Linear Coding Schemes for the Distributed Computation of Subspaces

Let X-1,..., X-m be a set of m statistically dependent sources over the common alphabet F-q, that are linearly independent when considered as functions over the sample space. We consider a distributed function computation setting in which the receiver is interested in the lossless computation of the elements of an s-dimensional subspace W spanned by the elements of the row vector X-1,..., X-m]Gamma in which the (m x s) matrix Gamma has rank s. A sequence of three increasingly refined approaches is presented, all based on linear encoders. The first approach uses a common matrix to encode all the sources and a Korner-Marton like receiver to directly compute W. The second improves upon the first by showing that it is often more efficient to compute a carefully chosen superspace U of W. The superspace is identified by showing that the joint distribution of the {X-i} induces a unique decomposition of the set of all linear combinations of the {X-i}, into a chain of subspaces identified by a normalized measure of entropy. This subspace chain also suggests a third approach, one that employs nested codes. For any joint distribution of the {X-i} and any W, the sum-rate of the nested code approach is no larger than that under the Slepian-Wolf (SW) approach. Under the SW approach, W is computed by first recovering each of the {X-i}. For a large class of joint distributions and subspaces W, the nested code approach is shown to improve upon SW. Additionally, a class of source distributions and subspaces are identified, for which the nested-code approach is sum-rate optimal.

Physical Layer Network Coding for the K-User Multiple Access Relay Channel

We propose a Physical layer Network Coding (PNC) scheme for the K-user wireless Multiple Access Relay Channel, in which K source nodes want to transmit messages to a destination node D with the help of a relay node R. The proposed scheme involves (i) Phase 1 during which the source nodes alone transmit and (ii) Phase 2 during which the source nodes and the relay node transmit. At the end of Phase 1, the relay node decodes the messages of the source nodes and during Phase 2 transmits a many-to-one function of the decoded messages. To counter the error propagation from the relay node, we propose a novel decoder which takes into account the possibility of error events at R. It is shown that if certain parameters are chosen properly and if the network coding map used at R forms a Latin Hypercube, the proposed decoder offers the maximum diversity order of two. Also, it is shown that for a proper choice of the parameters, the proposed decoder admits fast decoding, with the same decoding complexity order as that of the reference scheme based on Complex Field Network Coding (CFNC). Simulation results indicate that the proposed PNC scheme offers a large gain over the CFNC scheme.

Wireless Network Coding for MIMO Two-Way Relaying

The design of modulation schemes for the physical layer network-coded two-way MIMO relaying scenario is considered, with the denoise-and-forward protocol which employs two phases: Multiple Access phase and Broadcast phase. It is shown that for MIMO two-way relaying, the minimum distance of the effective constellation at the relay becomes zero when all the rows of the channel fade coefficient matrix belong to a finite number of vector subspaces referred to as the singular fade subspaces. The singular fade subspaces can be classified into two kinds based on whether their harmful effects can be removed or not: (i) the removable and (ii) the non-removable singular fade subspaces. It is shown that network coding maps obtained by the completion of appropriate partially filled Latin Rectangles can remove the harmful effects of all the removable singular fade subspaces. For 2(lambda)-PSK signal set, the removable and non-removable singular fade subspaces are characterized and, it is shown that the number of non-removable singular fade subspaces is a small fraction of the total number of singular fade subspaces and this fraction tends to zero as the constellation size tends to infinity. The Latin Rectangles for the case when the end nodes use different number of antennas are shown to be obtainable from the Latin Squares for the case when they use the same number of antennas. Also, the network coding maps which remove all the removable singular singular fade subspaces are shown to be obtainable from a small set of Latin Squares. The removal of all the singular fade subspaces by properly choosing the network coding map, provides a gain of 5.5 dB over the conventional Exclusive-OR network coding, in a Rayleigh fading scenario with 2 antennas at the end nodes and one antenna at the relay node, for 4-PSK signal set.

A transform approach to linear network coding for acyclic networks with delay

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Fast-Decodable MIDO Codes With Large Coding Gain

In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of two complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input double output (MIDO) systems. Using this method, rate-2 STBCs for 4 x 2, 6 x 2, 8 x 2, and 12 x 2 systems are constructed and these STBCs are fast ML-decodable, have large coding gains, and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems. It is also shown that the Srinath-Rajan code for the 4 x 2 system, which has the lowest ML-decoding complexity among known rate-2 STBCs for the 4x2 MIDO system with a large coding gain for 4-/16-QAM, has the same algebraic structure as the STBC constructed in this paper for the 4 x 2 system. This also settles in positive a previous conjecture that the STBC-scheme that is based on the Srinath-Rajan code has the NVD property and hence is DMT-optimal for the 4 x 2 system.

EESM-Based Link Adaptation in Point-to-Point and Multi-Cell OFDM Systems: Modeling and Analysis

In contemporary wideband orthogonal frequency division multiplexing (OFDM) systems, such as Long Term Evolution (LTE) and WiMAX, different subcarriers over which a codeword is transmitted may experience different signal-to-noise-ratios (SNRs). Thus, adaptive modulation and coding (AMC) in these systems is driven by a vector of subcarrier SNRs experienced by the codeword, and is more involved. Exponential effective SNR mapping (EESM) simplifies the problem by mapping this vector into a single equivalent fiat-fading SNR. Analysis of AMC using EESM is challenging owing to its non-linear nature and its dependence on the modulation and coding scheme. We first propose a novel statistical model for the EESM, which is based on the Beta distribution. It is motivated by the central limit approximation for random variables with a finite support. It is simpler and as accurate as the more involved ad hoc models proposed earlier. Using it, we develop novel expressions for the throughput of a point-to-point OFDM link with multi-antenna diversity that uses EESM for AMC. We then analyze a general, multi-cell OFDM deployment with co-channel interference for various frequency-domain schedulers. Extensive results based on LTE and WiMAX are presented to verify the model and analysis, and gain new insights.

A Communication-Theoretic Framework for 2-DMR Channel Modeling: Performance Evaluation of Coding and Signal Processing Methods

We develop a communication theoretic framework for modeling 2-D magnetic recording channels. Using the model, we define the signal-to-noise ratio (SNR) for the channel considering several physical parameters, such as the channel bit density, code rate, bit aspect ratio, and noise parameters. We analyze the problem of optimizing the bit aspect ratio for maximizing SNR. The read channel architecture comprises a novel 2-D joint self-iterating equalizer and detection system with noise prediction capability. We evaluate the system performance based on our channel model through simulations. The coded performance with the 2-D equalizer detector indicates similar to 5.5 dB of SNR gain over uncoded data.

Precoding-Based Network Alignment Using Transform Approach for Acyclic Networks With Delay

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)m-linear combination of the input symbols across different generations, where F(p)m denotes the field over which the network operates (p is prime and m is a positive integer). We use finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)m-linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three precoding-based network alignment (PBNA) schemes for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n' + 1/2n' + 1, n'/2n' + 1, and n'/2n' + 1 are achieved for the three source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n' is a positive integer. For PBNA using time-varying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three source-destination pairs in a 3-S 3-D MUN-D, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

Dictionary-Learning-Based Post-Filter for HMM-Based Speech Synthesis

Oversmoothing of speech parameter trajectories is one of the causes for quality degradation of HMM-based speech synthesis. Various methods have been proposed to overcome this effect, the most recent ones being global variance (GV) and modulation-spectrum-based post-filter (MSPF). However, there is still a significant quality gap between natural and synthesized speech. In this paper, we propose a two-fold post-filtering technique to alleviate to a certain extent the oversmoothing of spectral and excitation parameter trajectories of HMM-based speech synthesis. For the spectral parameters, we propose a sparse coding-based post-filter to match the trajectories of synthetic speech to that of natural speech, and for the excitation trajectory, we introduce a perceptually motivated post-filter. Experimental evaluations show quality improvement compared with existing methods.

A Bayesian wavelet-based multidimensional deconvolution with sub-band emphasis

This paper proposes a new algorithm for waveletbased multidimensional image deconvolution which employs subband-dependent minimization and the dual-tree complex wavelet transform in an iterative Bayesian framework. In addition, this algorithm employs a new prior instead of the popular ℓ1 norm, and is thus able to embed a learning scheme during the iteration which helps it to achieve better deconvolution results and faster convergence. © 2008 IEEE.

Compression of Chinese document images based on morphologic analysis and pattern matching

We propose a highly efficient content-lossless compression scheme for Chinese document images. The scheme combines morphologic analysis with pattern matching to cluster patterns. In order to achieve the error maps with minimal error numbers, the morphologic analysis is applied to decomposing and recomposing the Chinese character patterns. In the pattern matching, the criteria are adapted to the characteristics of Chinese characters. Since small-size components sometimes can be inserted into the blank spaces of large-size components, we can achieve small-size pattern library images. Arithmetic coding is applied to the final compression. Our method achieves much better compression performance than most alternative methods, and assures content-lossless reconstruction. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Beyond Watson and Crick : programming the self-assembly and reconfiguration of DNA nanostructures based on stacking interactions

Life is the result of the execution of molecular programs: like how an embryo is fated to become a human or a whale, or how a person’s appearance is inherited from their parents, many biological phenomena are governed by genetic programs written in DNA molecules. At the core of such programs is the highly reliable base pairing interaction between nucleic acids. DNA nanotechnology exploits the programming power of DNA to build artificial nanostructures, molecular computers, and nanomachines. In particular, DNA origami—which is a simple yet versatile technique that allows one to create various nanoscale shapes and patterns—is at the heart of the technology. In this thesis, I describe the development of programmable self-assembly and reconfiguration of DNA origami nanostructures based on a unique strategy: rather than relying on Watson-Crick base pairing, we developed programmable bonds via the geometric arrangement of stacking interactions, which we termed stacking bonds. We further demonstrated that such bonds can be dynamically reconfigurable.

The first part of this thesis describes the design and implementation of stacking bonds. Our work addresses the fundamental question of whether one can create diverse bond types out of a single kind of attractive interaction—a question first posed implicitly by Francis Crick while seeking a deeper understanding of the origin of life and primitive genetic code. For the creation of multiple specific bonds, we used two different approaches: binary coding and shape coding of geometric arrangement of stacking interaction units, which are called blunt ends. To construct a bond space for each approach, we performed a systematic search using a computer algorithm. We used orthogonal bonds to experimentally implement the connection of five distinct DNA origami nanostructures. We also programmed the bonds to control cis/trans configuration between asymmetric nanostructures.

The second part of this thesis describes the large-scale self-assembly of DNA origami into two-dimensional checkerboard-pattern crystals via surface diffusion. We developed a protocol where the diffusion of DNA origami occurs on a substrate and is dynamically controlled by changing the cationic condition of the system. We used stacking interactions to mediate connections between the origami, because of their potential for reconfiguring during the assembly process. Assembling DNA nanostructures directly on substrate surfaces can benefit nano/microfabrication processes by eliminating a pattern transfer step. At the same time, the use of DNA origami allows high complexity and unique addressability with six-nanometer resolution within each structural unit.

The third part of this thesis describes the use of stacking bonds as dynamically breakable bonds. To break the bonds, we used biological machinery called the ParMRC system extracted from bacteria. The system ensures that, when a cell divides, each daughter cell gets one copy of the cell’s DNA by actively pushing each copy to the opposite poles of the cell. We demonstrate dynamically expandable nanostructures, which makes stacking bonds a promising candidate for reconfigurable connectors for nanoscale machine parts.

Coding for information storage

Storage systems are widely used and have played a crucial rule in both consumer and industrial products, for example, personal computers, data centers, and embedded systems. However, such system suffers from issues of cost, restricted-lifetime, and reliability with the emergence of new systems and devices, such as distributed storage and flash memory, respectively. Information theory, on the other hand, provides fundamental bounds and solutions to fully utilize resources such as data density, information I/O and network bandwidth. This thesis bridges these two topics, and proposes to solve challenges in data storage using a variety of coding techniques, so that storage becomes faster, more affordable, and more reliable.

We consider the system level and study the integration of RAID schemes and distributed storage. Erasure-correcting codes are the basis of the ubiquitous RAID schemes for storage systems, where disks correspond to symbols in the code and are located in a (distributed) network. Specifically, RAID schemes are based on MDS (maximum distance separable) array codes that enable optimal storage and efficient encoding and decoding algorithms. With r redundancy symbols an MDS code can sustain r erasures. For example, consider an MDS code that can correct two erasures. It is clear that when two symbols are erased, one needs to access and transmit all the remaining information to rebuild the erasures. However, an interesting and practical question is: What is the smallest fraction of information that one needs to access and transmit in order to correct a single erasure? In Part I we will show that the lower bound of 1/2 is achievable and that the result can be generalized to codes with arbitrary number of parities and optimal rebuilding.

We consider the device level and study coding and modulation techniques for emerging non-volatile memories such as flash memory. In particular, rank modulation is a novel data representation scheme proposed by Jiang et al. for multi-level flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. It eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells. In order to decrease the decoding complexity, we propose two variations of this scheme in Part II: bounded rank modulation where only small sliding windows of cells are sorted to generated permutations, and partial rank modulation where only part of the n cells are used to represent data. We study limits on the capacity of bounded rank modulation and propose encoding and decoding algorithms. We show that overlaps between windows will increase capacity. We present Gray codes spanning all possible partial-rank states and using only ``push-to-the-top'' operations. These Gray codes turn out to solve an open combinatorial problem called universal cycle, which is a sequence of integers generating all possible partial permutations.

On erasure coding for distributed storage and streaming communications

The work presented in this thesis revolves around erasure correction coding, as applied to distributed data storage and real-time streaming communications.

First, we examine the problem of allocating a given storage budget over a set of nodes for maximum reliability. The objective is to find an allocation of the budget that maximizes the probability of successful recovery by a data collector accessing a random subset of the nodes. This optimization problem is challenging in general because of its combinatorial nature, despite its simple formulation. We study several variations of the problem, assuming different allocation models and access models, and determine the optimal allocation and the optimal symmetric allocation (in which all nonempty nodes store the same amount of data) for a variety of cases. Although the optimal allocation can have nonintuitive structure and can be difficult to find in general, our results suggest that, as a simple heuristic, reliable storage can be achieved by spreading the budget maximally over all nodes when the budget is large, and spreading it minimally over a few nodes when it is small. Coding would therefore be beneficial in the former case, while uncoded replication would suffice in the latter case.

Second, we study how distributed storage allocations affect the recovery delay in a mobile setting. Specifically, two recovery delay optimization problems are considered for a network of mobile storage nodes: the maximization of the probability of successful recovery by a given deadline, and the minimization of the expected recovery delay. We show that the first problem is closely related to the earlier allocation problem, and solve the second problem completely for the case of symmetric allocations. It turns out that the optimal allocations for the two problems can be quite different. In a simulation study, we evaluated the performance of a simple data dissemination and storage protocol for mobile delay-tolerant networks, and observed that the choice of allocation can have a significant impact on the recovery delay under a variety of scenarios.

Third, we consider a real-time streaming system where messages created at regular time intervals at a source are encoded for transmission to a receiver over a packet erasure link; the receiver must subsequently decode each message within a given delay from its creation time. For erasure models containing a limited number of erasures per coding window, per sliding window, and containing erasure bursts whose maximum length is sufficiently short or long, we show that a time-invariant intrasession code asymptotically achieves the maximum message size among all codes that allow decoding under all admissible erasure patterns. For the bursty erasure model, we also show that diagonally interleaved codes derived from specific systematic block codes are asymptotically optimal over all codes in certain cases. We also study an i.i.d. erasure model in which each transmitted packet is erased independently with the same probability; the objective is to maximize the decoding probability for a given message size. We derive an upper bound on the decoding probability for any time-invariant code, and show that the gap between this bound and the performance of a family of time-invariant intrasession codes is small when the message size and packet erasure probability are small. In a simulation study, these codes performed well against a family of random time-invariant convolutional codes under a number of scenarios.

Finally, we consider the joint problems of routing and caching for named data networking. We propose a backpressure-based policy that employs virtual interest packets to make routing and caching decisions. In a packet-level simulation, the proposed policy outperformed a basic protocol that combines shortest-path routing with least-recently-used (LRU) cache replacement.

Compression of Chinese document images based on morphologic analysis and pattern matching

We propose a highly efficient content-lossless compression scheme for Chinese document images. The scheme combines morphologic analysis with pattern matching to cluster patterns. In order to achieve the error maps with minimal error numbers, the morphologic analysis is applied to decomposing and recomposing the Chinese character patterns. In the pattern matching, the criteria are adapted to the characteristics of Chinese characters. Since small-size components sometimes can be inserted into the blank spaces of large-size components, we can achieve small-size pattern library images. Arithmetic coding is applied to the final compression. Our method achieves much better compression performance than most alternative methods, and assures content-lossless reconstruction. (c) 2006 Society of Photo-Optical Instrumentation Engineers.