Alexei Ashikhmin

Design of low-density parity-check codes for modulation and detection

A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.

Pilot Contamination and Precoding in Multi-Cell TDD Systems

This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

Extrinsic information transfer functions: model and erasure channel properties

Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) codes, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat-accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT function of a code to its Helleseth-Klove-Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual.

An Overview of Massive MIMO: Benefits and Challenges

Presents a list of articles published by the IEEE Signal Processing Society (SPS) that ranked among the top 100 most downloaded IEEE Xplore articles.Massive multiple-input multiple-output (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of state-of-the-art research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of non-orthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient single-carrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.

Nonbinary quantum stabilizer codes

We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between self-orthogonal codes over F/sub 4/ and binary quantum codes to one between self-orthogonal codes over F(q/sup 2/) and q-ary quantum codes for any prime power q.

Inter-Cell Interference in Noncooperative TDD Large Scale Antenna Systems

In this paper we study the performance of cellular networks when their base stations have an unlimited number of antennas. In previous work, the asymptotic behavior of the signal to interference plus nose ratio (SINR) was obtained. We revisit these results by deriving the rigorous expression for the SINR of both downlink and uplink in the scenario of infinite number of antennas. We show that the contamination of the channel estimates happens whenever a pilot sequence is received at a base station simultaneously with non-orthogonal signals coming from other users. We propose a method to avoid such simultaneous transmissions from adjacent cells, thus significantly decreasing interference. We also investigate the effects of power allocation in this interference-limited scenario, and show that it results in gains of over 15dB in the signal to interference ratio for the scenario simulated here. The combination of these two techniques results in rate gains of about 18 times in our simulations.

Pilot contamination precoding in multi-cell large scale antenna systems

An LSAS entails a large number (tens or hundreds) of base station antennas serving a much smaller number of terminals, with large gains in spectral-efficiency and energy-efficiency compared with conventional MIMO technology. Until recently it was believed that in multi-cellular LSAS, even in the asymptotic regime, as the number of service antennas tends to infinity, the performance is limited by directed inter-cellular interference. The interference results from unavoidable re-use of reverse-link pilot sequences (pilot contamination) by terminals in different cells. We devise a new concept that leads to the effective elimination of inter-cell interference in TDD LSAS systems. This is achieved by outer multi-cellular pre-coding, which we call pilot contamination pre-coding (PCP). The main idea of PCP is that each base station linearly combines messages aimed to terminals from different cells that re-use the same pilot sequence. Crucially, the combining coefficients depend only on the slow-fading coefficients between the terminals and the base stations. Each base station independently transmits its PCP-combined symbols using conventional linear pre-coding that is based on estimated fast-fading coefficients. Further we derive estimates for SINRs and a capacity lower bound for the case of LSASs with PCP and finite number of antennas M.

Pilot contamination problem in multi-cell TDD systems

This paper considers a multi-cell multiple antenna system with precoding at the base stations for downlink transmission. To enable precoding, channel state information (CSI) is obtained via uplink training. This paper mathematically characterizes the impact that uplink training has on the performance of multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, it is shown that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells. This problem of pilot contamination is analyzed in this paper. A multi-cell MMSE-based precoding is proposed that, when combined with frequency/time/pilot reuse techniques, mitigate this problem.

Minimal vectors in linear codes

Minimal vectors in linear codes arise in numerous applications, particularly, in constructing decoding algorithms and studying linear secret sharing schemes. However, properties and structure of minimal vectors have been largely unknown. We prove basic properties of minimal vectors in general linear codes. Then we characterize minimal vectors of a given weight and compute their number in several classes of codes, including the Hamming codes and second-order Reed-Muller codes. Further, we extend the concept of minimal vectors to codes over rings and compute them for several examples. Turning to applications, we introduce a general gradient-like decoding algorithm of which minimal-vectors decoding is an example. The complexity of minimal-vectors decoding for long codes is determined by the size of the set of minimal vectors. Therefore, we compute this size for long randomly chosen codes. Another example of algorithms in this class is given by zero-neighbors decoding. We discuss relations between the two decoding methods. In particular, we show that for even codes the set of zero neighbors is strictly optimal in this class of algorithms. This also implies that general asymptotic improvements of the zero-neighbors algorithm in the frame of gradient-like approach are impossible. We also discuss a link to secret-sharing schemes.

Pilot Contamination Reduction in Multi-User TDD Systems

This paper considers the problem of interference mitigation in multi-cell multi-antenna time division duplex (TDD) wireless systems for downlink transmission. An efficient way to obtain channel state information (CSI) at the base station is by using uplink pilots and reciprocity of the downlink channel. At the same time, it has been shown that pilots from different cells contaminate each other, resulting in corruption of precoding matrices used by base stations, and high inter-cell interference. This paper studies the effects of shifting the location of pilots in time frames used in neighboring cells, and its effectiveness in obtaining better channel estimates, and, thereby, inter-cell interference reduction.