arXiv subjects

Aditya Ramamoorthy

Publications and source records attributed to Aditya Ramamoorthy.

At least 55 records · Page 3Linked to original sources

arXiv2016

On Computation Rates for Arithmetic Sum

For zero-error function computation over directed acyclic networks, existing upper and lower bounds on the computation capacity are known to be loose. In this work we consider the problem of computing the arithmetic sum over a specific directed acyclic network that is not a tree. We assume the sources to be i.i.d. Bernoulli with parameter $1/2$. Even in this simple setting, we demonstrate that upper bounding the computation rate is quite nontrivial. In particular, it requires us to consider variable length network codes and relate the upper bound to equivalently lower bounding the entropy of descriptions observed by the terminal conditioned on the function value. This lower bound is obtained by further lower bounding the entropy of a so-called \textit{clumpy distribution}. We also demonstrate an achievable scheme that uses variable length network codes and in-network compression.

cs.IT↗

arXiv2015

Capacity of Sum-networks for Different Message Alphabets

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 $1$ to close to $0$.

cs.IT↗

arXiv2013

Replication based storage systems with local repair

We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving nodes and (b) the number of surviving nodes contacted is strictly smaller than the number of nodes that need to be contacted for reconstructing the stored file. Our codes consist of an outer MDS code and an inner fractional repetition code that specifies the placement of the encoded symbols on the storage nodes. For our class of codes, we identify the tradeoff between the local repair property and the minimum distance. We present codes based on graphs of high girth, affine resolvable designs and projective planes that meet the minimum distance bound for specific choices of file sizes.

cs.IT↗

arXiv2013

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

We consider the multiple unicast problem with three source-terminal pairs over directed acyclic networks with unit-capacity edges. The three $s_i-t_i$ pairs wish to communicate at unit-rate via network coding. The connectivity between the $s_i - t_i$ pairs is quantified by means of a connectivity level vector, $[k_1 k_2 k_3]$ such that there exist $k_i$ edge-disjoint paths between $s_i$ and $t_i$. 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 $k_i \geq 3$, for all $i = 1, \dots, 3$. In this work, we consider, connectivity level vectors such that $\min_{i = 1, \dots, 3} k_i < 3$. 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 $[1~2~4]$ (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.

cs.IT↗

arXiv2013

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

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.

cs.IT↗

arXiv2013

Communicating the sum of sources over a network

We consider the network communication scenario, over directed acyclic networks with unit capacity edges in which a number of sources $s_i$ each holding independent unit-entropy information $X_i$ wish to communicate the sum $\sum{X_i}$ to a set of terminals $t_j$. We show that in the case in which there are only two sources or only two terminals, communication is possible if and only if each source terminal pair $s_i/t_j$ is connected by at least a single path. For the more general communication problem in which there are three sources and three terminals, we prove that a single path connecting the source terminal pairs does not suffice to communicate $\sum{X_i}$. We then present an efficient encoding scheme which enables the communication of $\sum{X_i}$ for the three sources, three terminals case, given that each source terminal pair is connected by {\em two} edge disjoint paths.

cs.IT↗

arXiv2012

Repairable Replication-based Storage Systems Using Resolvable Designs

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 $β\geq 1$ packets from a subset of the surviving nodes (prior work only considered the case of $β= 1$). 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.

cs.IT↗

arXiv2011

An achievable region for the double unicast problem based on a minimum cut analysis

We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, $s_1-t_1$ and $s_2-t_2$. Current characterizations of the multiple unicast capacity region in this setting have a large number of inequalities, which makes them hard to explicitly evaluate. In this work we consider a slightly different problem. We assume that we only know certain minimum cut values for the network, e.g., mincut$(S_i, T_j)$, where $S_i \subseteq \{s_1, s_2\}$ and $T_j \subseteq \{t_1, t_2\}$ for different subsets $S_i$ and $T_j$. Based on these values, we propose an achievable rate region for this problem based on linear codes. Towards this end, we begin by defining a base region where both sources are multicast to both the terminals. Following this we enlarge the region by appropriately encoding the information at the source nodes, such that terminal $t_i$ is only guaranteed to decode information from the intended source $s_i$, while decoding a linear function of the other source. The rate region takes different forms depending upon the relationship of the different cut values in the network.

cs.IT↗

arXiv2011

Degrees of Freedom Region for an Interference Network with General Message Demands

We consider a single hop interference network with $K$ transmitters and $J$ receivers, all having $M$ antennas. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. This generalizes the well-known $K$-user $M$-antenna interference channel, where each message is requested by a unique receiver. For our setup, we derive the degrees of freedom (DoF) region. The achievability scheme generalizes the interference alignment schemes proposed by Cadambe and Jafar. In particular, we achieve general points in the DoF region by using multiple base vectors and aligning all interferers at a given receiver to the interferer with the largest DoF. As a byproduct, we obtain the DoF region for the original interference channel. We also discuss extensions of our approach where the same region can be achieved by considering a reduced set of interference alignment constraints, thus reducing the time-expansion duration needed. The DoF region for the considered system depends only on a subset of receivers whose demands meet certain characteristics. The geometric shape of the DoF region is also discussed.

cs.IT↗

arXiv2011

Algebraic codes for Slepian-Wolf code design

Practical constructions of lossless distributed source codes (for the Slepian-Wolf problem) have been the subject of much investigation in the past decade. In particular, near-capacity achieving code designs based on LDPC codes have been presented for the case of two binary sources, with a binary-symmetric correlation. However, constructing practical codes for the case of non-binary sources with arbitrary correlation remains by and large open. From a practical perspective it is also interesting to consider coding schemes whose performance remains robust to uncertainties in the joint distribution of the sources. In this work we propose the usage of Reed-Solomon (RS) codes for the asymmetric version of this problem. We show that algebraic soft-decision decoding of RS codes can be used effectively under certain correlation structures. In addition, RS codes offer natural rate adaptivity and performance that remains constant across a family of correlation structures with the same conditional entropy. The performance of RS codes is compared with dedicated and rate adaptive multistage LDPC codes (Varodayan et al. '06), where each LDPC code is used to compress the individual bit planes. Our simulations show that in classical Slepian-Wolf scenario, RS codes outperform both dedicated and rate-adaptive LDPC codes under $q$-ary symmetric correlation, and are better than rate-adaptive LDPC codes in the case of sparse correlation models, where the conditional distribution of the sources has only a few dominant entries. In a feedback scenario, the performance of RS codes is comparable with both designs of LDPC codes. Our simulations also demonstrate that the performance of RS codes in the presence of inaccuracies in the joint distribution of the sources is much better as compared to multistage LDPC codes.

cs.IT↗

arXiv2011

A note on the multiple unicast capacity of directed acyclic networks

We consider the multiple unicast problem under network coding over directed acyclic networks with unit capacity edges. There is a set of n source-terminal (s_i - t_i) pairs that wish to communicate at unit rate over this network. The connectivity between the s_i - t_i pairs is quantified by means of a connectivity level vector, [k_1 k_2 ... k_n] such that there exist k_i edge-disjoint paths between s_i and t_i. Our main aim is to characterize the feasibility of achieving this for different values of n and [k_1 ... k_n]. For 3 unicast connections (n = 3), we characterize several achievable and unachievable values of the connectivity 3-tuple. In addition, in this work, we have found certain network topologies, and capacity characterizations that are useful in understanding the case of general n.

cs.IT↗

arXiv2010

Overlay Protection Against Link Failures Using Network Coding

This paper introduces a network coding-based protection scheme against single and multiple link failures. The proposed strategy ensures that in a connection, each node receives two copies of the same data unit: one copy on the working circuit, and a second copy that can be extracted from linear combinations of data units transmitted on a shared protection path. This guarantees instantaneous recovery of data units upon the failure of a working circuit. The strategy can be implemented at an overlay layer, which makes its deployment simple and scalable. While the proposed strategy is similar in spirit to the work of Kamal '07 & '10, there are significant differences. In particular, it provides protection against multiple link failures. The new scheme is simpler, less expensive, and does not require the synchronization required by the original scheme. The sharing of the protection circuit by a number of connections is the key to the reduction of the cost of protection. The paper also conducts a comparison of the cost of the proposed scheme to the 1+1 and shared backup path protection (SBPP) strategies, and establishes the benefits of our strategy.

cs.IT↗

arXiv2010

Improved Combinatorial Algorithms for Wireless Information Flow

The work of Avestimehr et al. '07 has recently proposed a deterministic model for wireless networks and characterized the unicast capacity C of such networks as the minimum rank of the adjacency matrices describing all possible source-destination cuts. Amaudruz & Fragouli first proposed a polynomial-time algorithm for finding the unicast capacity of a linear deterministic wireless network in their 2009 paper. In this work, we improve upon Amaudruz & Fragouli's work and further reduce the computational complexity of the algorithm by fully exploring the useful combinatorial features intrinsic in the problem. Our improvement applies generally with any size of finite fields associated with the channel model. Comparing with other algorithms on solving the same problem, our improved algorithm is very competitive in terms of complexity.

cs.IT↗

arXiv2010

Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes

Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of a given storage solution is defined as the sum of the storage cost and the cost of the flows required to support the multicast. Our interest is in finding the storage capacities and flows at minimum combined cost. We formulate the corresponding optimization problems by using the theory of information measures. In particular, we show that when there are two source nodes, there is no loss in considering subset sources. For three source nodes, we derive a tight upper bound on the cost gap between the coded and uncoded cases. We also present algorithms for determining the content of the source nodes.

cs.IT↗

arXiv2010

Protection against link errors and failures using network coding

We propose a network-coding based scheme to protect multiple bidirectional unicast connections against adversarial errors and failures in a network. The network consists of a set of bidirectional primary path connections that carry the uncoded traffic. The end nodes of the bidirectional connections are connected by a set of shared protection paths that provide the redundancy required for protection. Such protection strategies are employed in the domain of optical networks for recovery from failures. In this work we consider the problem of simultaneous protection against adversarial errors and failures. Suppose that n_e paths are corrupted by the omniscient adversary. Under our proposed protocol, the errors can be corrected at all the end nodes with 4n_e protection paths. More generally, if there are n_e adversarial errors and n_f failures, 4n_e + 2n_f protection paths are sufficient. The number of protection paths only depends on the number of errors and failures being protected against and is independent of the number of unicast connections.

cs.IT↗

arXiv2010

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

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.

cs.IT↗

arXiv2010

Performance evaluation for ML sequence detection in ISI channels with Gauss Markov Noise

Inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been used to model read channels in magnetic recording and other data storage systems. The Viterbi algorithm can be adapted for performing maximum likelihood sequence detection in such channels. However, the problem of finding an analytical upper bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. Current techniques rely on an exhaustive enumeration of short error events and determine the BER using a union bound. In this work, we consider a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive an upper bound on the pairwise error probability (PEP) between the transmitted bit sequence and the decoded bit sequence that can be expressed as a product of functions depending on current and previous states in the (incorrect) decoded sequence and the (correct) transmitted sequence. In general, the PEP is asymmetric. The average BER over all possible bit sequences is then determined using a pairwise state diagram. Simulations results which corroborate the analysis of upper bound, demonstrate that analytic bound on BER is tight in high SNR regime. In the high SNR regime, our proposed upper bound obviates the need for computationally expensive simulation.

cs.IT↗

arXiv2010

Improved compression of network coding vectors using erasure decoding and list decoding

Practical random network coding based schemes for multicast include a header in each packet that records the transformation between the sources and the terminal. The header introduces an overhead that can be significant in certain scenarios. In previous work, parity check matrices of error control codes along with error decoding were used to reduce this overhead. In this work we propose novel packet formats that allow us to use erasure decoding and list decoding. Both schemes have a smaller overhead compared to the error decoding based scheme, when the number of sources combined in a packet is not too small.

cs.IT↗