Alpha Entanglement Codes: Practical Erasure Codes to Archive Data in Unreliable Environments

Data centres that use consumer-grade disks drives and distributed peer-to-peer systems are unreliable environments to archive data without enough redundancy. Most redundancy schemes are not completely effective for providing high availability, durability and integrity in the long-term. We propose alpha entanglement codes, a mechanism that creates a virtual layer of highly interconnected storage devices to propagate redundant information across a large scale storage system. Our motivation is to design flexible and practical erasure codes with high fault-tolerance to improve data durability and availability even in catastrophic scenarios. By flexible and practical, we mean code settings that can be adapted to future requirements and practical implementations with reasonable trade-offs between security, resource usage and performance. The codes have three parameters. Alpha increases storage overhead linearly but increases the possible paths to recover data exponentially. Two other parameters increase fault-tolerance even further without the need of additional storage. As a result, an entangled storage system can provide high availability, durability and offer additional integrity: it is more difficult to modify data undetectably. We evaluate how several redundancy schemes perform in unreliable environments and show that alpha entanglement codes are flexible and practical codes. Remarkably, they excel at code locality, hence, they reduce repair costs and become less dependent on storage locations with poor availability. Our solution outperforms Reed-Solomon codes in many disaster recovery scenarios.Comment: The publication has 12 pages and 13 figures. This work was partially supported by Swiss National Science Foundation SNSF Doc.Mobility 162014, 2018 48th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Robust Lattice Alignment for K-user MIMO Interference Channels with Imperfect Channel Knowledge

In this paper, we consider a robust lattice alignment design for K-user quasi-static MIMO interference channels with imperfect channel knowledge. With random Gaussian inputs, the conventional interference alignment (IA) method has the feasibility problem when the channel is quasi-static. On the other hand, structured lattices can create structured interference as opposed to the random interference caused by random Gaussian symbols. The structured interference space can be exploited to transmit the desired signals over the gaps. However, the existing alignment methods on the lattice codes for quasi-static channels either require infinite SNR or symmetric interference channel coefficients. Furthermore, perfect channel state information (CSI) is required for these alignment methods, which is difficult to achieve in practice. In this paper, we propose a robust lattice alignment method for quasi-static MIMO interference channels with imperfect CSI at all SNR regimes, and a two-stage decoding algorithm to decode the desired signal from the structured interference space. We derive the achievable data rate based on the proposed robust lattice alignment method, where the design of the precoders, decorrelators, scaling coefficients and interference quantization coefficients is jointly formulated as a mixed integer and continuous optimization problem. The effect of imperfect CSI is also accommodated in the optimization formulation, and hence the derived solution is robust to imperfect CSI. We also design a low complex iterative optimization algorithm for our robust lattice alignment method by using the existing iterative IA algorithm that was designed for the conventional IA method. Numerical results verify the advantages of the proposed robust lattice alignment method

Multiple Description Quantization via Gram-Schmidt Orthogonalization

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient multiple description quantization schemes is proposed in this paper. We provide a systematic treatment of the El Gamal-Cover (EGC) achievable MD rate-distortion region, and show that any point in the EGC region can be achieved via a successive quantization scheme along with quantization splitting. For the quadratic Gaussian case, the proposed scheme has an intrinsic connection with the Gram-Schmidt orthogonalization, which implies that the whole Gaussian MD rate-distortion region is achievable with a sequential dithered lattice-based quantization scheme as the dimension of the (optimal) lattice quantizers becomes large. Moreover, this scheme is shown to be universal for all i.i.d. smooth sources with performance no worse than that for an i.i.d. Gaussian source with the same variance and asymptotically optimal at high resolution. A class of low-complexity MD scalar quantizers in the proposed general framework also is constructed and is illustrated geometrically; the performance is analyzed in the high resolution regime, which exhibits a noticeable improvement over the existing MD scalar quantization schemes.Comment: 48 pages; submitted to IEEE Transactions on Information Theor

Joint Wyner-Ziv/Dirty Paper coding by modulo-lattice modulation

The combination of source coding with decoder side-information (Wyner-Ziv problem) and channel coding with encoder side-information (Gel'fand-Pinsker problem) can be optimally solved using the separation principle. In this work we show an alternative scheme for the quadratic-Gaussian case, which merges source and channel coding. This scheme achieves the optimal performance by a applying modulo-lattice modulation to the analog source. Thus it saves the complexity of quantization and channel decoding, and remains with the task of "shaping" only. Furthermore, for high signal-to-noise ratio (SNR), the scheme approaches the optimal performance using an SNR-independent encoder, thus it is robust to unknown SNR at the encoder.Comment: Submitted to IEEE Transactions on Information Theory. Presented in part in ISIT-2006, Seattle. New version after revie

Nested turbo codes for the costa problem

Driven by applications in data-hiding, MIMO broadcast channel coding, precoding for interference cancellation, and transmitter cooperation in wireless networks, Costa coding has lately become a very active research area. In this paper, we first offer code design guidelines in terms of source- channel coding for algebraic binning. We then address practical code design based on nested lattice codes and propose nested turbo codes using turbo-like trellis-coded quantization (TCQ) for source coding and turbo trellis-coded modulation (TTCM) for channel coding. Compared to TCQ, turbo-like TCQ offers structural similarity between the source and channel coding components, leading to more efficient nesting with TTCM and better source coding performance. Due to the difference in effective dimensionality between turbo-like TCQ and TTCM, there is a performance tradeoff between these two components when they are nested together, meaning that the performance of turbo-like TCQ worsens as the TTCM code becomes stronger and vice versa. Optimization of this performance tradeoff leads to our code design that outperforms existing TCQ/TCM and TCQ/TTCM constructions and exhibits a gap of 0.94, 1.42 and 2.65 dB to the Costa capacity at 2.0, 1.0, and 0.5 bits/sample, respectively