Abhinav Ganesan

Interference Alignment With Diversity for the 2

A transmission scheme based on the Alamouti code, which we call the Li-Jafarkhani-Jafar (LJJ) scheme, was recently proposed for the 2 × 2 X-network [i.e., two-transmitter (Tx) two-receiver X-network] with two antennas at each node. This scheme was claimed to achieve a sum degrees of freedom (DoF) of 8/3 and also a diversity gain of two when fixed finite constellations are employed at each Tx. Furthermore, each Tx required the knowledge of only its own channel unlike the Jafar-Shamai scheme which required global CSIT to achieve the maximum possible sum DoF of 8/3. In this paper, we extend the LJJ scheme to the 2 × 2 X-network with four antennas at each node. The proposed scheme also assumes only local channel knowledge at each Tx. We prove that the proposed scheme achieves the maximum possible sum DoF of 16/3. In addition, we also prove that, using any fixed finite constellation with appropriate rotation at each Tx, the proposed scheme achieves a diversity gain of at least four.

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This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of di independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i=1,2,..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I[Xi;Yi]. A set of necessary and sufficient conditions on the precoders under which [IXi; Yi] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascent-based algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with di=1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.

2 X-Network With Four Antennas

In the two-user Gaussian Strong Interference Channel (GSIC) with finite constellation inputs, it is known that relative rotation between the constellations of the two users enlarges the Constellation Constrained (CC) capacity region. In this paper, a metric for finding the approximate angle of rotation to maximally enlarge the CC capacity is presented. It is shown that for some portion of the Strong Interference (SI) regime, with Gaussian input alphabets, the FDMA rate curve touches the capacity curve of the GSIC. Even as the Gaussian alphabet FDMA rate curve touches the capacity curve of the GSIC, at high powers, with both the users using the same finite constellation, we show that the CC FDMA rate curve lies strictly inside the CC capacity curve for the constellations BPSK, QPSK, 8-PSK, 16-QAM and 64-QAM. It is known that, with Gaussian input alphabets, the FDMA inner-bound at the optimum sum-rate point is always better than the simultaneous-decoding inner-bound throughout the Weak Interference (WI) regime. For a portion of the WI regime, it is shown that, with identical finite constellation inputs for both the users, the simultaneous-decoding inner-bound enlarged by relative rotation between the constellations can be strictly better than the FDMA inner-bound.

On Precoding for Constant

It is well known that the interference alignment (IA) based transmission scheme proposed by Jafar and Shamai achieves the 4M over 3 sum-degrees of freedom (DoF) of the twotransmitter, two-receiver multiple-input multiple-output (MIMO) X-Network with M antennas at each node, referred to as the (2 × 2, M) X-Network. The Jafar-Shamai scheme assumes the availability of “global” channel-state-information at the transmitter (CSIT). “Local” CSIT based transmission schemes that couple IA with space-time block codes (STBC) in order to achieve the sum-DoF of the (2 × 2, M) X-Network are known specifically for M = 2; 3; 4. Further, these schemes have been proven to guarantee a diversity gain of M when finite-sized input constellations are employed. In this paper, an explicit transmission scheme that achieves the 4M over 3 sum-DoF of the (2 × 2, M) X-Network, for arbitrary M, is presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai scheme. In addition, it is shown analytically that the proposed scheme guarantees a diversity gain of M + 1 when finite-sized input constellations are employed.

K

Group testing with inhibitors (GTI) introduced by Farach at al. is studied in this paper. There are three types of items, d defectives, r inhibitors and n-d-r normal items in a population of n items. The presence of any inhibitor in a test can prevent the expression of a defective. For this model, we propose a probabilistic non-adaptive pooling design with a low complexity decoding algorithm. We show that the sample complexity of the number of tests required for guaranteed recovery with vanishing error probability using the proposed algorithm scales as T = O(d log n) and equation in the regimes r = O(d) and d = o(r) respectively. In the former regime, the number of tests meets the lower bound order while in the latter regime, the number of tests is shown to exceed the lower bound order by a log r over d multiplicative factor. The decoding complexity of the proposed decoding algorithm scales as O(nT).

-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for constant channel-coefficient K-User MIMO Gaussian Interference Channel (K-MIMO GIC) where each transmitter-i (Tx-i) requires to send di independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i), for i = 1, 2, ..., K. The maximum rate achieved by Tx-i as the signal to noise ratio (SNR) tends to infinity, using any linear precoder, when the interference channel-coefficients are zero is termed as Constellation Constrained Saturation Capacity (CCSC) for Tx-i. In this paper, we derive a high SNR approximation for the rate achieved by Tx-i when interference is treated as noise, which is given by the mutual information between Tx-i and Rx-i, denoted by I[Xi;Yi] where, Xi denotes the symbols generated at Tx-i before precoding and Yi denotes the symbols received at the antennas of Rx-i. Based on this high SNR approximation, we derive a set of necessary and sufficient conditions on the precoders under which I[Xi;Yi] tends to CCSC for Tx-i. Interestingly, the precoders that achieve interference alignment (IA) satisfy these necessary and sufficient conditions. However, finding precoders that achieve IA is known to be NP-hard in general whereas, the precoders that satisfy the derived necessary and sufficient conditions are easy to find for any given channel-coefficients. Further, we propose a gradient-ascent based algorithm to optimize the sum-rate achieved by precoding with finite constellation inputs and treating interference as noise. Simulation study for a 3-MIMO GIC with di = 1, for all i, equipped with two antennas at each node and QPSK inputs shows an improvement of 1.07 bits/sec/Hz in the ergodic sum-rate using the precoders obtained from the proposed algorithm over the precoders that achieve IA, at SNR = -2 dB.

Two-User Gaussian Interference Channel with Finite Constellation Input and FDMA

A transmission scheme based on the Alamouti code, which we call the Li-Jafarkhani-Jafar (LJJ) scheme, was recently proposed for the 2×2 X Network (i.e., two-transmitter (Tx) two-receiver (Rx) X Network) with two antennas at each node. This scheme was claimed to achieve a sum degrees of freedom (DoF) of 8/3 and also a diversity gain of two when fixed finite constellations are employed at each Tx. Furthermore, each Tx required the knowledge of only its own channel unlike the Jafar-Shamai scheme which required global CSIT to achieve the maximum possible sum DoF of 8/3. In this paper, we extend the LJJ scheme to the 2 × 2 X Network with four antennas at each node. The proposed scheme also assumes only local channel knowledge at each Tx. We prove that the proposed scheme achieves the maximum possible sum DoF of 16/3. In addition, we also prove that, using any fixed finite constellation with appropriate rotation at each Tx, the proposed scheme achieves a diversity gain of at least four.

Interference aligned space-time transmission with diversity for the 2 × 2 X-Network

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Non-adaptive group testing with inhibitors

This paper abstracts the unified problem of drug discovery and pathogen identification as an inhibitor-defective classification problem and learning of “association pattern” between the inhibitors and defectives. We refer to the “association graph” between the inhibitors and defectives as the Immune-Defectives Graph (IDG). Here, the expression of a defective might be inhibited by a subset of the inhibitors rather than all the inhibitors as in the well-known 1-inhibitor model. A test containing a defective is positive iff it does not contain its associated inhibitor. The goal of this paper is to identify the defectives, inhibitors, and their “associations” with high probability, or in other words, learn the IDG using group tests. We propose a probabilistic non-adaptive pooling design, a probabilistic two-stage adaptive pooling design and decoding algorithms for learning the IDG. The sample complexity of the number of tests required for the proposed two-stage adaptive pooling design is shown to be close to the lower bound, while that for the proposed non-adaptive pooling design is close to the lower bound in the large inhibitor regime.

On precoding for constant K-User MIMO Gaussian interference channel with finite constellation inputs

The capacity region of the 3-user Gaussian Interference Channel (GIC) with mixed strong-very strong interference was established in [1]. The mixed strong-very strong interference conditions considered in [1] correspond to the case where, at each receiver, one of the interfering signals is strong and the other is very strong. In this paper, we derive the capacity region of K-user (K ≥ 3) Discrete Memoryless Interference Channels (DMICs) with a mixed strong-very strong interference. This corresponds to the case where, at each receiver one of the interfering signals is strong and the other (K − 2) interfering signals are very strong. This includes, as a special case, the 3-user DMIC with mixed strong-very strong interference. The proof is specialized to the 3-user GIC case and hence an alternative derivation for the capacity region of the 3-user GIC with mixed strong-very strong interference is provided.