arXiv subjects

Amir K. Khandani

Publications and source records attributed to Amir K. Khandani.

At least 55 records · Page 3Linked to original sources

arXiv2008

The Secrecy Rate Region of the Broadcast Channel

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma. Finally, we assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality.

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arXiv2008

On the Diversity-Multiplexing Tradeoff in Multiple-Relay Network

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between a/several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh fading channel, or disconnected. We propose a new scheme, which we call \textit{random sequential} (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity-multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay ($K>1$) networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple access single relay setup, we show that the RS scheme reduces to the naive amplify-and-forward relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward scheme is shown to be optimum for this scenario.

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arXiv2008

Optimal Coding for the Erasure Channel with Arbitrary Alphabet Size

An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming maximum likelihood decoding). Assuming a memoryless erasure channel, the error exponent of MDS codes are compared with that of random codes and linear random codes. It is shown that the envelopes of all these exponents are identical for rates above the critical rate. Noting the optimality of MDS codes, it is concluded that both random codes and linear random codes are exponentially optimal, whether the block sizes is larger or smaller than the alphabet size.

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arXiv2008

Capacity of Block-Memoryless Channels with Causal Channel Side Information

The capacity of a time-varying block-memoryless channel in which the transmitter and the receiver have access to (possibly different) noisy causal channel side information (CSI) is obtained. It is shown that the capacity formula obtained in this correspondence reduces to the capacity formula reported in \cite{Gold07} for the special case where the transmitter CSI is a deterministic function of the receiver CSI.

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arXiv2008

On the Capacity of Wireless Multicast Networks

The problem of maximizing the average rate in a multicast network subject to a coverage constraint (minimum quality of service) is studied. Assuming the channel state information is available only at the receiver side and single antenna nodes, the highest expected rate achievable by a random user in the network, called expected typical rate, is derived in two scenarios: hard coverage constraint and soft coverage constraint. In the first case, the coverage is expressed in terms of the outage probability, while in the second case, the expected rate should satisfy certain minimum requirement. It is shown that the optimum solution in both cases (achieving the highest expected typical rate for given coverage requirements) is achieved by an infinite layer superposition code for which the optimum power allocation among the different layers is derived. For the MISO case, a suboptimal coding scheme is proposed, which is shown to be asymptotically optimal, when the number of transmit antennas grows at least logarithmically with the number of users in the network.

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arXiv2008

Robust Joint Source-Channel Coding for Delay-Limited Applications

In this paper, we consider the problem of robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme which achieves the optimal slope of the signal-to-distortion (SDR) curve (unlike the previously known coding schemes). Also, we propose a family of robust codes which together maintain a bounded gap with the optimum SDR curve (in terms of dB). To show the importance of this result, we drive some theoretical bounds on the asymptotic performance of delay-limited hybrid digital-analog (HDA) coding schemes. We show that, unlike the delay-unlimited case, for any family of delay-limited HDA codes, the asymptotic performance loss is unbounded (in terms of dB).

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arXiv2008

On the Capacity of the Diamond Half-Duplex Relay Channel

We consider a diamond-shaped dual-hop communication system consisting a source, two parallel half-duplex relays and a destination. In a single antenna configuration, it has been previously shown that a two-phase node-scheduling algorithm, along with the decode and forward strategy can achieve the capacity of the diamond channel for a certain symmetric channel gains [1]. In this paper, we obtain a more general condition for the optimality of the scheme in terms of power resources and channel gains. In particular, it is proved that if the product of the capacity of the simultaneously active links are equal in both transmission phases, the scheme achieves the capacity of the channel.

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arXiv2008

Path Diversity over Packet Switched Networks: Performance Analysis and Rate Allocation

Path diversity works by setting up multiple parallel connections between the end points using the topological path redundancy of the network. In this paper, \textit{Forward Error Correction} (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. Network paths are modeled as erasure Gilbert-Elliot channels. It is known that over any erasure channel, \textit{Maximum Distance Separable} (MDS) codes achieve the minimum probability of irrecoverable loss among all block codes of the same size. Based on the adopted model for the error behavior, we prove that the probability of irrecoverable loss for MDS codes decays exponentially for an asymptotically large number of paths. Then, optimal rate allocation problem is solved for the asymptotic case where the number of paths is large. Moreover, it is shown that in such asymptotically optimal rate allocation, each path is assigned a positive rate \textit{iff} its quality is above a certain threshold. The quality of a path is defined as the percentage of the time it spends in the bad state. Finally, using dynamic programming, a heuristic suboptimal algorithm with polynomial runtime is proposed for rate allocation over a finite number of paths. This algorithm converges to the asymptotically optimal rate allocation when the number of paths is large. The simulation results show that the proposed algorithm approximates the optimal rate allocation (found by exhaustive search) very closely for practical number of paths, and provides significant performance improvement compared to the alternative schemes of rate allocation.

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arXiv2008

Capacity Bounds for the Gaussian Interference Channel

The capacity region of the two-user Gaussian Interference Channel (IC) is studied. Three classes of channels are considered: weak, one-sided, and mixed Gaussian IC. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The sum capacity for a certain range of channel parameters is derived. For this range, it is proved that using Gaussian codebooks and treating interference as noise is optimal. It is shown that when Gaussian codebooks are used, the full Han-Kobayashi achievable rate region can be obtained by using the naive Han-Kobayashi achievable scheme over three frequency bands (equivalently, three subspaces). For the one-sided Gaussian IC, an alternative proof for the Sato's outer bound is presented. We derive the full Han-Kobayashi achievable rate region when Gaussian codebooks are utilized. For the mixed Gaussian IC, a new outer bound is obtained that outperforms previously known outer bounds. For this case, the sum capacity for the entire range of channel parameters is derived. It is proved that the full Han-Kobayashi achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of channel parameters.

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arXiv2007

To Decode the Interference or To Consider it as Noise

We address single-user data transmission over a channel where the received signal incurs interference from a finite number of users (interfering users) that use single codebooks for transmitting their own messages. The receiver, however, is allowed to decode interfering users' messages. This means the signal transmitted from any interfering user is either decoded or considered as noise at the receiver side. We propose the following method to obtain an achievable rate for this channel. Assuming its own data is decoded successfully, the receiver partitions the set of interfering users into two disjoint subsets, namely the set of decodable users and the set of non-decodable users. Then the transmitter's rate is chosen such that the intended signal can be jointly decoded with the set of decodable users. To show the strength of this method, we prove that for the additive Gaussian channel with Gaussian interfering users, the Gaussian distribution is optimal and the achievable rate is the capacity of this channel. To obtain the maximum achievable rate, one needs to find the maximum decodable subset of interfering users. Due to the large number of possible choices, having efficient algorithms that find the set of decodable users with maximum cardinality is desired. To this end, we propose an algorithm that enables the receiver to accomplish this task in polynomial time.

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arXiv2007

Rate-Constrained Wireless Networks with Fading Channels: Interference-Limited and Noise-Limited Regimes

A network of $n$ wireless communication links is considered in a Rayleigh fading environment. It is assumed that each link can be active and transmit with a constant power $P$ or remain silent. The objective is to maximize the number of active links such that each active link can transmit with a constant rate $λ$. An upper bound is derived that shows the number of active links scales at most like $\frac{1}λ \log n$. To obtain a lower bound, a decentralized link activation strategy is described and analyzed. It is shown that for small values of $λ$, the number of supported links by this strategy meets the upper bound; however, as $λ$ grows, this number becomes far below the upper bound. To shrink the gap between the upper bound and the achievability result, a modified link activation strategy is proposed and analyzed based on some results from random graph theory. It is shown that this modified strategy performs very close to the optimum. Specifically, this strategy is \emph{asymptotically almost surely} optimum when $λ$ approaches $\infty$ or 0. It turns out the optimality results are obtained in an interference-limited regime. It is demonstrated that, by proper selection of the algorithm parameters, the proposed scheme also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a multiplicative factor of $\log \log n$.

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arXiv2007

Matrix-Lifting Semi-Definite Programming for Decoding in Multiple Antenna Systems

This paper presents a computationally efficient decoder for multiple antenna systems. The proposed algorithm can be used for any constellation (QAM or PSK) and any labeling method. The decoder is based on matrix-lifting Semi-Definite Programming (SDP). The strength of the proposed method lies in a new relaxation algorithm applied to the method of Mobasher et al. This results in a reduction of the number of variables from $(NK+1)^2$ to $(2N+K)^2$, where $N$ is the number of antennas and $K$ is the number of constellation points in each real dimension. Since the computational complexity of solving SDP is a polynomial function of the number of variables, we have a significant complexity reduction. Moreover, the proposed method offers a better performance as compared to the best quasi-maximum likelihood decoding methods reported in the literature.

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arXiv2007

On The Limitations of The Naive Lattice Decoding

In this paper, the inherent drawbacks of the naive lattice decoding for MIMO fading systems is investigated. We show that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the rate-diversity trade-off. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal rate-diversity trade-off. Indeed, we show that in the case of naive lattice decoding, when we fix the underlying lattice, all the codes based on full-rate lattices have the same rate-diversity trade-off as V-BLAST. Also, we drive a lower bound on the symbol error probability of the naive lattice decoding for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the naive lattice decoding has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.

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arXiv2007

Throughput Scaling Laws for Wireless Networks with Fading Channels

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading (i) the maximum throughput scales like $\log n$ (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a decentralized link activation strategy is proposed and analyzed.

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arXiv2007

Precoding for the AWGN Channel with Discrete Interference

For a state-dependent DMC with input alphabet $\mathcal{X}$ and state alphabet $\mathcal{S}$ where the i.i.d. state sequence is known causally at the transmitter, it is shown that by using at most $|\mathcal{X}||\mathcal{S}|-|\mathcal{S}|+1$ out of $|\mathcal{X}|^{|\mathcal{S}|}$ input symbols of the Shannon's \emph{associated} channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter, $M$-ary signal transmission over AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. For the special case where the Gaussian noise power is zero, a sufficient condition, which is independent of interference, is given for the capacity to be $\log_2 M$ bits per channel use. The problem of maximization of the transmission rate under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet is investigated. For this setting, the general structure of a communication system with optimal precoding is proposed.

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arXiv2007

Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction

A simple scheme for communication over MIMO broadcast channels is introduced which adopts the lattice reduction technique to improve the naive channel inversion method. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. Simulation results show that the proposed scheme performs well, and as compared to the more complex methods (such as the perturbation method) has a negligible loss. Moreover, the proposed method is extended to the case of different rates for different users. The asymptotic behavior of the symbol error rate of the proposed method and the perturbation technique, and also the outage probability for the case of fixed-rate users is analyzed. It is shown that the proposed method, based on LLL lattice reduction, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). Also, the outage probability for the case of fixed sum-rate is analyzed.

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arXiv2007

LLL Reduction Achieves the Receive Diversity in MIMO Decoding

Diversity order is an important measure for the performance of communication systems over MIMO fading channels. In this paper, we prove that in MIMO multiple access systems (or MIMO point-to-point systems with V-BLAST transmission), lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, we prove that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity.

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arXiv2007

A Near Maximum Likelihood Decoding Algorithm for MIMO Systems Based on Semi-Definite Programming

In Multi-Input Multi-Output (MIMO) systems, Maximum-Likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on Semi-Definite Programming (SDP). We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models. The proposed relaxation models are also used for soft output decoding in MIMO systems.

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