198 research outputs found

    PREMIER - PRobabilistic Error-correction using Markov Inference in Errored Reads

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    In this work we present a flexible, probabilistic and reference-free method of error correction for high throughput DNA sequencing data. The key is to exploit the high coverage of sequencing data and model short sequence outputs as independent realizations of a Hidden Markov Model (HMM). We pose the problem of error correction of reads as one of maximum likelihood sequence detection over this HMM. While time and memory considerations rule out an implementation of the optimal Baum-Welch algorithm (for parameter estimation) and the optimal Viterbi algorithm (for error correction), we propose low-complexity approximate versions of both. Specifically, we propose an approximate Viterbi and a sequential decoding based algorithm for the error correction. Our results show that when compared with Reptile, a state-of-the-art error correction method, our methods consistently achieve superior performances on both simulated and real data sets.Comment: Submitted to ISIT 201

    Maximum-Likelihood Sequence Detector for Dynamic Mode High Density Probe Storage

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    There is an increasing need for high density data storage devices driven by the increased demand of consumer electronics. In this work, we consider a data storage system that operates by encoding information as topographic profiles on a polymer medium. A cantilever probe with a sharp tip (few nm radius) is used to create and sense the presence of topographic profiles, resulting in a density of few Tb per in.2. The prevalent mode of using the cantilever probe is the static mode that is harsh on the probe and the media. In this article, the high quality factor dynamic mode operation, that is less harsh on the media and the probe, is analyzed. The read operation is modeled as a communication channel which incorporates system memory due to inter-symbol interference and the cantilever state. We demonstrate an appropriate level of abstraction of this complex nanoscale system that obviates the need for an involved physical model. Next, a solution to the maximum likelihood sequence detection problem based on the Viterbi algorithm is devised. Experimental and simulation results demonstrate that the performance of this detector is several orders of magnitude better than the performance of other existing schemes.Comment: This paper is published in IEEE Trans. on communicatio

    Capacity of Sum-networks for Different Message Alphabets

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    A sum-network is a directed acyclic network in which all terminal nodes demand the `sum' of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem also hold for sum-networks due to a known reduction between instances of these two problems. Our main result is that unlike a multiple unicast network, the coding capacity of a sum-network is dependent on the message alphabet. We demonstrate this using a construction procedure and show that the choice of a message alphabet can reduce the coding capacity of a sum-network from 11 to close to 00

    On the multiple unicast capacity of 3-source, 3-terminal directed acyclic networks

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    We consider the multiple unicast problem with three source-terminal pairs over directed acyclic networks with unit-capacity edges. The three si‚ąítis_i-t_i pairs wish to communicate at unit-rate via network coding. The connectivity between the si‚ąítis_i - t_i pairs is quantified by means of a connectivity level vector, [k1k2k3][k_1 k_2 k_3] such that there exist kik_i edge-disjoint paths between sis_i and tit_i. In this work we attempt to classify networks based on the connectivity level. It can be observed that unit-rate transmission can be supported by routing if ki‚Č•3k_i \geq 3, for all i=1,‚Ķ,3i = 1, \dots, 3. In this work, we consider, connectivity level vectors such that min‚Ā°i=1,‚Ķ,3ki<3\min_{i = 1, \dots, 3} k_i < 3. We present either a constructive linear network coding scheme or an instance of a network that cannot support the desired unit-rate requirement, for all such connectivity level vectors except the vector [1¬†2¬†4][1~2~4] (and its permutations). The benefits of our schemes extend to networks with higher and potentially different edge capacities. Specifically, our experimental results indicate that for networks where the different source-terminal paths have a significant overlap, our constructive unit-rate schemes can be packed along with routing to provide higher throughput as compared to a pure routing approach.Comment: To appear in the IEEE/ACM Transactions on Networkin

    Leveraging Coding Techniques for Speeding up Distributed Computing

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    Large scale clusters leveraging distributed computing frameworks such as MapReduce routinely process data that are on the orders of petabytes or more. The sheer size of the data precludes the processing of the data on a single computer. The philosophy in these methods is to partition the overall job into smaller tasks that are executed on different servers; this is called the map phase. This is followed by a data shuffling phase where appropriate data is exchanged between the servers. The final so-called reduce phase, completes the computation. One potential approach, explored in prior work for reducing the overall execution time is to operate on a natural tradeoff between computation and communication. Specifically, the idea is to run redundant copies of map tasks that are placed on judiciously chosen servers. The shuffle phase exploits the location of the nodes and utilizes coded transmission. The main drawback of this approach is that it requires the original job to be split into a number of map tasks that grows exponentially in the system parameters. This is problematic, as we demonstrate that splitting jobs too finely can in fact adversely affect the overall execution time. In this work we show that one can simultaneously obtain low communication loads while ensuring that jobs do not need to be split too finely. Our approach uncovers a deep relationship between this problem and a class of combinatorial structures called resolvable designs. Appropriate interpretation of resolvable designs can allow for the development of coded distributed computing schemes where the splitting levels are exponentially lower than prior work. We present experimental results obtained on Amazon EC2 clusters for a widely known distributed algorithm, namely TeraSort. We obtain over 4.69√ó\times improvement in speedup over the baseline approach and more than 2.6√ó\times over current state of the art

    Repairable Replication-based Storage Systems Using Resolvable Designs

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    We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair process that is exact and uncoded, but table-based. These codes were introduced in prior work and consist of an outer MDS code followed by an inner fractional repetition (FR) code where copies of the coded symbols are placed on the storage nodes. The main challenge in this domain is the design of the inner FR code. In our work, we consider generalizations of FR codes, by establishing their connection with a family of combinatorial structures known as resolvable designs. Our constructions based on affine geometries, Hadamard designs and mutually orthogonal Latin squares allow the design of systems where a new node can be exactly regenerated by downloading ő≤‚Č•1\beta \geq 1 packets from a subset of the surviving nodes (prior work only considered the case of ő≤=1\beta = 1). Our techniques allow the design of systems over a large range of parameters. Specifically, the repetition degree of a symbol, which dictates the resilience of the system can be varied over a large range in a simple manner. Moreover, the actual table needed for the repair can also be implemented in a rather straightforward way. Furthermore, we answer an open question posed in prior work by demonstrating the existence of codes with parameters that are not covered by Steiner systems
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