This paper considers communication networks where individual links can be described as those based on multiple-input multiple-output channels. Unlike orthogonal modulation methods (such as the ...singular-value decomposition), we allow interference between subchannels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis, and corresponding decomposition, which are simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of subchannel gains of two broadcast-channel receivers. We then apply this decomposition to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which uses only scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user multiple-input multiple-output channel, where we show the existence of nontrivial cases, where the optimal distortion pair (which for high signal-to-noise ratios (SNRs) equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network. Thus, we coin the approach "network modulation".
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the ...following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for a system which employs the optimal detection rule. We conjecture that the resulting random-coding bound is ensemble-tight, and consequently optimal within the class of quantization-and-binning schemes.
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both ...informative and well-justified. For testing in the simple normal location problem (that is, testing for the mean of multivariate Gaussians), we overcome the difficulty as follows. In this problem there exists a natural "hardness" order between parameters as for different parameters the error-probabilities curves (when the parameter is known) are either identical, or one dominates the other. We can thus define minimax performance as the worst-case among parameters which are below some hardness level. Fortunately, there exists a universal minimax test, in the sense that it is minimax for all hardness levels simultaneously. Under this criterion we also find the optimal test for composite hypothesis testing with training data. THIS criterion extends to the wide class of local asymptotic normal models, in an asymptotic sense where the approximation of the error probabilities is additive. Since we have the asymptotically optimal tests for composite hypothesis testing with and without training data, we quantify the loss of universality and gain of training data for these models.
We consider the problem of discrimination between two pure quantum states. It is well known that the optimal measurement under both the error-probability and log-loss criteria is a projection, while ...under an "erasure-distortion" criterion it is a three-outcome positive operator-valued measure (POVM). These results were derived separately. We present a unified approach which finds the optimal measurement under any distortion measure that satisfies a convexity relation with respect to the Bhattacharyya distance. Namely, whenever the measure is relatively convex (resp. concave), the measurement is the projection (resp. three-outcome POVM) above. The three above-mentioned results are obtained as special cases of this simple derivation. As for further measures for which our result applies, we prove that Rényi entropies of order 1 and above (resp. 1/2 and below) are relatively convex (resp. concave). A special setting of great practical interest, is the discrimination between two coherent-light waveforms. In a remarkable work by Dolinar it was shown that a simple detector consisting of a photon counter and a feedback-controlled local oscillator obtains the quantum-optimal error probability. Later it was shown that the same detector (with the same local signal) is also optimal in the log-loss sense. By applying a similar convexity approach, we obtain in a unified manner the optimal signal for a variety of criteria.
We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the long-standing open problem of finding the ...rate of convergence of the smallest attainable expected distortion to its asymptotic value, as a function of the blocklength <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>. Our main result is that in general the convergence rate is not faster than <inline-formula> <tex-math notation="LaTeX">n^{-1/2} </tex-math></inline-formula>. In particular, we show that for the problem of transmitting i.i.d uniform bits over a binary symmetric channels with Hamming distortion, the smallest attainable distortion (bit error rate) is at least <inline-formula> <tex-math notation="LaTeX">\Omega (n^{-1/2}) </tex-math></inline-formula> above the asymptotic value, if the "bandwidth expansion ratio" is above 1.
The MIMO Wiretap Channel Decomposed Khina, Anatoly; Kochman, Yuval; Khisti, Ashish
IEEE transactions on information theory,
02/2018, Volume:
64, Issue:
2
Journal Article
Peer reviewed
Open access
The problem of sending a secret message over the Gaussian multiple-input multiple-output (MIMO) wiretap channel is studied. While the capacity of this channel is known, it is not clear how to ...construct optimal coding schemes that achieve this capacity. In this paper, we use linear operations along with successive interference cancellation to attain effective parallel single-antenna wiretap channels. By using independent scalar Gaussian wiretap codebooks over the resulting parallel channels, the capacity of the MIMO wiretap channel is achieved. The derivation of the schemes is based upon joint triangularization of the channel matrices. We find that the same technique can be used to rederive capacity expressions for the MIMO wiretap channel in a way that is simple and closely connected to a transmission scheme. This technique allows to extend the previously proven strong security for scalar Gaussian channels to the MIMO case. We further consider the problem of transmitting confidential messages over a two-user broadcast MIMO channel. For that problem, we find that derivation of both the capacity and a transmission scheme is a direct corollary of the proposed analysis for the MIMO wiretap channel.
The Dirty MIMO Multiple-Access Channel Khina, Anatoly; Kochman, Yuval; Erez, Uri
IEEE transactions on information theory,
09/2017, Volume:
63, Issue:
9
Journal Article
Peer reviewed
Open access
In the scalar dirty multiple-access channel, in addition to Gaussian noise, two additive interference signals are present, each known non-causally to a single transmitter. It was shown by Philosof et ...al. that for strong interferences, an independent identically distributed ensemble of codes does not achieve the capacity region. Rather, a structured-codes approach was presented that was shown to be optimal in the limit of high signal-to-noise ratios, where the sum capacity is dictated by the minimal ("bottleneck") channel gain. In this paper, we consider the multiple-input multiple-output (MIMO) variant of this setting. In order to incorporate structured codes in this case, one can utilize matrix decompositions that transform the channel into effective parallel scalar dirty multiple-access channels. This approach, however, suffers from a "bottleneck" effect for each effective scalar channel and, therefore, the achievable rates strongly depend on the chosen decomposition. It is shown that a recently proposed decomposition, where the diagonals of the effective channel matrices are equal up to a scaling factor, is optimal at high signal-to-noise ratios, under an equal rank assumption. This approach is then extended to any number of transmitters. Finally, an application to physical-layer network coding for the MIMO two-way relay channel is presented.
Upper bounds on the error probability of channel coding are derived for codebooks drawn from random codebook ensembles with various independence and symmetry assumptions. For regular decoding ...(without an erasure option), the random coding union bound of Polyanskiy et al. is improved by carefully taking ties (equal likelihood scores) into account. It is shown that the improved bound is always better than threshold-decoding based bounds. The framework is extended to the case of decoding with an erasure option, deriving several achievability bounds in the same spirit. In order to exemplify the merits of the approach, the bounds are evaluated for the case of pairwise-independent uniformly-distributed ensembles (e.g., shifted random linear codes).
In this paper, we obtain an improved lower bound on the error exponent of the memoryless multiple-access channel via the use of linear codes, thus demonstrating that structure can be beneficial even ...when capacity may be achieved via random codes. We show that if the multiple-access channel is additive over a finite field, then any error probability, and hence any error exponent, achievable by a linear code for the associated single-user channel, is also achievable for the multiple-access channel. In particular, linear codes allow to attain joint expurgation, and hence, attain the single-user expurgated exponent of the single-user channel, whenever the latter is achieved by a uniform distribution. Thus, for additive channels, at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used for at most one of the users. Even when the multiple-access channel is not additive, it may be transformed into such a channel. While the transformation is information-lossy, we show that the distributed structure gain in some "nearly additive" cases outweighs the loss. Finally, we apply a similar approach to the Gaussian multiple-access channel. While we believe that due to the power constraints, it is impossible to attain the singleuser error exponent, we do obtain an improvement over the best known achievable error exponent, given by Gallager, for certain parameters. This is accomplished using a nested lattice triplet with judiciously chosen parameters.
We consider a line network of nodes, connected by additive white noise channels, equipped with local feedback. We study the velocity at which information spreads over this network. For transmission ...of a data packet, we give an explicit positive lower bound on the velocity, for any packet size. Furthermore, we consider streaming, that is, transmission of data packets generated at a given average arrival rate. We show that a positive velocity exists as long as the arrival rate is below the individual Gaussian channel capacity, and provide an explicit lower bound. Our analysis involves applying pulse-amplitude modulation to the data (successively in the streaming case), and using linear mean-squared error estimation at the network nodes. For general white noise, we derive exponential error-probability bounds. For single-packet transmission over channels with (sub-)Gaussian noise, we show a doubly-exponential behavior, which reduces to the celebrated Schalkwijk-Kailath scheme when considering a single node. Viewing the constellation as an "analog source", we also provide bounds on the exponential decay of the mean-squared error of source transmission over the network.
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