Low-Complexity Puncturing and Shortening of Polar Codes

In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique, low-complexity construction encompassing both techniques in order to achieve any code length and rate. We observe that our solution significantly reduces the construction complexity as compared to state-of-the-art solutions while providing a block error rate performance comparable to constructions that are highly optimized for specific lengths and rates. This makes the constructed polar codes highly suitable for practical application in future communication systems requiring a large set of polar codes with different lengths and rates.Comment: to appear in WCNC 2017 - "Polar Coding in Wireless Communications: Theory and Implementation" Worksho

Polar codes combined with physical layer security on impulsive noise channels

Ph. D. ThesisThe need for secure communications is becoming more and more impor- tant in modern society as wired and wireless connectivity becomes more ubiquitous. Currently, security is achieved by using well established encryption techniques in the upper layers that rely on computational complexity to ensure security. However, processing power is continu- ally increasing and well-known encryption schemes are more likely to be cracked. An alternative approach to achieving secure communication is to exploit the properties of the communication channel. This is known as physical layer security and is mathematically proven to be secure. Phys- ical layer security is an active research area, with a significant amount of literature covering many different aspects. However, one issue that does not appear to have been investigated in the literature is the effect on physical layer security when the noise in the communication channel is impulsive. Impulsive noise adds large spikes to the transmitted signal for very short durations that can significantly degrade the signal. The main source of impulsive noise in wireless communications is electromag- netic interference generated by machinery. Therefore, this project will investigate the effect of impulsive noise on physical layer security. To ensure a high level of performance, advanced error-correcting codes are needed to correct the multiple errors due to this harsh channel. Turbo and Low-Density Parity-Check (LDPC) codes are capacity-approaching codes commonly used in current wireless communication standards, but their complexity and latency can be quite high and can be a limiting fac- tor when required very high data rates. An alternative error-correcting code is the polar code, which can actually achieve the Shannon capacity on any symmetric binary input discrete memoryless channel (B-DMC). Furthermore, the complexity of polar codes is low and this makes them an attractive error-correcting code for high data rate wireless commu- nications. In this project, polar codes are combined with physical layer security and the performance and security of the system is evaluated on impulsive noise channels for the first time. This project has three contributions: Polar codes designed for impulsive noise channels using density evo- lution are combined with physical layer security on a wire-tap chan- nel experiencing impulsive noise. The secrecy rate of polar codes is maximised. In the decoding of polar codes, the frozen bits play an important part. The posi- tions of the frozen bits has a significant impact on performance and therefore, the selection of optimal frozen bits is presented to opti- mise the performance while maintaining secure communications on impulsive noise wire-tap channels. Optimal puncturing patterns are investigated to obtain polar codes with arbitrary block lengths and can be applied to different modu- lation schemes, such as binary phase shift keying (BPSK) and M- ary Quadrature Amplitude Modulation (QAM), that can be rate compatible with practical communication systems. The punctured polar codes are combined with physical layer security, allowing the construction of a variety of different code rates while maintaining good performance and security on impulsive noise wire-tap chan- nels. The results from this work have demonstrated that polar codes are ro- bust to the effects of impulsive noise channel and can achieve secure communications. The work also addresses the issue of security on im- pulsive noise channels and has provided important insight into scenarios where the main channel between authorised users has varying levels of impulsiveness compared with the eavesdropper's channel. One of the most interesting results from this thesis is the observation that polar codes combined with physical layer security can achieve good perfor- mance and security even when the main channel is more impulsive than the eavesdropper's channel, which was unexpected. Therefore, this thesis concludes that the low-complexity polar codes are an excellent candidate for the error-correcting codes when combined with physical layer security in more harsh impulsive wireless communication channels

Problems on q-Analogs in Coding Theory

The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. There are many interesting theoretical, algebraic, and combinatorial coding problems concerning these q-analogs which remained unsolved. The first goal of this paper is to make a short summary of the large amount of research which was done in the area mainly in the last few years and to provide most of the relevant references. The second goal of this paper is to present one hundred open questions and problems for future research, whose solution will advance the knowledge in this area. The third goal of this paper is to present and start some directions in solving some of these problems.Comment: arXiv admin note: text overlap with arXiv:0805.3528 by other author

Performance Improvement of Space Missions Using Convolutional Codes by CRC-Aided List Viterbi Algorithms

Recently, CRC-aided list decoding of convolutional codes has gained attention thanks to its remarkable performance in the short blocklength regime. This paper studies the convolutional and CRC codes of the Consultative Committee for Space Data System Telemetry recommendation used in space missions by all international space agencies. The distance spectrum of the concatenated CRC-convolutional code and an upper bound on its frame error rate are derived, showing the availability of a 3 dB coding gain when compared to the maximum likelihood decoding of the convolutional code alone. The analytic bounds are then compared with Monte Carlo simulations for frame error rates achieved by list Viterbi decoding of the concatenated codes, for various list sizes. A remarkable outcome is the possibility of approaching the 3 dB coding gain with nearly the same decoding complexity of the plain Viterbi decoding of the inner convolutional code, at the expense of slightly increasing the undetected frame error rates at medium-high signal-to-noise ratios. Comparisons with CCSDS turbo codes and low-density parity check codes highlight the effectiveness of the proposed solution for onboard utilization on small satellites and cubesats, due to the reduced encoder complexity and excellent error rate performance

Combined Time, Frecuency and Space Diversity in Multimedia Mobile Broadcasting Systems

El uso combinado de diversidad en el dominio temporal, frecuencial y espacial constituye una valiosa herramienta para mejorar la recepción de servicios de difusión móviles. Gracias a la mejora conseguida por las técnicas de diversidad es posible extender la cobertura de los servicios móviles además de reducir la infraestructura de red. La presente tesis investiga el uso de técnicas de diversidad para la provisión de servicios móviles en la familia europea de sistemas de difusión terrestres estandarizada por el prpoyecto DVB (Digital Video Broadcasting). Esto incluye la primera y segunda generación de sistemas DVB-T (Terrestrial), DVB-NGH (Handheld), y DVB-T2 (Terrestrial 2nd generation), así como el sistema de siguiente generación DVB-NGH. No obstante, el estudio llevado a cabo en la tesis es genérico y puede aplicarse a futuras evoluciones de estándares como el japonés ISDB-T o el americano ATSC. Las investigaciones realizadas dentro del contexto de DVB-T, DVB-H y DVBT2 tienen como objetivo la transmisión simultánea de servicios fijos y móviles en redes terrestres. Esta Convergencia puede facilitar la introducción de servicios móviles de TB debido a la reutilización de espectro, contenido e infraestructura. De acuerdo a los resultados, la incorporación de entrelazado temporal en la capa física para diversidad temporal, y de single-input multiple-output (SIMO) para diversidad espacial, son esenciales para el rendimiento de sistemas móviles de difusión. A pesar de que las técnicas upper later FEC (UL-FEC) pueden propocionar diversidad temporal en sistemas de primera generación como DVB-T y DVB-H, requieren la transmisión de paridad adicional y no son útiles para la recepción estática. El análisis en t�ñerminos de link budjget revela que las técnicas de diversidad noson suficientes para facilitar la provision de servicios móviles en redes DVB-T y DVB-T2 planificadas para recepción fija. Sin embargo, el uso de diversidad en redes planificadas para recepción portableGozálvez Serrano, D. (2012). Combined Time, Frecuency and Space Diversity in Multimedia Mobile Broadcasting Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/16273Palanci