Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szkoła mapping. The lower bound provides a unified recovery of converse results across all major asymptotic regimes, including large-, moderate-, and small-deviations. Unlike existing bounds, which either rely on technically involved information-spectrum arguments or suffer from fixed prefactors and limited applicability in the non-asymptotic regime, the proposed bound arises from a single expression and enables, in some cases, the direct use of classical results. It is further demonstrated that the proposed bound provides accurate approximations to the optimal quantum error trade-off function at small blocklengths. Numerical comparisons with existing bounds, including those based on fidelity and information spectrum methods, highlight its improved tightness.

This paper studies the capacity of massive random-access networks modeled as a multiple-input multiple-output fading channel with infinitely many interfering users. The network is assumed to operate in a noncoherent regime, where transmitters and receivers know the fading statistics but not their realizations. Users access the network via random activation with a given probability. To characterize the symmetric sum rate, a random-coding argument is invoked together with the assumption that users and interferers draw their codebooks according to the same distribution. For this channel model, rigorous upper and lower bounds on the network capacity are derived. The behavior of these bounds depends critically on the spatial decay of the large-scale fading statistics from interfering users. In particular, if the large-scale fading coefficients of the interferers (ordered according to their distance to the receiver) decay exponentially or more slowly, then the capacity is bounded in the transmit power. This occurs because the aggregate interference scales with the transmit power, and reveals an inherent saturation effect in interference-limited networks. Moreover, in this regime, random user activity cannot fundamentally eliminate the resulting capacity ceiling. In contrast, if the large-scale fading coefficients of the interferers decay faster than double-exponentially, then the capacity becomes unbounded in the transmit power. Note that proving an unbounded capacity is nontrivial even if the number of interfering users is finite, since the condition that the users’ codebooks follow the same distribution prevents interference-avoiding strategies such as time-, frequency-, or code-division multiple access, and cooperation among users associated with different access nodes is not allowed. An unbounded coding rate is achieved by using bursty signaling together with treating interference as noise.

We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain$N$-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality.

This paper studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. New lower bounds are presented for the minimum error probability of codes satisfying maximal and average power constraints. These bounds are tighter than previous results in the finite blocklength regime, and yield a better understanding on the structure of good codes under an average power limitation. Evaluation of these bounds for short and moderate blocklengths is also discussed.

In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more.

This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB, blocklengths of 168 channel uses or more, and when the channel's coherence interval is not smaller than two. It is demonstrated that the derived approximations recover both the normal approximation and the reliability function of the channel.

For an additive white Gaussian noise channel, we prove that Th. 41 in [Polyanskiy, Poor, Verdά2010] is a lower bound to the error probability of any channel code satisfying the maximal power constraint. In contrast, the (tighter) lower bound to the error probability in Eq. (20) in [Shannon 1959] only holds under equal power constraint.

We introduce a definition of perfect and quasi-perfect codes for discrete symmetric channels based on the packing and covering properties of generalized spheres whose shape is tilted using an auxiliary probability measure. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to coincide with the estimate provided by the meta-converse lower bound. We illustrate how the proposed definition naturally extends to cover almost-lossless source-channel coding and lossy compression.

We propose a saddlepoint approximation of the error probability of a binary hypothesis test between two i.i.d. distributions. The approximation is accurate, simple to compute, and yields a unified analysis in different asymptotic regimes. The proposed formulation is used to efficiently compute the meta-converse lower bound for moderate block-lengths in several cases of interest.

We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This new definition generalizes previous definitions and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to attain the meta-converse lower bound.

The nonnegativity of relative entropy implies that the differential entropy of a random vector X with probability density function (pdf) f is upper bounded by -E[log g(X)] for any arbitrary pdf g. Using this inequality with a cleverly chosen g, we derive a lower bound on the asymptotic excess rate of entropy-constrained vector quantization for d-dimensional sources and rth-power distortion, where the asymptotic excess rate is defined as the difference between the smallest output entropy of a vector quantizer satisfying the distortion constraint and the rate-distortion function in the limit as the distortion tends to zero. Specialized to the one-dimensional case, this lower bound coincides with the asymptotic excess rate achieved by a uniform quantizer, thereby recovering the result by Gish and Pierce that uniform quantizers are asymptotically optimal as the allowed distortion tends to zero. Furthermore, in the one-dimensional case, the derivation of the lower bound reveals a necessary condition for a sequence of quantizers to be asymptotically optimal. This condition implies that any sequence of asymptotically optimal almost-regular quantizers must converge to a uniform quantizer as the distortion tends to zero. While the obtained lower bound itself is not novel, to the best of our knowledge, we present the first rigorous derivation that follows the direct approach by Gish and Pierce without resorting to heuristic high-resolution approximations commonly found in the quantization literature. Furthermore, our derivation holds for all d-dimensional sources having finite differential entropy and whose integer part has finite entropy. In contrast to Gish and Pierce, we do not require additional constraints on the continuity or decay of the source pdf.

We derive a lower bound on the smallest output entropy that can be achieved via scalar quantization of a source with given expected quadratic distortion. As the allowed distortion tends to zero, the bound converges to the output entropy achieved by a uniform quantizer, thereby recovering the result by Gish and Pierce that uniform quantizers are asymptotically optimal. The proposed derivation applies for any memoryless source that has a probability density function (pdf), a finite differential entropy, and whose integer part has a finite entropy. In contrast to Gish and Pierce, we do not require any additional constraints on the continuity or decay of the source pdf.

Alternative exact expressions are derived for the minimum error probability of a hypothesis test discriminating among M quantum states. The first expression corresponds to the error probability of a binary hypothesis test with certain parameters; the second involves the optimization of a given information-spectrum measure. Particularized in the classical-quantum channel coding setting, this characterization implies the tightness of two existing converse bounds; one derived by Matthews and Wehner using hypothesis-testing, and one obtained by Hayashi and Nagaoka via an information-spectrum approach.

This paper studies an almost-lossless source-channel coding scheme in which source messages are assigned to different classes and encoded with a channel code that depends on the class index. The code performance is analyzed by means of random-coding error exponents and validated by simulation of a low-complexity implementation using existing source and channel codes. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding when the number of classes increases.

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.

We derive the channel-coding sphere-packing exponent under a per-codeword cost constraint. The proof is based on hypothesis testing and holds for continuous memoryless channels.

We study a source-channel coding scheme in which source messages are assigned to classes and encoded using a channel code that depends on the class index. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding as the number of classes increases. The performance of this scheme is studied by means of random-coding bounds and validated by simulation of a low-complexity implementation using existing source and channel codes.

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight.

We show that the meta-converse bound derived by Polyanskiy et al. provides the exact error probability for a fixed joint source-channel code and an appropriate choice of the bound parameters. While the expression is not computable in general, it identifies the weaknesses of known converse bounds to the minimum achievable error probability.

Many problems in digital communications involve wideband radio signals. As the most recent example, the impressive advances in Cognitive Radio systems make even more necessary the development of sampling schemes for wideband radio signals with spectral holes. This is equivalent to considering a sparse multiband signal in the framework of Compressive Sampling theory. Starting from previous results on multicoset sampling and recent advances in compressive sampling, we analyze the matrix involved in the corresponding reconstruction equation and define a new method for the design of universal multicoset codes, that is, codes guaranteeing perfect reconstruction of the sparse multiband signal.

We derive a random-coding upper bound on the average probability of error of joint source-channel coding that recovers Csiszár's error exponent when used with product distributions over the channel inputs. Our proof technique for the error probability analysis employs a code construction for which source messages are assigned to subsets and codewords are generated with a distribution that depends on the subset.

Spectrum sensing is a challenging key component of the Cognitive Radio paradigm, since primary signals must be detected in the face of noise uncertainty and at signal-to-noise ratios (SNRs) well below decodability levels. Multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness. Here, we study the problem of detecting Gaussian signals with unknown rank-P spatial covariance matrix when the noise at the receiver is independent across the antennas and with unknown power. A generic diagonal noise covariance matrix is allowed to model calibration uncertainties in the different antenna frontends. We derive the generalized likelihood ratio test (GLRT) for this detection problem. Although, in general, the corresponding statistic must be obtained by numerical means, in the low SNR regime the GLRT does admit a closed form. Numerical simulations show that the proposed asymptotic detector offers good performance even for moderate SNR values.

In the context of spectrum sensing, we investigate the performance of detectors equipped with M antennas (co-located or distributed) under Rayleigh fading, in terms of detection diversity. Rather than the high-SNR concept of diversity order common in the communications literature, we adopt the notion recently advocated by Daher and Adve in the radar community: the slope of the average probability of detection (P̅D) vs. SNR curve at P̅D= 0.5. This definition is well suited to spectrum sensing, which invariably deals with low SNR levels. It is shown that the diversity order grows as M for an optimal centralized detector having access to all observations, whereas for the two distributed schemes considered (the multiantenna energy detector and the OR detector) it grows no faster than √M.

Random-coding exact characterizations and bounds to the error probability of joint source-channel coding are presented. In particular, upper bounds using maximum-a-posteriori and threshold decoding are derived as well as a lower bound motivated by Verdú-Han's lemma.

Dynamic Spectrum Access (DSA) is receiving considerable interest as a means to improve spectral usage in licensed bands. In order to avoid interference to licensed users, spectrum sensing has emerged as an enabling technology for DSA. The requirements for spectrum sensors are stringent, as licensed user detection must be performed reliably at low signal-to-noise ratios (SNR). Sensing performance can be improved by exploiting signal features not present in the background noise. These approaches result in tradeoffs among performance and robustness to departures from the signal model. We consider second-order signal features and develop detectors exploiting spatial (by using multiple antennas) as well as temporal signal correlation, taking advantage of the fact that the power spectrum of the primary signal at each antenna can be known up to a complex scalar representing the unknown propagation channel. A low-SNR Generalized Likelihood Ratio approach is adopted in order to overcome this uncertainty, resulting in different tests intimately related to familiar diversity combining techniques. The performance of the proposed detectors is analyzed and tested in different scenarios.

In Cognitive Radio scenarios channelization information from primary network may be available to the spectral monitor. Under this assumption we propose a spectral estimation algorithm from compressed measurements of a multichannel wideband signal. The analysis of the Cramer-Rao Lower Bound (CRLB) for this estimation problem shows the importance of detecting the underlaying sparsity pattern of the signal. To this end we describe a Bayesian based iterative algorithm that discovers the set of active signals conforming the band and simultaneously reconstructs the spectrum. This iterative spectral estimator is shown to perform close to a Genie-Aided CRLB that includes full knowledge about the sparsity pattern of the channels.

Dynamic spectrum leasing (DSL) is one of the schemes proposed for dynamic spectrum sharing (DSS) in cognitive radio networks. In DSL, spectrum owners, denoted as primary users, dynamically adjust the amount of secondary interference they are willing to tolerate in response to the demand from secondary transmitters. In this correspondence we investigate how much can be gained by primary users if this limited interaction with secondary system is allowed, compared to a scheme in which the interference cap allowed by primary users is fixed {a priori} by a regulatory authority. To that end, we define performance metrics for both primary and secondary systems based on the theoretically achievable multiuser sum-rate of the secondary system and analyze both schemes' behavior with respect to different system parameters. This analysis shows that (i) in dynamic environments DSL based schemes may present an important advantage over other schemes with fixed interference constraints, and (ii) DSL schemes are robust against inaccurate a priori information that may degrade system performance.

Certain deterministic interference channels have been shown to accurately model Gaussian interference channels in the asymptotic low-noise regime. Motivated by this correspondence, we investigate a K user-pair, cyclically symmetric, deterministic interference channel in which each receiver experiences interference only from its neighboring transmitters (Wyner model). We establish the sum capacity for a large set of channel parameters, thus generalizing previous results for the 2-pair case.

Since multi-antenna (MIMO) systems are becoming more popular thanks to their inherent potential for capacity improvement, interference from MIMO transceivers is an increasingly serious concern. Spatial multiplexing schemes are particularly vulnerable to multi-user interference. Fortunately, this interference can be mitigated, when the channel matrices show a sufficient spatial separation. In this paper, we quantify the separability of multi-user MIMO channels using actual measurements in a scenario where a single outdoor base station transmits to two indoor mobile receivers. To quantify the spatial distance between the two users, we compare the spatial correlation matrices using two simple measures: (i) matrix collinearity, and (ii) the condition number ratio. Both measures are directly linked to MIMO system performance. Our measurement-based evaluations demonstrate that the downlink channels of different users can have a significantly different spatial structure, even when the users are in the same room. This leads to the following conclusions: (i) new multi-user MIMO models are needed to describe the spatial characteristics of different users, and (ii) spatial interference can be well managed by appropriate scheduling and precoding algorithms.