Entanglement-assisted quantum turbo codes

An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin et al., in order to have the constituent decoders pass along only "extrinsic information" to each other rather than a posteriori probabilities as in the decoder of Poulin et al., and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.Comment: 31 pages, software for simulating EA turbo codes is available at http://code.google.com/p/ea-turbo/ and a presentation is available at http://markwilde.com/publications/10-10-EA-Turbo.ppt ; v2, revisions based on feedback from journal; v3, modification of the quantum turbo decoding algorithm that leads to improved performance over results in v2 and the results of Poulin et al. in arXiv:0712.288

Spread spectrum-based video watermarking algorithms for copyright protection

Merged with duplicate record 10026.1/2263 on 14.03.2017 by CS (TIS)Digital technologies know an unprecedented expansion in the last years. The consumer can now benefit from hardware and software which was considered state-of-the-art several years ago. The advantages offered by the digital technologies are major but the same digital technology opens the door for unlimited piracy. Copying an analogue VCR tape was certainly possible and relatively easy, in spite of various forms of protection, but due to the analogue environment, the subsequent copies had an inherent loss in quality. This was a natural way of limiting the multiple copying of a video material. With digital technology, this barrier disappears, being possible to make as many copies as desired, without any loss in quality whatsoever. Digital watermarking is one of the best available tools for fighting this threat. The aim of the present work was to develop a digital watermarking system compliant with the recommendations drawn by the EBU, for video broadcast monitoring. Since the watermark can be inserted in either spatial domain or transform domain, this aspect was investigated and led to the conclusion that wavelet transform is one of the best solutions available. Since watermarking is not an easy task, especially considering the robustness under various attacks several techniques were employed in order to increase the capacity/robustness of the system: spread-spectrum and modulation techniques to cast the watermark, powerful error correction to protect the mark, human visual models to insert a robust mark and to ensure its invisibility. The combination of these methods led to a major improvement, but yet the system wasn't robust to several important geometrical attacks. In order to achieve this last milestone, the system uses two distinct watermarks: a spatial domain reference watermark and the main watermark embedded in the wavelet domain. By using this reference watermark and techniques specific to image registration, the system is able to determine the parameters of the attack and revert it. Once the attack was reverted, the main watermark is recovered. The final result is a high capacity, blind DWr-based video watermarking system, robust to a wide range of attacks.BBC Research & Developmen

Entanglement-assisted quantum turbo codes

An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin , in order to have the constituent decoders pass along only extrinsic information to each other rather than a posteriori probabilities as in the decoder of Poulin , and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them. © 1963-2012 IEEE

Turbo codes and turbo algorithms

In the first part of this paper, several basic ideas that prompted the coming of turbo codes are commented on. We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes and double-binary turbo codes associated with Max-Log-MAP decoding. A novel evaluation method, called genieinitialised iterative processing (GIIP), is introduced to assess the error performance of iterative processing. We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance. Finally, two wireless communication systems are presented to illustrate recent applications of the turbo principle, the first one being multiple-input/multiple-output channel iterative detection and the second one multi-carrier modulation with linear precoding

Coded modulation techniques with bit interleaving and iterative processing for impulsive noise channels

Power line communications (PLC) surfers performance degradation due mainly to impulsive noise interference generated by electrical appliances. This thesis studies coded modulation techniques to improve the spectral efficiency and error performance of PLC. Considered in the first part is the application of bit-interleaved coded modulation with iterative decoding (BICM-ID) in class-A impulsive noise environment. In particular, the optimal soft-output demodulator and its suboptimal version are presented for an additive class-A noise (AWAN) channel so that iterative demodulation and decoding can be performed at the receiver. The effect of signal mapping on the error performance of BICM-ID systems in impulsive noise is then investigated, with both computer simulations and a tight error bound on the asymptotic performance. Extrinsic information transfer (EXIT) chart analysis is performed to illustrate the convergence properties of different mappings. The superior performance of BICMID compared to orthogonal frequency-division multiplexing (OFDM) is also clearly demonstrated.Motivated by the successes of both BICM-ID and OFDM in improving the error performance of communications systems in impulsive noise environment, the second part of this thesis introduces a novel scheme of bit-interleaved coded OFDM with iterative decoding (BI-COFDM-ID) over the class-A impulsive noise channel. Here, an iterative receiver composed of outer and inner iteration loops is first described in detail. Error performance improvements of the proposed iterative receiver with different iteration strategies are presented and discussed. Performance comparisons of BI-COFDM-ID, BICM-ID and iteratively decoded OFDM are made to illustrate the superiority of BI-COFDM-ID. The effect of signal mapping on the error performance of BI-COFDM-ID is also studied

Coding Theory

Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete mathematics and combinatorics, complexity theory, and statistical physics. The workshop on coding theory covered many facets of the recent research advances

Energy-efficient design and implementation of turbo codes for wireless sensor network

The objective of this thesis is to apply near Shannon limit Error-Correcting Codes (ECCs), particularly the turbo-like codes, to energy-constrained wireless devices, for the purpose of extending their lifetime. Conventionally, sophisticated ECCs are applied to applications, such as mobile telephone networks or satellite television networks, to facilitate long range and high throughput wireless communication. For low power applications, such as Wireless Sensor Networks (WSNs), these ECCs were considered due to their high decoder complexities. In particular, the energy efficiency of the sensor nodes in WSNs is one of the most important factors in their design. The processing energy consumption required by high complexity ECCs decoders is a significant drawback, which impacts upon the overall energy consumption of the system. However, as Integrated Circuit (IC) processing technology is scaled down, the processing energy consumed by hardware resources reduces exponentially. As a result, near Shannon limit ECCs have recently begun to be considered for use in WSNs to reduce the transmission energy consumption [1,2]. However, to ensure that the transmission energy consumption reduction granted by the employed ECC makes a positive improvement on the overall energy efficiency of the system, the processing energy consumption must still be carefully considered.The main subject of this thesis is to optimise the design of turbo codes at both an algorithmic and a hardware implementation level for WSN scenarios. The communication requirements of the target WSN applications, such as communication distance, channel throughput, network scale, transmission frequency, network topology, etc, are investigated. Those requirements are important factors for designing a channel coding system. Especially when energy resources are limited, the trade-off between the requirements placed on different parameters must be carefully considered, in order to minimise the overall energy consumption. Moreover, based on this investigation, the advantages of employing near Shannon limit ECCs in WSNs are discussed. Low complexity and energy-efficient hardware implementations of the ECC decoders are essential for the target applications