arXiv subjects

Bruce Hajek

Publications and source records attributed to Bruce Hajek.

44 records · Page 3Linked to original sources

arXiv2008

Low SNR Capacity of Noncoherent Fading Channels

Discrete-time Rayleigh fading single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter or the receiver. The fading is assumed to be stationary and correlated in time, but independent from antenna to antenna. Peak-power and average-power constraints are imposed on the transmit antennas. For MIMO channels, these constraints are either imposed on the sum over antennas, or on each individual antenna. For SISO channels and MIMO channels with sum power constraints, the asymptotic capacity as the peak signal-to-noise ratio tends to zero is identified; for MIMO channels with individual power constraints, this asymptotic capacity is obtained for a class of channels called transmit separable channels. The results for MIMO channels with individual power constraints are carried over to SISO channels with delay spread (i.e. frequency selective fading).

cs.IT↗

arXiv2008

Substitute Valuations: Generation and Structure

Substitute valuations (in some contexts called gross substitute valuations) are prominent in combinatorial auction theory. An algorithm is given in this paper for generating a substitute valuation through Monte Carlo simulation. In addition, the geometry of the set of all substitute valuations for a fixed number of goods K is investigated. The set consists of a union of polyhedrons, and the maximal polyhedrons are identified for K=4. It is shown that the maximum dimension of the maximal polyhedrons increases with K nearly as fast as two to the power K. Consequently, under broad conditions, if a combinatorial algorithm can present an arbitrary substitute valuation given a list of input numbers, the list must grow nearly as fast as two to the power K.

cs.GT↗

arXiv2007

Low SNR Capacity of Fading Channels -- MIMO and Delay Spread

Discrete-time Rayleigh fading multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter and receiver. The fading is assumed to be correlated in time and independent from antenna to antenna. Peak and average transmit power constraints are imposed, either on the sum over antennas, or on each individual antenna. In both cases, an upper bound and an asymptotic lower bound, as the signal-to-noise ratio approaches zero, on the channel capacity are presented. The limit of normalized capacity is identified under the sum power constraints, and, for a subclass of channels, for individual power constraints. These results carry over to a SISO channel with delay spread (i.e. frequency selective fading).

cs.IT↗

arXiv2007

Paging and Registration in Cellular Networks: Jointly Optimal Policies and an Iterative Algorithm

This paper explores optimization of paging and registration policies in cellular networks. Motion is modeled as a discrete-time Markov process, and minimization of the discounted, infinite-horizon average cost is addressed. The structure of jointly optimal paging and registration policies is investigated through the use of dynamic programming for partially observed Markov processes. It is shown that there exist policies with a certain simple form that are jointly optimal, though the dynamic programming approach does not directly provide an efficient method to find the policies. An iterative algorithm for policies with the simple form is proposed and investigated. The algorithm alternates between paging policy optimization and registration policy optimization. It finds a pair of individually optimal policies, but an example is given showing that the policies need not be jointly optimal. Majorization theory and Riesz's rearrangement inequality are used to show that jointly optimal paging and registration policies are given for symmetric or Gaussian random walk models by the nearest-location-first paging policy and distance threshold registration policies.

cs.IT↗

arXiv2006

Gossiping with Multiple Messages

This paper investigates the dissemination of multiple pieces of information in large networks where users contact each other in a random uncoordinated manner, and users upload one piece per unit time. The underlying motivation is the design and analysis of piece selection protocols for peer-to-peer networks which disseminate files by dividing them into pieces. We first investigate one-sided protocols, where piece selection is based on the states of either the transmitter or the receiver. We show that any such protocol relying only on pushes, or alternatively only on pulls, is inefficient in disseminating all pieces to all users. We propose a hybrid one-sided piece selection protocol -- INTERLEAVE -- and show that by using both pushes and pulls it disseminates $k$ pieces from a single source to $n$ users in $10(k+\log n)$ time, while obeying the constraint that each user can upload at most one piece in one unit of time, with high probability for large $n$. An optimal, unrealistic centralized protocol would take $k+\log_2 n$ time in this setting. Moreover, efficient dissemination is also possible if the source implements forward erasure coding, and users push the latest-released coded pieces (but do not pull). We also investigate two-sided protocols where piece selection is based on the states of both the transmitter and the receiver. We show that it is possible to disseminate $n$ pieces to $n$ users in $n+O(\log n)$ time, starting from an initial state where each user has a unique piece.

cs.NI↗

arXiv2006

Low SNR Capacity of Fading Channels with Peak and Average Power Constraints

Flat-fading channels that are correlated in time are considered under peak and average power constraints. For discrete-time channels, a new upper bound on the capacity per unit time is derived. A low SNR analysis of a full-scattering vector channel is used to derive a complimentary lower bound. Together, these bounds allow us to identify the exact scaling of channel capacity for a fixed peak to average ratio, as the average power converges to zero. The upper bound is also asymptotically tight as the average power converges to zero for a fixed peak power. For a continuous time infinite bandwidth channel, Viterbi identified the capacity for M-FSK modulation. Recently, Zhang and Laneman showed that the capacity can be achieved with non-bursty signaling (QPSK). An additional contribution of this paper is to obtain similar results under peak and average power constraints.

cs.IT↗

arXiv2005

Comments on `Bit Interleaved Coded Modulation'

Caire, Taricco and Biglieri presented a detailed analysis of bit interleaved coded modulation, a simple and popular technique used to improve system performance, especially in the context of fading channels. They derived an upper bound to the probability of error, called the expurgated bound. In this correspondence, the proof of the expurgated bound is shown to be flawed. A new upper bound is also derived. It is not known whether the original expurgated bound is valid for the important special case of square QAM with Gray labeling, but the new bound is very close to, and slightly tighter than, the original bound for a numerical example.

cs.IT↗

arXiv2005

Capacity per Unit Energy of Fading Channels with a Peak Constraint

A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of Verdu for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are extended to a channel with side information, showing that the capacity per unit energy is one nat per Joule, independently of the peak power constraint. A continuous-time version of the model is also considered. The capacity per unit energy subject to a peak constraint (but no bandwidth constraint) is given by an expression similar to that for discrete time, and is evaluated for Gauss-Markov and Clarke fading channels.

cs.IT↗