim of source coding is to represent information as accurately as possible using as few bits as possible and in order to do so redundancy from the source needs to be removed. The aim of channel coding is in some sense the contrary, namely to introduce redundancy that can be exploited to protect the information when being transmitted over a nonideal channel. Combining these two techniques leads to the area of joint source–channel coding which in general makes it possible to achieve a better performance when designing a communication system than in the case when source and channel codes are designed separately. In this thesis two particular areas in joint source–channel coding are studied: multiple description coding (MDC) and soft decoding. Two new MDC schemes are proposed and investigated. The first is based on sorting a frame of samples and transmitting, as side-information/redundancy, an index that describes the resulting permutation. In case that some of the transmitted descriptors are lost during transmission this side information (if received) can be used to estimate the lost descriptors based on the received ones. The second scheme uses permutation codes to produce different descriptions of a block of source data. These descriptions can be used jointly to estimate the original source data. Finally, also the MDC method multiple description coding using pairwise correlating transforms as introduced by Wang et al is studied. A modification of the quantization in this method is proposed which yields a performance gain. A well known result in joint source–channel coding is that the performance of a communication system can be improved by using soft decoding of the channel output at the cost of a higher decoding complexity. An alternative to this is to quantize the soft information and store the pre-calculated soft decision values in a lookup table. In this thesis we propose new methods for quantizing soft channel information, to be used in conjunction with soft-decision source decoding. The issue on how to best construct finite-bandwidth representations of soft information is also studied.</p>

The aim of source coding is to represent information as accurately as possible using as few bits as possible and in order to do so redundancy from the source needs to be removed. The aim of channel coding is in some sense the contrary, namely to introduce redundancy that can be exploited to protect the information when being transmitted over a nonideal channel. Combining these two techniques leads to the area of joint source–channel coding which in general makes it possible to achieve a better performance when designing a communication system than in the case when source and channel codes are designed separately. In this thesis two particular areas in joint source–channel coding are studied: multiple description coding (MDC) and soft decoding. Two new MDC schemes are proposed and investigated. The first is based on sorting a frame of samples and transmitting, as side-information/redundancy, an index that describes the resulting permutation. In case that some of the transmitted descriptors are lost during transmission this side information (if received) can be used to estimate the lost descriptors based on the received ones. The second scheme uses permutation codes to produce different descriptions of a block of source data. These descriptions can be used jointly to estimate the original source data. Finally, also the MDC method multiple description coding using pairwise correlating transforms as introduced by Wang et al is studied. A modification of the quantization in this method is proposed which yields a performance gain. A well known result in joint source–channel coding is that the performance of a communication system can be improved by using soft decoding of the channel output at the cost of a higher decoding complexity. An alternative to this is to quantize the soft information and store the pre-calculated soft decision values in a lookup table. In this thesis we propose new methods for quantizing soft channel information, to be used in conjunction with soft-decision source decoding. The issue on how to best construct finite-bandwidth representations of soft information is also studied. / QC 20101124

[pt] Códigos de permutação são uma interessante ferramenta matemática que pode ser empregada para construir tanto esquemas de compressão com perdas quanto esquemas de modulação em um sistema de transmissão digital. Códigos de permutação vetorial, uma extensão mais poderosa dos códigos de permutação escalar, foram recentemente introduzidos no contexto de compressão de fontes. Este trabalho apresenta novas contribuições a essa teoria e introduz os códigos de permutação vetorial no contexto de modulação. Para compressão de fontes, é demonstrado matematicamente que os códigos de permutação vetorial (VPC) têm desempenho assintótico idêntico ao do quantizador vetorial com restrição de entropia (ECVQ). Baseado neste desenvolvimento, é proposto um método eficiente para o projeto de VPC s. O bom desempenho dos códigos projetados com esse método é verificado através de resultados experimentais para as fontes uniforme e gaussiana: são exibidos VPC s cujo desempenho é semelhante ao do ECVQ e superior ao de sua versão escalar. Para o propósito de transmissão digital, é verificado que também a modulação baseada em códigos de permutação vetorial (VPM) possui desempenho superior ao de sua versão escalar. São desenvolvidas as expressões para o projeto ótimo de VPM, e um método é apresentado para detecção ótima de VPM em canais AWGN e com desvanecimento. / [en] Permutation codes are an interesting mathematical tool which can be used to devise both lossy compression schemes and modulation schemes for digital transmission systems. Vector permutation codes, a more powerful extension of scalar permutation codes, were recently introduced for the purpose of source compression. This work presents new contributions to this theory and also introduces vector permutation codes for the purpose of modulation. For source compression, it is proved that vector permutation codes (VPC) have an asymptotical performance equal to that of an entropy-constrained vector quantizer (ECVQ). Based on this development, an efficient method is proposed for VPC design. Experimental results for Gaussian and uniform sources show that the codes designed by this method have indeed a good performance: VPC s are exhibited whose performances are similar to that of ECVQ and superior to those of their scalar counterparts. In the context of digital transmission, it is verified that also vector permutation modulation (VPM) is superior in performance to scalar permutation modulation. Expressions are developed for the optimal design of VPM, and a method is presented for maximum-likelihood detection of VPM in AWGN and fading channels.

<p>Un code de permutations G(n,d) un sous-ensemble C de Sym(n) tel que la distance de Hamming D entre deux éléments de C est supérieure ou égale à d. Dans cette thèse, le groupe des isométries de (Sym(n),D) est déterminé et il est prouvé que ces isométries sont des automorphismes du schéma d'association induit sur Sym(n) par ses classes de conjugaison. Ceci mène, par programmation linéaire, à de nouveaux majorants de la taille maximale des G(n,d) pour n et d fixés et n compris entre 11 et 13. Des algorithmes de génération avec rejet d'objets isomorphes sont développés. Pour classer les G(n,d) non isométriques, des invariants ont été construits et leur efficacité étudiée. Tous les G(4,3) et les G(5,4) ont été engendrés à une isométrie près, il y en a respectivement 61 et 9445 (dont 139 sont maximaux et décrits explicitement). D’autres classes de G(n,d) sont étudiées.<p><p><p><p> <p><p><p><p>A permutation code G(n,d) is a subset C of Sym(n) such that the Hamming distance D between two elements of C is larger than or equal to d. In this thesis, we characterize the isometry group of the metric space (Sym(n),D) and we prove that these isometries are automorphisms of the association scheme induced on Sym(n) by the conjugacy classes. This leads, by linear programming, to new upper bounds for the maximal size of G(n,d) codes for n and d fixed and n between 11 and 13. We develop generating algorithms with rejection of isomorphic objects. In order to classify the G(n,d) codes up to isometry, we construct invariants and study their efficiency. We generate all G(4,3) and G(4,5)codes up to isometry; there are respectively 61 and 9445 of them. Precisely 139 out of the latter codes are maximal and explicitly described. We also study other classes of G(n,d)codes.<p><p><p><p> / Doctorat en sciences, Spécialisation mathématiques / info:eu-repo/semantics/nonPublished