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Register a new userExplicit Lower Bounds on the Outage Probability of Integer Forcing over Nrx2 Channels
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Added by
Elad Domanovitz
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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The performance of integer-forcing equalization for communication over the compound multiple-input multipleoutput channel is investigated. An upper bound on the resulting outage probability as a function of the gap to capacity has been derived previously, assuming a random precoding matrix drawn from the circular unitary ensemble is applied prior to transmission. In the present work a simple and explicit lower bound on the worst-case outage probability is derived for the case of a system with two transmit antennas and two or more receive antennas, leveraging the properties of the Jacobi ensemble. The derived lower bound is also extended to random space-time precoding, and may serve as a useful benchmark for assessing the relative merits of various algebraic space-time precoding schemes. We further show that the lower bound may be adapted to the case of a $1 times N_t$ system. As an application of this, we derive closed-form bounds for the symmetric-rate capacity of the Rayleigh fading multiple-access channel where all terminals are equipped with a single antenna. Lastly, we demonstrate that the integer-forcing equalization coupled with distributed space-time coding is able to approach these bounds.
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Integer forcing is an equalization scheme for the multiple-input multiple-output communication channel that has been demonstrated to allow operating close to capacity for most channels. In this work, the measure of bad channels is quantified by considering a compound channel setting where the transmitter communicates over a fixed channel but knows only its mutual information. The transmitter encodes the data into independent streams, all taken from the same linear code. The coded streams are transmitted after applying a unitary transformation. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. Considering pre-processing matrices drawn from a random ensemble, outage corresponds to the event that the target rate exceeds the achievable rate of integer forcing for a given channel matrix. For the case of the circular unitary ensemble, an explicit universal bound on the outage probability for a given target rate is derived that holds for any channel in the compound class. The derived bound depends only on the gap-to-capacity and the number of transmit antennas. The results are also applied to obtain universal bounds on the gap-to-capacity of multiple-antenna closed-loop multicast, achievable via linear pre-processed integer forcing.
Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result modulo a coarse lattice. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. It has been observed that the method works very well for most but not all source covariance matrices. The present work quantifies the measure of bad covariance matrices by studying the probability that integer-forcing source coding fails as a function of the allocated rate, %in excess of the %Berger-Tung benchmark, where the probability is with respect to a random orthonormal transformation that is applied to the sources prior to quantization. For the important case where the signals to be compressed correspond to the antenna inputs of relays in an i.i.d. Rayleigh fading environment, this orthonormal transformation can be viewed as being performed by nature. Hence, the results provide performance guarantees for distributed source coding via integer forcing in this scenario.
In this work, novel upper and lower bounds for the capacity of channels with arbitrary constraints on the support of the channel input symbols are derived. As an immediate practical application, the case of multiple-input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the high amplitude regime, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive antennas, similarly to the case of average power-constrained inputs.
This paper studies the performance of hybrid-ARQ (automatic repeat request) in Rayleigh block fading channels. The long-term average transmitted rate is analyzed in a fast-fading scenario where the transmitter only has knowledge of channel statistics, and, consistent with contemporary wireless systems, rate adaptation is performed such that a target outage probability (after a maximum number of H-ARQ rounds) is maintained. H-ARQ allows for early termination once decoding is possible, and thus is a coarse, and implicit, mechanism for rate adaptation to the instantaneous channel quality. Although the rate with H-ARQ is not as large as the ergodic capacity, which is achievable with rate adaptation to the instantaneous channel conditions, even a few rounds of H-ARQ make the gap to ergodic capacity reasonably small for operating points of interest. Furthermore, the rate with H-ARQ provides a significant advantage compared to systems that do not use H-ARQ and only adapt rate based on the channel statistics.
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This work applies the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure. All encoders use the same nested lattice codebook. Each encoder quantizes its observation using the fine lattice as a quantizer and reduces the result modulo the coarse lattice, which plays the role of binning. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. In general, the linear combinations have smaller average powers than the original signals. This allows to increase the density of the coarse lattice, which in turn translates to smaller compression rates. We also propose and analyze a one-shot version of IF source coding, that is simple enough to potentially lead to a new design principle for analog-to-digital converters that can exploit spatial correlations between the sampled signals.
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