Codeword-Independent Performance of Nonbinary Linear Codes Under Linear-Programming and Sum-Product Decoding

A coded modulation system is considered in which nonbinary coded symbols are mapped directly to nonbinary modulation signals. It is proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. It is shown that this result holds for both linear-programming decoders and sum-product decoders. In particular, this provides a natural modulation mapping for nonbinary codes mapped to PSK constellations for transmission over memoryless channels such as AWGN channels or flat fading channels with AWGN.Comment: 5 pages, Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 6-11, 200

Optimization of a Coded-Modulation System with Shaped Constellation

Conventional communication systems transmit signals that are selected from a signal constellation with uniform probability. However, information-theoretic results suggest that performance may be improved by shaping the constellation such that lower-energy signals are selected more frequently than higher-energy signals. This dissertation presents an energy efficient approach for shaping the constellations used by coded-modulation systems. The focus is on designing shaping techniques for systems that use a combination of amplitude phase shift keying (APSK) and low-density parity check (LDPC) coding. Such a combination is typical of modern satellite communications, such as the system used by the DVB-S2 standard.;The system implementation requires that a subset of the bits at the output of the LDPC encoder are passed through a nonlinear shaping encoder whose output bits are more likely to be a zero than a one. The constellation is partitioned into a plurality of sub-constellations, each with a different average signal energy, and the shaping bits are used to select the sub-constellation. An iterative receiver exchanges soft information among the demodulator, LDPC decoder, and shaping decoder. Parameters associated with the modulation and shaping code are optimized with respect to information rate, while the design of the LDPC code is optimized for the shaped modulation with the assistance of extrinsic-information transfer (EXIT) charts. The rule for labeling the constellation with bits is optimized using a novel hybrid cost function and a binary switching algorithm.;Simulation results show that the combination of constellation shaping, LDPC code optimization, and optimized bit labeling can achieve a gain in excess of 1 dB in an additive white Gaussian noise (AWGN) channel at a rate of 3 bits/symbol compared with a system that adheres directly to the DVB-S2 standard

Constellation Optimization in the Presence of Strong Phase Noise

In this paper, we address the problem of optimizing signal constellations for strong phase noise. The problem is investigated by considering three optimization formulations, which provide an analytical framework for constellation design. In the first formulation, we seek to design constellations that minimize the symbol error probability (SEP) for an approximate ML detector in the presence of phase noise. In the second formulation, we optimize constellations in terms of mutual information (MI) for the effective discrete channel consisting of phase noise, additive white Gaussian noise, and the approximate ML detector. To this end, we derive the MI of this discrete channel. Finally, we optimize constellations in terms of the MI for the phase noise channel. We give two analytical characterizations of the MI of this channel, which are shown to be accurate for a wide range of signal-to-noise ratios and phase noise variances. For each formulation, we present a detailed analysis of the optimal constellations and their performance in the presence of strong phase noise. We show that the optimal constellations significantly outperform conventional constellations and those proposed in the literature in terms of SEP, error floors, and MI.Comment: 10 page, 10 figures, Accepted to IEEE Trans. Commu

Limites práticos de segurança da distribuição de chaves quânticas de variáveis contínuas

Discrete Modulation Continuous Variable Quantum Key Distribution (DM-CV-QKD) systems are very attractive for modern quantum cryptography, since they manage to surpass all Gaussian modulation (GM) system’s disadvantages while maintaining the advantages of using CVs. Nonetheless, DM-CV-QKD is still underdeveloped, with a very limited study of large constellations. This work intends to increase the knowledge on DM-CV-QKD systems considering large constellations, namely M-symbol Amplitude Phase Shift Keying (M-APSK) irregular and regular constellations. As such, a complete DM-CV-QKD system was implemented, con sidering collective attacks and reverse reconciliation under the realistic scenario, assuming Bob detains the knowledge of his detector’s noise. Tight security bounds were obtained considering M-APSK constellations and GM, both for the mutual information between Bob and Alice and the Holevo bound between Bob and Eve. M-APSK constellations with binomial distribution can approximate GM’s results for the secret key rate. Without the consideration of the finite size effects (FSEs), the regular constellation 256-APSK (reg. 32) with binomial distribution achieves 242.9 km, only less 7.2 km than GM for a secret key rate of 10¯⁶ photons per symbol. Considering FSEs, 256-APSK (reg. 32) achieves 96.4% of GM’s maximum transmission distance (2.3 times more than 4-PSK), and 78.4% of GM’s maximum compatible excess noise (10.2 times more than 4-PSK). Additionally, larger constellations allow the use of higher values of modulation variance in a practical implementation, i.e., we are no longer subjected to the sub-one limit for the mean number of photons per symbol. The information reconciliation step considering a binary symmetric channel, the sum-product algorithm and multi-edge type low den sity parity check matrices, constructed from the progressive edge growth algorithm, allowed the correction of keys up to 18 km. The consideration of multidimensional reconciliation allows 256-APSK (reg. 32) to reconcile keys up to 55 km. Privacy amplification was carried out considering the application of fast Fourier transforms to the Toeplitz extractor, being unable of extracting keys for more than, approximately, 49 km, almost haft the theoretical value, and for excess noises larger than 0.16 SNU, like the theoretical value.Os sistemas de distribuição de chaves quânticas com variáveis contínuas e modulação discreta (DM-CV-QKD) são muito atrativos para a criptografia quântica moderna, pois conseguem superar todas as desvantagens do sistema com modulação Gaussiana (GM) enquanto mantêm as vantagens do uso de CVs. No entanto, DM-CV-QKD ainda está subdesenvolvida, sendo o estudo de grandes constelações muito reduzido. Este trabalho pretende aumentar o conhecimento sobre os sistemas DM-CV-QKD com constelações grandes, nomeadamente as do tipo M-symbol Amplitude Phase Shift Keying (M-APSK) irregulares e regulares. Com isto, foi simulado um sistema DM-CV-QKD completo, considerando ataques coletivos e reconciliação reversa tendo em conta o cenário realista, assumindo que o Bob co nhece o ruído de seu detetor. Os limites de segurança foram obtidos considerando constelações M-APSK e GM, tanto para a informação mútua entre o Bob e a Alice, quanto para o limite de Holevo entre o Bob e a Eve. As constelações M-APSK com distribuição binomial aproximam-se à GM quanto à taxa de chave secreta. Sem considerar o efeito de tamanho finito (FSE), a constelação regular 256-APSK (reg. 32) com distribuição binomial atinge 242.9 km, apenas menos 7.2 km do que GM para uma taxa de chave secreta de 10¯⁶ fotões por símbolo. Considerando FSEs, a 256-APSK (reg. 32) atinge 96.4% da distância máxima de transmissão para GM (2.3 vezes mais que a 4-PSK), e 78.4% do valor máximo de excesso de ruído compatível para GM (10.2 vezes mais do que a 4-PSK). Adicionalmente, grandes constelações permitem o uso de valores mais altos de variância de modulação em implementações práticas, pelo que deixa de ser necessário um número de fotões por símbolo abaixo de um. A etapa de reconciliação de informação considerou um canal binário simétrico, o algoritmo soma-produto e matrizes multi-edge type low density parity check, construídas a partir do algoritmo progressive edge growth, permitindo a correção de chaves até 18 km. A consideração de reconciliação multidimensional permite que a 256-APSK (reg. 32) reconcilie chaves até 55 km. A amplificação de privacidade foi realizada considerando a aplicação de transformadas de Fourier rápidas ao extrator de Toeplitz, mostrando-se incapaz de extrair chaves para mais de, aproximadamente, 49 km, quase metade do valor teórico, e para excesso de ruído superior a 0.16 SNU, semelhante ao valor teórico.Mestrado em Engenharia Físic

Spectrally Efficient FDM over Satellite Systems with Advanced Interference Cancellation

For high data rates satellite systems, where multiple carriers are frequency division multiplexed with a slight overlap, the overall spectral efficiency is limited. This work applies highly overlapped carriers for satellite broadcast and broadband scenarios to achieve higher spectral efficiency. Spectrally efficient frequency division multiplexing (SEFDM) compresses subcarrier spacing to increase the spectral efficiency at the expense of orthogonality violation. SEFDM systems performance degrades compared to orthogonal signals, unless efficient interference cancellation is used. Turbo equalisation with interference cancellation is implemented to improve receiver performance for variable coding, compression and modulation/constellation proposals that may be applied in satellite communications settings. Such parameters may be set to satisfy pre-defined spectral efficiency values for a given quality index (QI) or associated application. Assuming LDPC coded data, the work proposes two approaches to receiver design; a simple matched filter approach and an approach utilising an iterative interference cancellation structure specially designed for SEFDM. Mathematical models and simulations studies are presented indicating promising gains to be achieved for SEFDM transmission with advanced transceiver architectures at the cost of increased complexity at the receiver