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Alexei Ashikhmin

Publications and source records attributed to Alexei Ashikhmin.

45 records · Page 3Linked to original sources
arXiv2011

Channel Estimation and Linear Precoding in Multiuser Multiple-Antenna TDD Systems

Traditional approaches in the analysis of downlink systems decouple the precoding and the channel estimation problems. However, in cellular systems with mobile users, these two problems are in fact tightly coupled. In this paper, this coupling is explicitly studied by accounting for channel training overhead and estimation error while determining the overall system throughput. The paper studies the problem of utilizing imperfect channel estimates for efficient linear precoding and user selection. It presents precoding methods that take into account the degree of channel estimation error. Information-theoretic lower and upper bounds are derived to evaluate the performance of these precoding methods. In typical scenarios, these bounds are close.

cs.IT↗
arXiv2010

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. For precoding at the base stations, channel state information (CSI) is essential at the base stations. A popular technique for obtaining this CSI in time division duplex (TDD) systems is uplink training by utilizing the reciprocity of the wireless medium. 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 mitigate this problem. In addition to being a linear precoding method, this precoding method has a simple closed-form expression that results from an intuitive optimization problem formulation. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

cs.IT↗
arXiv2010

Nonbinary Quantum Cyclic and Subsystem Codes Over Asymmetrically-decohered Quantum Channels

Quantum computers theoretically are able to solve certain problems more quickly than any deterministic or probabilistic computers. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, one has to mitigate the resulting noise and decoherence effects to avoid computational errors in order to successfully build quantum computers. In this paper, we construct asymmetric quantum codes to protect quantum information over asymmetric quantum channels, $\Pr Z \geq \Pr X$. Two generic methods are presented to derive asymmetric quantum cyclic codes using the generator polynomials and defining sets of classical cyclic codes. Consequently, the methods allow us to construct several families of quantum BCH, RS, and RM codes over asymmetric quantum channels. Finally, the methods are used to construct families of asymmetric subsystem codes.

cs.IT↗
arXiv2008

Scheduling and Pre-Conditioning in Multi-User MIMO TDD Systems

The downlink transmission in multi-user multiple-input multiple-output (MIMO) systems has been extensively studied from both communication-theoretic and information-theoretic perspectives. Most of these papers assume perfect/imperfect channel knowledge. In general, the problem of channel training and estimation is studied separately. However, in interference-limited communication systems with high mobility, this problem is tightly coupled with the problem of maximizing throughput of the system. In this paper, scheduling and pre-conditioning based schemes in the presence of reciprocal channel are considered to address this. In the case of homogeneous users, a scheduling scheme is proposed and an improved lower bound on the sum capacity is derived. The problem of choosing training sequence length to maximize net throughput of the system is studied. In the case of heterogeneous users, a modified pre-conditioning method is proposed and an optimized pre-conditioning matrix is derived. This method is combined with a scheduling scheme to further improve net achievable weighted-sum rate.

cs.IT↗
arXiv2007

Decoding of Expander Codes at Rates Close to Capacity

The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small decoding error probability. Specifically, it is assumed that there exists a family of codes of length N and rate R=(1-ε)C (C is a capacity of a binary symmetric channel), whose decoding probability decreases polynomially in 1/N. It is shown that if the decoding probability decreases sufficiently fast, but still only polynomially fast in 1/N, then there exists another such family of codes whose decoding error probability decreases exponentially fast in N. Moreover, if the decoding time complexity of the assumed family of codes is polynomial in N and 1/ε, then the decoding time complexity of the presented family is linear in N and polynomial in 1/ε. These codes are compared to the recently presented codes of Barg and Zemor, ``Error Exponents of Expander Codes,'' IEEE Trans. Inform. Theory, 2002, and ``Concatenated Codes: Serial and Parallel,'' IEEE Trans. Inform. Theory, 2005. It is shown that the latter families can not be tuned to have exponentially decaying (in N) error probability, and at the same time to have decoding time complexity linear in N and polynomial in 1/ε.

cs.IT↗
arXiv2000

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 selforthogonal codes over $GF_{4}$ and binary quantum codes to one between selforthogonal codes over $GF_{q^2}$ and $q$-ary quantum codes for any prime power $q$.

quant-ph↗
arXiv1999

Quantum Error Detection I: Statement of the Problem

I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of undetected error under natural physical assumptions concerning transmission with error detection over the depolarizing channel. We discuss possible transmission protocols with stabilizer and unrestricted quantum codes. The set of results proved in Part I shows that in all the cases considered the average probability of undetected error for a given code is essentially given by one and the same function of its weight enumerators. This enables us to give a consistent definition of the undetected error event.

quant-ph↗
arXiv1997

Upper Bounds on the Size of Quantum Codes

Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.

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