Chained Successive Cancellation Decoding of the Extended Golay code

The extended Golay code is shown to be representable as a chained polar subcode. This enables its decoding with the successive cancellation algorithm and its stack generalization. The decoder can be further simplified by employing fast Hadamard transform. The complexity of the obtained algorithm is comparable with that of the Vardy algorithm

On maximal cliques in the graph of simplex codes

The induced subgraph of the corresponding Grassmann graph formed by simplex codes is considered. We show that this graph, as the Grassmann graph, contains two types of maximal cliques. For any two cliques of the first type there is a monomial linear automorphism transferring one of them to the other. Cliques of the second type are more complicated and can contain different numbers of elements

Algebraic Properties of Polar Codes From a New Polynomial Formalism

Polar codes form a very powerful family of codes with a low complexity decoding algorithm that attain many information theoretic limits in error correction and source coding. These codes are closely related to Reed-Muller codes because both can be described with the same algebraic formalism, namely they are generated by evaluations of monomials. However, finding the right set of generating monomials for a polar code which optimises the decoding performances is a hard task and channel dependent. The purpose of this paper is to reveal some universal properties of these monomials. We will namely prove that there is a way to define a nontrivial (partial) order on monomials so that the monomials generating a polar code devised fo a binary-input symmetric channel always form a decreasing set. This property turns out to have rather deep consequences on the structure of the polar code. Indeed, the permutation group of a decreasing monomial code contains a large group called lower triangular affine group. Furthermore, the codewords of minimum weight correspond exactly to the orbits of the minimum weight codewords that are obtained from (evaluations) of monomials of the generating set. In particular, it gives an efficient way of counting the number of minimum weight codewords of a decreasing monomial code and henceforth of a polar code.Comment: 14 pages * A reference to the work of Bernhard Geiger has been added (arXiv:1506.05231) * Lemma 3 has been changed a little bit in order to prove that Proposition 7.1 in arXiv:1506.05231 holds for any binary input symmetric channe

A characterization of MDS codes that have an error correcting pair

Error-correcting pairs were introduced in 1988 by R. Pellikaan, and were found independently by R. K\"otter (1992), as a general algebraic method of decoding linear codes. These pairs exist for several classes of codes. However little or no study has been made for characterizing those codes. This article is an attempt to fill the vacuum left by the literature concerning this subject. Since every linear code is contained in an MDS code of the same minimum distance over some finite field extension we have focused our study on the class of MDS codes. Our main result states that an MDS code of minimum distance $2t+1$ has a $t$-ECP if and only if it is a generalized Reed-Solomon code. A second proof is given using recent results Mirandola and Z\'emor (2015) on the Schur product of codes

Multiuser non coherent massive MIMO schemes based on DPSK for future communication systems

The explosive usage of rich multimedia content in wireless devices has overloaded the communication networks. Moreover, the fifth generation (5G) of wireless communications involves new requirements in the radio access network (RAN) which require higher network capacities and new capabilities such as ultra-reliable and low-latency communication (URLLC), vehicular communications or augmented reality. All this has encouraged a remarkable spectrum crisis in the RF bands. A need for searching alternative techniques with more spectral efficiency to accommodate the needs of future emerging wireless communications is emerging. In this context, massive MIMO (m-MIMO) systems have been proposed as a promising solution for providing a substantial increase in the network capacity, becoming one of the key enabling technologies for 5G and beyond. m-MIMO provides high spectral- and energy-efficiency thanks to the deployment of a large number of antennas at the BS. However, we have to take into account that the current communication technologies are based on coherent transmission techniques so far, which require the transmission of a huge amount of signaling. This drawback is escalating with the excessive available number of antennas in m-MIMO. Therefore, the differential encoding and non coherent (NC) detection are an alternative solution to circumvent the drawbacks of m-MIMO in coherent systems. This Ph.D. Thesis is focused on signal processing techniques for NC detection in conjunction with m-MIMO, proposing new constellation designs and NC detection algorithms, where the information is transmitted in the signal differential phase. First, we design new constellation schemes for an uplink multiuser NC m-MIMO system in Rayleigh fading channels. These designs allow us to separate the users' signals at the receiver thanks to a one-to-one correspondence between the constellation for each user and the received joint constellation. Two approaches are considered in terms of BER: each user achieves a different performance and, on the other hand, the same performance is provided for all users. We analyze the number of antennas needed for those designs and compare to the required number by other designs in the literature. It is shown that our designs based on DPSK require a lower number of antennas than that required by their counterpart schemes based on energy. In addition, we compare the performance to their coherent counterpart systems, resulting NC-m-MIMO based on DPSK capable of outperforming the coherent systems with the suitable designs. Second, in order to reduce the number of antennas required for a target performance we propose a multi-user bit interleaved coded modulation - iterative decoding (BICM-ID) scheme as channel coding for a NC-m-MIMO system based on DPSK. We propose a novel NC approach for calculating EXIT curves based on the number of antennas. Then using the EXIT chart we find the best channel coding scheme for our NC-m-MIMO proposal. We show that the number of users served by the BS can be increased with a 70% reduction in the number of antennas with respect to the case without channel coding. In particular, we show that with 100 antennas for error protection equal design for all users and a coding rate of 1/2 we achieve the minimum probability of error. Third, we consider that current scenarios such as backhaul wireless systems, rural or suburban environments, and even new device-to-device (D2D) communications or the communications in higher frequencies (millimeter and the emerging ones in terahertz frequencies) can have a predominant line-of-sight (LOS) component, modeled by Rician fading. For all these new possible scenarios in 5G, we analyze the behavior of the NC m-MIMO systems when we have a Rician fading. We present a new constellation design to overcome the problem of the LOS channel component, as well as an associated detection algorithm to separate each user in reception taking into account the characterization of the constellation. In addition, for contemplating a more realistic scenario, we propose grouping users which experience a Rayleigh fading with those with Rician fading, analyzing the SINR and the performance of such combination in a multi-user NC m-MIMO system based on M-DPSK. The adequate user grouping allows unifying the constellation for both groups of users and the detection algorithm, reducing the complexity of the receiver. Also, the number of users that may be multiplexed may be further increased thanks to the improved performance. In the fourth part of this Thesis, we analyse the performance of multi-user NC m- MIMO based on DPSK in real environments and practical channels defined for the current standards such as LTE, the future technologies such as 5G and even for communications in the terahertz band. For this purpose, we use a metric to model the time-varying characteristics of the practical channels. We employ again the EXIT charts tool for analyzing and designing iteratively decoded systems. This analysis allows us to obtain an estimate of the degradation of the system's performance imposed by realistic channels. Hence, we show that our proposed system is robust to temporal variations, thus it is more recommendable the employment of NC-m-MIMO-DPSK in the future communication standards such as 5G. In order to reduce he number of hardware resources required in terms of RF chains, facilitating its implementation in a real system, we propose incorporating differential spatial modulation (DSM). We present and analyze a novel multiuser scheme for NC-m-MIMO combined with DSM with which we can see that the number of antennas is not a affected by the incorporation of DSM, even we have an improvement on the performance with respect to the coherent case. Finally, we study the viability of multiplexing users by constellation schemes against classical multiplexing techniques such as time division multiple access (TDMA). In order to fully characterize the system performance we analyze the block error rate (BLER) and the throughput of a NC-m-MIMO system. The results show a significant advantage regarding the number of antennas for multiplexing in the constellation against TDMA. However, in some cases, the demodulation of multiple users in constellation could require an excessively large number of antennas compared to TDMA. Therefore, it is necessary to properly manage the tradeoff between throughout and the number of antennas, to reach an optimal operational point, as shown in this Thesis.El inmenso uso de contenido multimedia en los dispositivos inalámbricos ha sobrecargado las redes de comunicaciones. Además, la quinta generación (5G) de sistemas de comunicaciones demanda nuevos requisitos para la red de acceso radio, la cual requiere ofrecer capacidades de red mayores y nuevas funcionalidades como comunicaciones ultra fiables y con muy poca letancia (URLLC), comunicaciones vehiculares o aplicaciones como la realidad aumentada. Todo esto ha propiciado una crisis notable en el espectro electromagnético, lo que ha llevado a una necesidad por buscar técnicas alternativas con más eficiencia espectral para acomodar todos los requisitos de las tecnologías de comunicaciones emergentes y futuras. En este contexto, los sistemas multi antena masivos, conocidos como massive MIMO, m-MIMO, han sido propuestos como una solución prometedora que proporciona un incremento substancial de la capacidad de red, convirtiéndose en una de las tecnologías claves para el 5G. Los sistemas m-MIMO elevan enormemente el número de antenas en la estación base, lo que les permite ofrecer alta eficiencia espectral y energética. No obstante, tenemos que tener en cuenta que las actuales tecnologías de comunicaciones emplean técnicas coherentes, las cuales requieren de información del estado del canal y por ello la transmisión de una enorme cantidad de información de señalización. Este inconveniente se ve agravado en el caso del m-MIMO debido al enorme número de antenas. Por ello, la codificación diferencial y la detección no coherente (NC) son una solución alternativa para solventar el problema de m-MIMO en los sistemas coherentes. Esta Tesis se centra en las técnicas de procesado de señal para detección NC junto con m-MIMO, proponiendo nuevos esquemas de constelación y algoritmos de detección NC, donde la información sea transmitida en la diferencia de fase de la señal. Primero, diseñamos nuevas constelaciones para un sistema multi usuario NC en m- MIMO en enlace ascendente (uplink) en canales con desvanecimiento tipo Rayleigh. Estos diseños nos permiten separar las señales de los usuarios en el receptor gracias a la correspondencia unívoca entre la constelación de cada usuario individual y la constelación conjunta recibida en la estación base. Hemos considerado dos enfoques para el diseño en términos de probabilidad de error: cada usuario consigue un rendimiento distinto, mientras que por otro lado, todos los usuarios son capaces de recibir las mismas prestaciones de probabilidad de error. Analizamos el número de antenas necesario para estos diseños y comparamos con el número requerido por otros diseños propuestos en la literatura. Nuestro diseño basado en DPSK requiere un número menor de antenas comparado con los sistemas basados en detección de energía. También comparamos con su homólogo coherente, resultando que NC-m-MIMO basado en DPSK es capaz de superar a los sistemas coherentes con los diseños adecuados. En segundo lugar, para reducir el número de antenas requerido para un rendimiento dado, proponemos incluir un esquema de codificación de canal. Hemos optado por un esquema de modulación codificado por bit entrelazado y decodificación iterativa (BICMID). Hemos empleado la herramienta EXIT chart para el diseño de la codificación de canal, proponiendo un nuevo enfoque para calcular las curvas EXIT de forma NC y basadas en el número de antenas. Los resultados muestran que el número de usuarios servidos por la estación base puede ser incrementado reduciendo un 70% el número de antenas con respecto al caso sin codificación de canal. En particular, para un array de 100 antenas y un diseño que ofrezca iguales prestaciones a todos los usuarios, con un código de tasa 1=2, podemos conseguir la mínima probabilidad de error. En tercer lugar, consideramos escenarios donde el canal tenga una componente predominante de visión directa (LOS) con la estación base modelada mediante un desvanecimiento tipo Rician. Por ejemplo, sistemas inalámbricos de backhaul, entornos rurales o sub urbanos, comunicaciones entre dispositivos (D2D), también cuando nos movemos hacia frecuencias superiores como son en la banda de milimétricas o más recientemente, la banda de terahercios para buscar mayores anchos de banda. Todos estos escenarios están contemplados en el futuro 5G. Los diseños presentados para canales Rayleigh ya no son válidos debido a la componente LOS del canal, por ello presentamos un nuevo diseño de constelación que resuelve el problema de la componente LOS, así como una guía para diseñar nuevas constelaciones. También proponemos un algoritmo asociado al diseñno de la constelación para poder separar a los usuarios en recepción. Además, para contemplar un escenario más realista donde podamos encontrar tanto desvanecimiento Rayleigh como Rice, proponemos agrupar usuarios de ambos grupos, analizando su rendimiento y relación señal a interferencia en la combinación. El adecuado agrupamiento permite unificar el diseño de la constelación para ambos desvanecimientos y por tanto reducir la complejidad en el receptor. También, el número de usuarios multiplicados en la constelación podría ser incrementado, gracias a la mejora en el rendimiento. El cuarto módulo de esta tesis es dedicado a analizar el rendimiento de los diseños propuestos en presencia de canales reales, donde disponemos de variabilidad temporal y en frecuencia. Proponemos usar una métrica que modela las características de la variabilidad temporal y, usando de nuevo la herramienta EXIT, analizamos los sistemas decodificados iterativamente considerando ahora los parámetros prácticos del canal. Este análisis nos permite obtener una estimación de la degradación que sufre el rendimiento del sistema impuesto por canales reales. Los resultados muestran que los sistemas NC-m-MIMO basados en DPSK son muy robustos a la variabilidad temporal por lo que son recomendables para los nuevos escenarios propuestos por el 5G, donde el canal cambia rápidamente. Otra consideración para introducir los sistemas NC con m-MIMO es la problemática de necesitar muchas cadenas de radio frecuencia que llevarían a tamaños de dispositivos enormes. Para reducir este número se propone la modulación espacial. En esta Tesis, estudiamos su uso con los sistemas NC, proponiendo una solución de modulación espacial diferencial para esquemas con múltiples usuarios combinado con NC-m-MIMO. Finalmente, estudiamos la viabilidad de multiplexar usuarios en la constelación frente a usar técnicas clásicas de multiplexación como TDMA. Para caracterizar completamente el rendimiento del sistema, analizamos la tasa de error de bloque (BLER) y el throughput de un sistema NC-m-MIMO. Los resultados muestran una ventaja significativa en cuanto al número de antennas para multiplexar usuarios en la constelación frente al requerido por TDMA. No obstante, en algunos casos, la demodulación de múltiples usuarios en la constelación podría requerir un número de antennas excesivamente grande comparado con la multiplexación en el tiempo. Por ello, es necesario gestionar adecuadamente un balance entre el throughput y el número de antenas para alcanzar un punto operacional óptimo, como se muestra en esta Tesis.Programa Oficial de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ana Isabel Pérez Neira.- Secretario: Máximo Morales Céspedes.- Vocal: María del Carmen Aguayo Torre

HARLEY QUINN COMICS AND ADOLESCENT FEMALE READERS: AN ANALYSIS OF GENDER REPRESENTATION AND INTERPRETATION

With roots that can be traced back to the pulp and dime novels of the past, comics are a uniquely American creation that interconnect word with image and allow for multiple ways of reading and interpreting, which results in multiple ways of knowing and understanding. As comics continue to grow in popularity in mainstream culture, it is important to consider the messages being interpreted from these texts by readers. This qualitative study explored how female adolescent readers experience and understand their gender through the comics of the popular character Harley Quinn (of DC Comics) and how Quinn is seen as performing gender within her stories. Using the lenses of critical literacy, feminism, and transactional theory, this investigation was conducted using content analysis of texts and language-in-use analysis of transcripts from interviews and a readers response meeting with five adolescent females. The data collected indicated gender to be more influential on Quinn’s characterization and storylines than anything else, including her superpowered nature; and participants saw Quinn as enacting the socially recognizable identity of “American Female.” Overall, the results showed Quinn to be more in alignment with cultural gender norms than not and, thus, she reinforced existing hegemonic patriarchal narratives seen in comics. It is only through recognition and knowledge of what exists in comic texts that readers can demand changes with these narratives and promote gender equity