Foliated quantum error-correcting codes

We show how to construct a large class of quantum error-correcting codes, known as Calderbank-Steane-Shor codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error-correction codes and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate Calderbank-Steane-Shor codes known as turbo codes, finding that they perform well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation

Design techniques for graph-based error-correcting codes and their applications

In ShannonÂs seminal paper, ÂA Mathematical Theory of CommunicationÂ, he defined ÂChannel Capacity which predicted the ultimate performance that transmission systems can achieve and suggested that capacity is achievable by error-correcting (channel) coding. The main idea of error-correcting codes is to add redundancy to the information to be transmitted so that the receiver can explore the correlation between transmitted information and redundancy and correct or detect errors caused by channels afterward. The discovery of turbo codes and rediscovery of Low Density Parity Check codes (LDPC) have revived the research in channel coding with novel ideas and techniques on code concatenation, iterative decoding, graph-based construction and design based on density evolution. This dissertation focuses on the design aspect of graph-based channel codes such as LDPC and Irregular Repeat Accumulate (IRA) codes via density evolution, and use the technique (density evolution) to design IRA codes for scalable image/video communication and LDPC codes for distributed source coding, which can be considered as a channel coding problem. The first part of the dissertation includes design and analysis of rate-compatible IRA codes for scalable image transmission systems. This part presents the analysis with density evolution the effect of puncturing applied to IRA codes and the asymptotic analysis of the performance of the systems. In the second part of the dissertation, we consider designing source-optimized IRA codes. The idea is to take advantage of the capability of Unequal Error Protection (UEP) of IRA codes against errors because of their irregularities. In video and image transmission systems, the performance is measured by Peak Signal to Noise Ratio (PSNR). We propose an approach to design IRA codes optimized for such a criterion. In the third part of the dissertation, we investigate Slepian-Wolf coding problem using LDPC codes. The problems to be addressed include coding problem involving multiple sources and non-binary sources, and coding using multi-level codes and nonbinary codes

Layered Wyner-Ziv video coding for noisy channels

The growing popularity of video sensor networks and video celluar phones has generated the need for low-complexity and power-efficient multimedia systems that can handle multiple video input and output streams. While standard video coding techniques fail to satisfy these requirements, distributed source coding is a promising technique for ??uplink?? applications. Wyner-Ziv coding refers to lossy source coding with side information at the decoder. Based on recent theoretical result on successive Wyner-Ziv coding, we propose in this thesis a practical layered Wyner-Ziv video codec using the DCT, nested scalar quantizer, and irregular LDPC code based Slepian-Wolf coding (or lossless source coding with side information) for noiseless channel. The DCT is applied as an approximation to the conditional KLT, which makes the components of the transformed block conditionally independent given the side information. NSQ is a binning scheme that facilitates layered bit-plane coding of the bin indices while reducing the bit rate. LDPC code based Slepian-Wolf coding exploits the correlation between the quantized version of the source and the side information to achieve further compression. Different from previous works, an attractive feature of our proposed system is that video encoding is done only once but decoding allowed at many lower bit rates without quality loss. For Wyner-Ziv coding over discrete noisy channels, we present a Wyner-Ziv video codec using IRA codes for Slepian-Wolf coding based on the idea of two equivalent channels. For video streaming applications where the channel is packet based, we apply unequal error protection scheme to the embedded Wyner-Ziv coded video stream to find the optimal source-channel coding trade-off for a target transmission rate over packet erasure channel

Multiterminal source coding: sum-rate loss, code designs, and applications to video sensor networks

Driven by a host of emerging applications (e.g., sensor networks and wireless video), distributed source coding (i.e., Slepian-Wolf coding, Wyner-Ziv coding and various other forms of multiterminal source coding), has recently become a very active research area. This dissertation focuses on multiterminal (MT) source coding problem, and consists of three parts. The first part studies the sum-rate loss of an important special case of quadratic Gaussian multi-terminal source coding, where all sources are positively symmetric and all target distortions are equal. We first give the minimum sum-rate for joint encoding of Gaussian sources in the symmetric case, and then show that the supremum of the sum-rate loss due to distributed encoding in this case is 1 2 log2 5 4 = 0:161 b/s when L = 2 and increases in the order of º L 2 log2 e b/s as the number of terminals L goes to infinity. The supremum sum-rate loss of 0:161 b/s in the symmetric case equals to that in general quadratic Gaussian two-terminal source coding without the symmetric assumption. It is conjectured that this equality holds for any number of terminals. In the second part, we present two practical MT coding schemes under the framework of Slepian-Wolf coded quantization (SWCQ) for both direct and indirect MT problems. The first, asymmetric SWCQ scheme relies on quantization and Wyner-Ziv coding, and it is implemented via source splitting to achieve any point on the sum-rate bound. In the second, conceptually simpler scheme, symmetric SWCQ, the two quantized sources are compressed using symmetric Slepian-Wolf coding via a channel code partitioning technique that is capable of achieving any point on the Slepian-Wolf sum-rate bound. Our practical designs employ trellis-coded quantization and turbo/LDPC codes for both asymmetric and symmetric Slepian-Wolf coding. Simulation results show a gap of only 0.139-0.194 bit per sample away from the sum-rate bound for both direct and indirect MT coding problems. The third part applies the above two MT coding schemes to two practical sources, i.e., stereo video sequences to save the sum rate over independent coding of both sequences. Experiments with both schemes on stereo video sequences using H.264, LDPC codes for Slepian-Wolf coding of the motion vectors, and scalar quantization in conjunction with LDPC codes for Wyner-Ziv coding of the residual coefficients give slightly smaller sum rate than separate H.264 coding of both sequences at the same video quality

Distributed signal processing using nested lattice codes

Multi-Terminal Source Coding (MTSC) addresses the problem of compressing correlated sources without communication links among them. In this thesis, the constructive approach of this problem is considered in an algebraic framework and a system design is provided that can be applicable in a variety of settings. Wyner-Ziv problem is first investigated: coding of an independent and identically distributed (i.i.d.) Gaussian source with side information available only at the decoder in the form of a noisy version of the source to be encoded. Theoretical models are first established and derived for calculating distortion-rate functions. Then a few novel practical code implementations are proposed by using the strategy of multi-dimensional nested lattice/trellis coding. By investigating various lattices in the dimensions considered, analysis is given on how lattice properties affect performance. Also proposed are methods on choosing good sublattices in multiple dimensions. By introducing scaling factors, the relationship between distortion and scaling factor is examined for various rates. The best high-dimensional lattice using our scale-rotate method can achieve a performance less than 1 dB at low rates from the Wyner-Ziv limit; and random nested ensembles can achieve a 1.87 dB gap with the limit. Moreover, the code design is extended to incorporate with distributed compressive sensing (DCS). Theoretical framework is proposed and practical design using nested lattice/trellis is presented for various scenarios. By using nested trellis, the simulation shows a 3.42 dB gap from our derived bound for the DCS plus Wyner-Ziv framework

Research and developments of distributed video coding

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The recent developed Distributed Video Coding (DVC) is typically suitable for the applications such as wireless/wired video sensor network, mobile camera etc. where the traditional video coding standard is not feasible due to the constrained computation at the encoder. With DVC, the computational burden is moved from encoder to decoder. The compression efficiency is achieved via joint decoding at the decoder. The practical application of DVC is referred to Wyner-Ziv video coding (WZ) where the side information is available at the decoder to perform joint decoding. This join decoding inevitably causes a very complex decoder. In current WZ video coding issues, many of them emphasise how to improve the system coding performance but neglect the huge complexity caused at the decoder. The complexity of the decoder has direct influence to the system output. The beginning period of this research targets to optimise the decoder in pixel domain WZ video coding (PDWZ), while still achieves similar compression performance. More specifically, four issues are raised to optimise the input block size, the side information generation, the side information refinement process and the feedback channel respectively. The transform domain WZ video coding (TDWZ) has distinct superior performance to the normal PDWZ due to the exploitation in spatial direction during the encoding. However, since there is no motion estimation at the encoder in WZ video coding, the temporal correlation is not exploited at all at the encoder in all current WZ video coding issues. In the middle period of this research, the 3D DCT is adopted in the TDWZ to remove redundancy in both spatial and temporal direction thus to provide even higher coding performance. In the next step of this research, the performance of transform domain Distributed Multiview Video Coding (DMVC) is also investigated. Particularly, three types transform domain DMVC frameworks which are transform domain DMVC using TDWZ based 2D DCT, transform domain DMVC using TDWZ based on 3D DCT and transform domain residual DMVC using TDWZ based on 3D DCT are investigated respectively. One of the important applications of WZ coding principle is error-resilience. There have been several attempts to apply WZ error-resilient coding for current video coding standard e.g. H.264/AVC or MEPG 2. The final stage of this research is the design of WZ error-resilient scheme for wavelet based video codec. To balance the trade-off between error resilience ability and bandwidth consumption, the proposed scheme emphasises the protection of the Region of Interest (ROI) area. The efficiency of bandwidth utilisation is achieved by mutual efforts of WZ coding and sacrificing the quality of unimportant area. In summary, this research work contributed to achieves several advances in WZ video coding. First of all, it is targeting to build an efficient PDWZ with optimised decoder. Secondly, it aims to build an advanced TDWZ based on 3D DCT, which then is applied into multiview video coding to realise advanced transform domain DMVC. Finally, it aims to design an efficient error-resilient scheme for wavelet video codec, with which the trade-off between bandwidth consumption and error-resilience can be better balanced

REGION-BASED ADAPTIVE DISTRIBUTED VIDEO CODING CODEC

The recently developed Distributed Video Coding (DVC) is typically suitable for the applications where the conventional video coding is not feasible because of its inherent high-complexity encoding. Examples include video surveillance usmg wireless/wired video sensor network and applications using mobile cameras etc. With DVC, the complexity is shifted from the encoder to the decoder. The practical application of DVC is referred to as Wyner-Ziv video coding (WZ) where an estimate of the original frame called "side information" is generated using motion compensation at the decoder. The compression is achieved by sending only that extra information that is needed to correct this estimation. An error-correcting code is used with the assumption that the estimate is a noisy version of the original frame and the rate needed is certain amount of the parity bits. The side information is assumed to have become available at the decoder through a virtual channel. Due to the limitation of compensation method, the predicted frame, or the side information, is expected to have varying degrees of success. These limitations stem from locationspecific non-stationary estimation noise. In order to avoid these, the conventional video coders, like MPEG, make use of frame partitioning to allocate optimum coder for each partition and hence achieve better rate-distortion performance. The same, however, has not been used in DVC as it increases the encoder complexity. This work proposes partitioning the considered frame into many coding units (region) where each unit is encoded differently. This partitioning is, however, done at the decoder while generating the side-information and the region map is sent over to encoder at very little rate penalty. The partitioning allows allocation of appropriate DVC coding parameters (virtual channel, rate, and quantizer) to each region. The resulting regions map is compressed by employing quadtree algorithm and communicated to the encoder via the feedback channel. The rate control in DVC is performed by channel coding techniques (turbo codes, LDPC, etc.). The performance of the channel code depends heavily on the accuracy of virtual channel model that models estimation error for each region. In this work, a turbo code has been used and an adaptive WZ DVC is designed both in transform domain and in pixel domain. The transform domain WZ video coding (TDWZ) has distinct superior performance as compared to the normal Pixel Domain Wyner-Ziv (PDWZ), since it exploits the ' spatial redundancy during the encoding. The performance evaluations show that the proposed system is superior to the existing distributed video coding solutions. Although the, proposed system requires extra bits representing the "regions map" to be transmitted, fuut still the rate gain is noticeable and it outperforms the state-of-the-art frame based DVC by 0.6-1.9 dB. The feedback channel (FC) has the role to adapt the bit rate to the changing ' statistics between the side infonmation and the frame to be encoded. In the unidirectional scenario, the encoder must perform the rate control. To correctly estimate the rate, the encoder must calculate typical side information. However, the rate cannot be exactly calculated at the encoder, instead it can only be estimated. This work also prbposes a feedback-free region-based adaptive DVC solution in pixel domain based on machine learning approach to estimate the side information. Although the performance evaluations show rate-penalty but it is acceptable considering the simplicity of the proposed algorithm. vii

ADAPTIVE CHANNEL AND SOURCE CODING USING APPROXIMATE INFERENCE

Channel coding and source coding are two important problems in communications. Although both channel coding and source coding (especially, the distributed source coding (DSC)) can achieve their ultimate performance by knowing the perfect knowledge of channel noise and source correlation, respectively, such information may not be always available at the decoder side. The reasons might be because of the time−varying characteristic of some communication systems and sources themselves, respectively. In this dissertation, I mainly focus on the study of online channel noise estimation and correlation estimation by using both stochastic and deterministic approximation inferences on factor graphs.In channel coding, belief propagation (BP) is a powerful algorithm to decode low−density parity check (LDPC) codes over additive white Gaussian noise (AWGN) channels. However, the traditional BP algorithm cannot adapt efficiently to the statistical change of SNR in an AWGN channel. To solve the problem, two common workarounds in approximate inference are stochastic methods (e.g. particle filtering (PF)) and deterministic methods (e.g. expectation approximation (EP)). Generally, deterministic methods are much faster than stochastic methods. In contrast, stochastic methods are more flexible and suitable for any distribution. In this dissertation, I proposed two adaptive LDPC decoding schemes, which are able to perform online estimation of time−varying channel state information (especially signal to noise ratio (SNR)) at the bit−level by incorporating PF and EP algorithms. Through experimental results, I compare the performance between the proposed PF based and EP based approaches, which shows that the EP based approach obtains the comparable estimation accuracy with less computational complexity than the PF based method for both stationary and time−varying SNR, and enhances the BP decoding performance simultaneously. Moreover, the EP estimator shows a very fast convergence speed, and the additional computational overhead of the proposed decoder is less than 10% of the standard BP decoder.Moreover, since the close relationship between source coding and channel coding, the proposed ideas are extended to source correlation estimation. First, I study the correlation estimation problem in lossless DSC setup, where I consider both asymmetric and non−asymmetric SW coding of two binary correlated sources. The aforementioned PF and EP based approaches are extended to handle the correlation between two binary sources, where the relationship is modeled as a virtual binary symmetric channel (BSC) with a time−varying crossover probability. Besides, to handle the correlation estimation problem of Wyner−Ziv (WZ) coding, a lossy DSC setup, I design a joint bit−plane model, by which the PF based approach can be applied to tracking the correlation between non−binary sources. Through experimental results, the proposed correlation estimation approaches significantly improve the compression performance of DSC.Finally, due to the property of ultra−low encoding complexity, DSC is a promising technique for many tasks, in which the encoder has only limited computing and communication power, e.g. the space imaging systems. In this dissertation, I consider a real−world application of the proposed correlation estimation scheme on the onboard low−complexity compression of solar stereo images, since such solutions are essential to reduce onboard storage, processing, and communication resources. In this dissertation, I propose an adaptive distributed compression solution using PF that tracks the correlation, as well as performs disparity estimation, at the decoder side. The proposed algorithm istested on the stereo solar images captured by the twin satellites systemof NASA’s STEREO project. The experimental results show the significant PSNR improvement over traditional separate bit−plane decoding without dynamic correlation and disparity estimation

Coding with side information

Source coding and channel coding are two important problems in communications. Although side information exists in everyday scenario, the effect of side information is not taken into account in the conventional setups. In this thesis, we focus on the practical designs of two interesting coding problems with side information: Wyner-Ziv coding (source coding with side information at the decoder) and Gel??fand-Pinsker coding (channel coding with side information at the encoder). For WZC, we split the design problem into the two cases when the distortion of the reconstructed source is zero and when it is not. We review that the first case, which is commonly called Slepian-Wolf coding (SWC), can be implemented using conventional channel coding. Then, we detail the SWC design using the low-density parity-check (LDPC) code. To facilitate SWC design, we justify a necessary requirement that the SWC performance should be independent of the input source. We show that a sufficient condition of this requirement is that the hypothetical channel between the source and the side information satisfies a symmetry condition dubbed dual symmetry. Furthermore, under that dual symmetry condition, SWC design problem can be simply treated as LDPC coding design over the hypothetical channel. When the distortion of the reconstructed source is non-zero, we propose a practical WZC paradigm called Slepian-Wolf coded quantization (SWCQ) by combining SWC and nested lattice quantization. We point out an interesting analogy between SWCQ and entropy coded quantization in classic source coding. Furthermore, a practical scheme of SWCQ using 1-D nested lattice quantization and LDPC is implemented. For GPC, since the actual design procedure relies on the more precise setting of the problem, we choose to investigate the design of GPC as the form of a digital watermarking problem as digital watermarking is the precise dual of WZC. We then introduce an enhanced version of the well-known spread spectrum watermarking technique. Two applications related to digital watermarking are presented