arXiv subjects

Ashish Khisti

Publications and source records attributed to Ashish Khisti.

At least 73 records · Page 4Linked to original sources

arXiv2017

Product Matrix MSR Codes with Bandwidth Adaptive Exact Repair

In a distributed storage systems (DSS) with $k$ systematic nodes, robustness against node failure is commonly provided by storing redundancy in a number of other nodes and performing repair mechanism to reproduce the content of the failed nodes. Efficiency is then achieved by minimizing the storage overhead and the amount of data transmission required for data reconstruction and repair, provided by coding solutions such as regenerating codes [1]. Common explicit regenerating code constructions enable efficient repair through accessing a predefined number, $d$, of arbitrary chosen available nodes, namely helpers. In practice, however, the state of the system dynamically changes based on the request load, the link traffic, etc., and the parameters which optimize system's performance vary accordingly. It is then desirable to have coding schemes which are able to operate optimally under a range of different parameters simultaneously. Specifically, adaptivity in the number of helper nodes for repair is of interest. While robustness requires capability of performing repair with small number of helpers, it is desirable to use as many helpers as available to reduce the transmission delay and total repair traffic. In this work we focus on the minimum storage regenerating (MSR) codes, where each node is supposed to store $α$ information units, and the source data of size $kα$ could be recovered from any arbitrary set of $k$ nodes. We introduce a class MSR codes that realize optimal repair bandwidth simultaneously with a set of different choices for the number of helpers, namely $D=\{d_{1}, \cdots, d_δ\}$. Our coding scheme follows the Product Matrix (PM) framework introduced in [2], and could be considered as a generalization of the PM MSR code presented in [2], such that any $d_{i} = (i+1)(k-1)$ helpers can perform an optimal repair. ...

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arXiv2017

Product Matrix Minimum Storage Regenerating Codes with Flexible Number of Helpers

In coding for distributed storage systems, efficient data reconstruction and repair through accessing a predefined number of arbitrarily chosen storage nodes is guaranteed by regenerating codes. Traditionally, code parameters, specially the number of helper nodes participating in a repair process, are predetermined. However, depending on the state of the system and network traffic, it is desirable to adapt such parameters accordingly in order to minimize the cost of repair. In this work a class of regenerating codes with minimum storage is introduced that can simultaneously operate at the optimal repair bandwidth, for a wide range of exact repair mechanisms, based on different number of helper nodes.

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arXiv2017

Bandwidth Adaptive & Error Resilient MBR Exact Repair Regenerating Codes

Regenerating codes are efficient methods for distributed storage in storage networks, where node failures are common. They guarantee low cost data reconstruction and repair through accessing only a predefined number of arbitrarily chosen storage nodes in the network. In this work we consider two simultaneous extensions to the original regenerating codes framework introduced in [1]; i) both data reconstruction and repair are resilient to the presence of a certain number of erroneous nodes in the network and ii) the number of helper nodes in every repair is not fixed, but is a flexible parameter that can be selected during the runtime. We study the fundamental limits of required total repair bandwidth and provide an upper bound for the storage capacity of these codes under these assumptions. We then focus on the minimum repair bandwidth (MBR) case and derive the exact storage capacity by presenting explicit coding schemes with exact repair, which achieve the upper bound of the storage capacity in the considered setup. To this end, we first provide a more natural extension of the well-known Product Matrix (PM) MBR codes [2], modified to provide flexibility in the choice of number of helpers in each repair, and simultaneously be robust to erroneous nodes in the network. This is achieved by proving the non-singularity of family of matrices in large enough finite fields. We next provide another extension of the PM codes, based on novel repair schemes which enable flexibility in the number of helpers and robustness against erroneous nodes without any extra cost in field size compared to the original PM codes.

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arXiv2017

Information-Theoretic Privacy for Smart Metering Systems with a Rechargeable Battery

Smart-metering systems report electricity usage of a user to the utility provider on almost real-time basis. This could leak private information about the user to the utility provider. In this work we investigate the use of a rechargeable battery in order to provide privacy to the user. We assume that the user load sequence is a first-order Markov process, the battery satisfies ideal charge conservation, and that privacy is measured using normalized mutual information (leakage rate) between the user load and the battery output. We consider battery charging policies in this setup that satisfy the feasibility constraints. We propose a series reductions on the original problem and ultimately recast it as a Markov Decision Process (MDP) that can be solved using a dynamic program. In the special case of i.i.d. demand, we explicitly characterize the optimal policy and show that the associated leakage rate can be expressed as a single-letter mutual information expression. In this case we show that the optimal charging policy admits an intuitive interpretation of preserving a certain invariance property of the state. Interestingly an alternative proof of optimality can be provided that does not rely on the MDP approach, but is based on purely information theoretic reductions.

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arXiv2017

Covert Communication with Channel-State Information at the Transmitter

We consider the problem of covert communication over a state-dependent channel, where the transmitter has causal or noncausal knowledge of the channel states. Here, "covert" means that a warden on the channel should observe similar statistics when the transmitter is sending a message and when it is not. When a sufficiently long secret key is shared between the transmitter and the receiver, we derive closed-form formulas for the maximum achievable covert communication rate ("covert capacity") for discrete memoryless channels and, when the transmitter's channel-state information (CSI) is noncausal, for additive white Gaussian noise (AWGN) channels. For certain channel models, including the AWGN channel, we show that the covert capacity is positive with CSI at the transmitter, but is zero without CSI. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.

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arXiv2016

The MIMO Wiretap Channel Decomposed

The problem of sending a secret message over the Gaussian multiple-input multiple-output (MIMO) wiretap channel is studied. While the capacity of this channel is known, it is not clear how to construct optimal coding schemes that achieve this capacity. In this work, we use linear operations along with successive interference cancellation to attain effective parallel single-antenna wiretap channels. By using independent scalar Gaussian wiretap codebooks over the resulting parallel channels, the capacity of the MIMO wiretap channel is achieved. The derivation of the schemes is based upon joint triangularization of the channel matrices. We find that the same technique can be used to re-derive capacity expressions for the MIMO wiretap channel in a way that is simple and closely connected to a transmission scheme. This technique allows to extend the previously proven strong security for scalar Gaussian channels to the MIMO case. We further consider the problem of transmitting confidential messages over a two-user broadcast MIMO channel. For that problem, we find that derivation of both the capacity and a transmission scheme is a direct corollary of the proposed analysis for the MIMO wiretap channel.

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arXiv2016

The Wiretapped Diamond-Relay Channel

In this paper, we study a diamond-relay channel where the source is connected to $M$ relays through orthogonal links and the relays transmit to the destination over a wireless multiple-access channel in the presence of an eavesdropper. The eavesdropper not only observes the relay transmissions through another multiple-access channel, but also observes a certain number of source-relay links. The legitimate terminals know neither the eavesdropper's channel state information nor the location of source-relay links revealed to the eavesdropper except the total number of such links. For this wiretapped diamond-relay channel, we establish the optimal secure degrees of freedom. In the achievability part, our proposed scheme uses the source-relay links to transmit a judiciously constructed combination of message symbols, artificial noise symbols as well as fictitious message symbols associated with secure network coding. The relays use a combination of beamforming and interference alignment in their transmission scheme. For the converse part, we take a genie-aided approach assuming that the location of wiretapped links is known.

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arXiv2016

Exact Moderate Deviation Asymptotics in Streaming Data Transmission

In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of $T$ blocks. In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels, the moderate deviations constant is shown to improve over the block coding or non-streaming setup by exactly a factor of $T$ for a certain range of moderate deviations scalings. For the converse proof, a more powerful decoder to which some extra information is fedforward is assumed. The error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change-of-measure lemma, where the speed of decay of the remainder term in the exponent is carefully characterized. For the achievability proof, a known coding technique that involves a joint encoding and decoding of fresh and past messages is applied with some manipulations in the error analysis.

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arXiv2016

Convolutional Codes with Maximum Column Sum Rank for Network Streaming

The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several known column Hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction involves finding a class of super-regular matrices that preserve this property after multiplication with non-singular block diagonal matrices in the ground field.

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arXiv2015

Secure Degrees of Freedom of the Gaussian Diamond-Wiretap Channel

In this paper, we consider the Gaussian diamond-wiretap channel that consists of an orthogonal broadcast channel from a source to two relays and a Gaussian fast-fading multiple access-wiretap channel from the two relays to a legitimate destination and an eavesdropper. For the multiple access part, we consider both the case with full channel state information (CSI) and the case with no eavesdropper's CSI, at the relays and the legitimate destination. For both the cases, we establish the exact secure degrees of freedom and generalize the results for multiple relays. For the converse part, we introduce a new technique of capturing the trade-off between the message rate and the amount of individual randomness injected at each relay. In the achievability part, we show (i) how to strike a balance between sending message symbols and common noise symbols from the source to the relays in the broadcast component and (ii) how to combine artificial noise-beamforming and noise-alignment techniques at the relays in the multiple access component. In the case with full CSI, we propose a scheme where the relays simultaneously beamform common noise signals in the null space of the legitimate destination's channel, and align them with the message signals at the eavesdropper. In the case with no eavesdropper's CSI, we present a scheme that efficiently utilizes the broadcast links by incorporating computation between the message and common noise symbols at the source. Finally, most of our achievability and converse techniques can also be adapted to the Gaussian (non-fading) channel model.

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arXiv2015

Streaming Data Transmission in the Moderate Deviations and Central Limit Regimes

We consider streaming data transmission over a discrete memoryless channel. A new message is given to the encoder at the beginning of each block and the decoder decodes each message sequentially, after a delay of $T$ blocks. In this streaming setup, we study the fundamental interplay between the rate and error probability in the central limit and moderate deviations regimes and show that i) in the moderate deviations regime, the moderate deviations constant improves over the block coding or non-streaming setup by a factor of $T$ and ii) in the central limit regime, the second-order coding rate improves by a factor of approximately $\sqrt{T}$ for a wide range of channel parameters. For both regimes, we propose coding techniques that incorporate a joint encoding of fresh and previous messages. In particular, for the central limit regime, we propose a coding technique with truncated memory to ensure that a summation of constants, which arises as a result of applications of the central limit theorem, does not diverge in the error analysis. Furthermore, we explore interesting variants of the basic streaming setup in the moderate deviations regime. We first consider a scenario with an erasure option at the decoder and show that both the exponents of the total error and the undetected error probabilities improve by factors of $T$. Next, by utilizing the erasure option, we show that the exponent of the total error probability can be improved to that of the undetected error probability (in the order sense) at the expense of a variable decoding delay. Finally, we also extend our results to the case where the message rate is not fixed but alternates between two values.

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arXiv2015

The Degraded Gaussian Diamond-Wiretap Channel

In this paper, we present nontrivial upper and lower bounds on the secrecy capacity of the degraded Gaussian diamond-wiretap channel and identify several ranges of channel parameters where these bounds coincide with useful intuitions. Furthermore, we investigate the effect of the presence of an eavesdropper on the capacity. We consider the following two scenarios regarding the availability of randomness: 1) a common randomness is available at the source and the two relays and 2) a randomness is available only at the source and there is no available randomness at the relays. We obtain the upper bound by taking into account the correlation between the two relay signals and the availability of randomness at each encoder. For the lower bound, we propose two types of coding schemes: 1) a decode-and-forward scheme where the relays cooperatively transmit the message and the fictitious message and 2) a partial DF scheme incorporated with multicoding in which each relay sends an independent partial message and the whole or partial fictitious message using dependent codewords.

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arXiv2014

Zero-Delay Sequential Transmission of Markov Sources Over Burst Erasure Channels

A setup involving zero-delay sequential transmission of a vector Markov source over a burst erasure channel is studied. A sequence of source vectors is compressed in a causal fashion at the encoder, and the resulting output is transmitted over a burst erasure channel. The destination is required to reconstruct each source vector with zero-delay, but those source sequences that are observed either during the burst erasure, or in the interval of length $W$ following the burst erasure need not be reconstructed. The minimum achievable compression rate is called the rate-recovery function. We assume that each source vector is sampled i.i.d. across the spatial dimension and from a stationary, first-order Markov process across the temporal dimension. For discrete sources the case of lossless recovery is considered, and upper and lower bounds on the rate-recovery function are established. Both these bounds can be expressed as the rate for predictive coding, plus a term that decreases at least inversely with the recovery window length $W$. For Gauss-Markov sources and a quadratic distortion measure, upper and lower bounds on the minimum rate are established when $W=0$. These bounds are shown to coincide in the high resolution limit. Finally another setup involving i.i.d. Gaussian sources is studied and the rate-recovery function is completely characterized in this case.

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arXiv2014

The Streaming-DMT of Fading Channels

We consider the sequential transmission of a stream of messages over a block-fading multi-input-multi-output (MIMO) channel. A new message arrives at the beginning of each coherence block, and the decoder is required to output each message sequentially, after a delay of $T$ coherence blocks. In the special case when $T=1$, the setup reduces to the quasi-static fading channel. We establish the optimal diversity-multiplexing tradeoff (DMT) in the high signal-to-noise-ratio (SNR) regime, and show that it equals $T$ times the DMT of the quasi-static channel. The converse is based on utilizing the delay constraint to amplify a local outage event associated with a message, globally across all the coherence blocks. This approach appears to be new. We propose two coding schemes that achieve the optimal DMT. The first scheme involves interleaving of messages, such that each message is transmitted across $T$ consecutive coherence blocks. This scheme requires the knowledge of the delay constraint at both the encoder and decoder. Our second coding scheme involves a sequential tree code and is delay-universal i.e., the knowledge of the decoding delay is not required by the encoder. However, in this scheme we require the coherence block-length to increase as $\log\mathrm{({SNR})}$, in order to attain the optimal DMT. Finally, we discuss the case when multiple messages arrive at uniform intervals {\em within} each coherence period. Through a simple example we exhibit the sub-optimality of interleaving, and propose another scheme that achieves the optimal DMT.

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arXiv2014

Parallel Gaussian Networks with a Common State-Cognitive Helper

A class of state-dependent parallel networks with a common state-cognitive helper, in which $K$ transmitters wish to send $K$ messages to their corresponding receivers over $K$ state-corrupted parallel channels, and a helper who knows the state information noncausally wishes to assist these receivers to cancel state interference. Furthermore, the helper also has its own message to be sent simultaneously to its corresponding receiver. Since the state information is known only to the helper, but not to the corresponding transmitters $1,\dots,K$, transmitter-side state cognition and receiver-side state interference are mismatched. Our focus is on the high state power regime, i.e., the state power goes to infinity. Three (sub)models are studied. Model I serves as a basic model, which consists of only one transmitter-receiver (with state corruption) pair in addition to a helper that assists the receiver to cancel state in addition to transmitting its own message. Model II consists of two transmitter-receiver pairs in addition to a helper, and only one receiver is interfered by a state sequence. Model III generalizes model I include multiple transmitter-receiver pairs with each receiver corrupted by independent state. For all models, inner and outer bounds on the capacity region are derived, and comparison of the two bounds leads to characterization of either full or partial boundary of the capacity region under various channel parameters.

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arXiv2013

MIMO Broadcast Channel with an Unknown Eavesdropper: Secrecy Degrees of Freedom

We study a multi-antenna broadcast channel with two legitimate receivers and an external eavesdropper. We assume that the channel matrix of the eavesdropper is unknown to the legitimate terminals but satisfies a maximum rank constraint. As our main result we characterize the associated secrecy degrees of freedom for the broadcast channel with common and private messages. We show that a direct extension of the single-user wiretap codebook does not achieve the secrecy degrees of freedom. Our proposed optimal scheme involves decomposing the signal space into a common subspace, which can be observed by both receivers, and private subspaces which can be observed by only one of the receivers, and carefully transmitting a subset of messages in each subspace. We also consider the case when each user's private message must additionally remain confidential from the other legitimate receiver and characterize the s.d.o.f.\ region in this case.

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arXiv2013

Layered Constructions for Low-Delay Streaming Codes

We propose a new class of error correction codes for low-delay streaming communication. We consider an online setup where a source packet arrives at the encoder every $M$ channel uses, and needs to be decoded with a maximum delay of $T$ packets. We consider a sliding-window erasure channel --- $\cC(N,B,W)$ --- which introduces either up to $N$ erasures in arbitrary positions, or $B$ erasures in a single burst, in any window of length $W$. When $M=1$, the case where source-arrival and channel-transmission rates are equal, we propose a class of codes --- MiDAS codes --- that achieve a near optimal rate. Our construction is based on a {\em layered} approach. We first construct an optimal code for the $\cC(N=1,B,W)$ channel, and then concatenate an additional layer of parity-check symbols to deal with $N>1$. When $M > 1$, the case where source-arrival and channel-transmission rates are unequal, we characterize the capacity when $N=1$ and $W \ge M(T+1),$ and for $N>1$, we propose a construction based on a layered approach. Numerical simulations over Gilbert-Elliott and Fritchman channel models indicate significant gains in the residual loss probability over baseline schemes. We also discuss the connection between the error correction properties of the MiDAS codes and their underlying column distance and column span.

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arXiv2013

Robust Streaming Erasure Codes based on Deterministic Channel Approximations

We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback deadline of $T$ packets. The underlying channel is a packet erasure channel that can introduce both burst and isolated losses. We first consider a class of channels that in any window of length ${T+1}$ introduce either a single erasure burst of a given maximum length $B,$ or a certain maximum number $N$ of isolated erasures. We demonstrate that for a fixed rate and delay, there exists a tradeoff between the achievable values of $B$ and $N,$ and propose a family of codes that is near optimal with respect to this tradeoff. We also consider another class of channels that introduce both a burst {\em and} an isolated loss in each window of interest and develop the associated streaming codes. All our constructions are based on a layered design and provide significant improvements over baseline codes in simulations over the Gilbert-Elliott channel.

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