arXiv subjects

Bikash Kumar Dey

Publications and source records attributed to Bikash Kumar Dey.

45 records · Page 3Linked to original sources

arXiv2009

Estimating Network Link Characteristics using Packet-Pair Dispersion: A Discrete Time Queueing Theoretic View

Packet-dispersion based measurement tools insert pairs of probe packets with a known separation into the network for transmission over a unicast path or a multicast tree. Samples of the separation between the probe pairs at the destination(s) are observed. Heuristic techniques are then used by these tools to estimate the path characteristics from the observations. In this paper we present a queueing theoretic setting for packet-dispersion based probing. Analogous to network tomography, we develop techniques to estimate the parameters of the arrival process to the individual links from the samples of the output separations, i.e., from the end-to-end measurements. The links are modeled as independent discrete time queues with i.i.d. arrivals. We first obtain an algorithm to obtain the (joint) distribution of the separation between the probes at the destination(s) for a given distribution of the spacing at the input. The parameter estimates of the arrival process are obtained as the minimizer of a cost function between the empirical and calculated distributions. We also carry out extensive simulations and numerical experiments to study the performance of the estimation algorithm under the fairly `harsh' conditions of non stationarity of the arrival process. We find that the estimations work fairly well for two queues in series and for multicast.

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arXiv2009

Some bounds on the capacity of communicating the sum of sources

We consider directed acyclic networks with multiple sources and multiple terminals where each source generates one i.i.d. random process over an abelian group and all the terminals want to recover the sum of these random processes. The different source processes are assumed to be independent. The solvability of such networks has been considered in some previous works. In this paper we investigate on the capacity of such networks, referred as {\it sum-networks}, and present some bounds in terms of min-cut, and the numbers of sources and terminals.

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arXiv2009

A Channel Coding Perspective of Collaborative Filtering

We consider the problem of collaborative filtering from a channel coding perspective. We model the underlying rating matrix as a finite alphabet matrix with block constant structure. The observations are obtained from this underlying matrix through a discrete memoryless channel with a noisy part representing noisy user behavior and an erasure part representing missing data. Moreover, the clusters over which the underlying matrix is constant are {\it unknown}. We establish a sharp threshold result for this model: if the largest cluster size is smaller than $C_1 \log(mn)$ (where the rating matrix is of size $m \times n$), then the underlying matrix cannot be recovered with any estimator, but if the smallest cluster size is larger than $C_2 \log(mn)$, then we show a polynomial time estimator with diminishing probability of error. In the case of uniform cluster size, not only the order of the threshold, but also the constant is identified.

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arXiv2009

Binary Causal-Adversary Channels

In this work we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=(x_1,...,x_n) bit-by-bit over a communication channel. The adversarial jammer can view the transmitted bits x_i one at a time, and can change up to a p-fraction of them. However, the decisions of the jammer must be made in an online or causal manner. Namely, for each bit x_i the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on x_j for j <= i. This is in contrast to the "classical" adversarial jammer which may base its decisions on its complete knowledge of x. We present a non-trivial upper bound on the amount of information that can be communicated. We show that the achievable rate can be asymptotically no greater than min{1-H(p),(1-4p)^+}. Here H(.) is the binary entropy function, and (1-4p)^+ equals 1-4p for p < 0.25, and 0 otherwise.

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arXiv2009

Feasible alphabets for communicating the sum of sources over a network

We consider directed acyclic {\em sum-networks} with $m$ sources and $n$ terminals where the sources generate symbols from an arbitrary alphabet field $F$, and the terminals need to recover the sum of the sources over $F$. We show that for any co-finite set of primes, there is a sum-network which is solvable only over fields of characteristics belonging to that set. We further construct a sum-network where a scalar solution exists over all fields other than the binary field $F_2$. We also show that a sum-network is solvable over a field if and only if its reverse network is solvable over the same field.

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arXiv2009

A Channel Coding Perspective of Recommendation Systems

Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix after unknown row and column permutations, erasures, and errors. We derive upper and lower bounds on the achievable probability of error. For fixed erasure and error probability, we show that there exists a constant $C_1$ such that if the cluster sizes are less than $C_1 \ln(mn)$, then for any algorithm the probability of error approaches one as $m, n \tends \infty$. On the other hand, we show that a simple polynomial time algorithm gives probability of error diminishing to zero provided the cluster sizes are greater than $C_2 \ln(mn)$ for a suitable constant $C_2$.

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arXiv2008

Codes against Online Adversaries

In this work we consider the communication of information in the presence of an online adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=x_1,...,x_n symbol-by-symbol over a communication channel. The adversarial jammer can view the transmitted symbols x_i one at a time, and can change up to a p-fraction of them. However, the decisions of the jammer must be made in an online or causal manner. More generally, for a delay parameter 0<d<1, we study the scenario in which the jammer's decision on the corruption of x_i must depend solely on x_j for j < i - dn. In this work, we initiate the study of codes for online adversaries, and present a tight characterization of the amount of information one can transmit in both the 0-delay and, more generally, the d-delay online setting. We prove tight results for both additive and overwrite jammers when the transmitted symbols are assumed to be over a sufficiently large field F. Finally, we extend our results to a jam-or-listen online model, where the online adversary can either jam a symbol or eavesdrop on it. We again provide a tight characterization of the achievable rate for several variants of this model. The rate-regions we prove for each model are informational-theoretic in nature and hold for computationally unbounded adversaries. The rate regions are characterized by "simple" piecewise linear functions of p and d. The codes we construct to attain the optimal rate for each scenario are computationally efficient.

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arXiv2008

Some results on communicating the sum of sources over a network

We consider the problem of communicating the sum of $m$ sources to $n$ terminals in a directed acyclic network. Recently, it was shown that for a network of unit capacity links with either $m=2$ or $n=2$, the sum of the sources can be communicated to the terminals if and only if every source-terminal pair is connected in the network. We show in this paper that for any finite set of primes, there exists a network where the sum of the sources can be communicated to the terminals only over finite fields of characteristic belonging to that set. As a corollary, this gives networks where the sum can not be communicated over any finite field even though every source is connected to every terminal.

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arXiv2008

"Real" Slepian-Wolf Codes

We provide a novel achievability proof of the Slepian-Wolf theorem for i.i.d. sources over finite alphabets. We demonstrate that random codes that are linear over the real field achieve the classical Slepian-Wolf rate-region. For finite alphabets we show that typicality decoding is equivalent to solving an integer program. Minimum entropy decoding is also shown to achieve exponentially small probability of error. The techniques used may be of independent interest for code design for a wide class of information theory problems, and for the field of compressed sensing.

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