We study a unified information-theoretic framework for integrated sensing and communications (ISAC), applicable to both monostatic and bistatic sensing scenarios. Special attention is given to the case where the sensing receiver (Rx) is required to produce a “soft" estimate of the state sequence, with logarithmic loss serving as the performance metric. We derive lower and upper bounds on the capacity-distortion function, which delineates the fundamental tradeoff between communication rate and sensing distortion. These bounds coincide when the channel between the ISAC transmitter (Tx) and the communication Rx is degraded with respect to the channel between the ISAC Tx and the sensing Rx, or vice versa. Furthermore, we provide a complete characterization of the capacity-distortion function for an ISAC system that simultaneously transmits information over a binary-symmetric channel and senses additive Bernoulli states through another binary-symmetric channel. The Gaussian counterpart of this problem is also explored, which, together with a state-splitting trick, fully determines the capacity-distortion-power function under the squared error distortion measure.

Bistatic sensing refers to scenarios where the transmitter (illuminating the target) and the sensing receiver (estimating the target state) are physically separated, in contrast to monostatic sensing, where both functions are co-located. In practical settings, bistatic sensing may be required either due to inherent system constraints or as a means to mitigate the strong self-interference encountered in monostatic configurations. A key practical challenge in bistatic radio-frequency radar systems is the synchronization and calibration of the separate transmitter and sensing receiver. In this paper, we are not concerned with these signal processing aspects and take a complementary information-theoretic perspective on bistatic integrated sensing and communication (ISAC). Namely, we aim to characterize the capacity-distortion function—the fundamental tradeoff between communication capacity and sensing accuracy. We consider a general discrete channel model for a bistatic ISAC system and derive a multi-letter representation of its capacity-distortion function. Then, we establish single-letter upper and lower bounds and provide exact single-letter characterizations for degraded bistatic ISAC channels. Numerical examples illustrate the theoretical results, highlighting the benefits of ISAC over separate communication and sensing, as well as the role of leveraging communication to assist sensing in bistatic systems.

In this paper, we examine the Rényi entropy rate of stationary ergodic processes. For a special class of stationary ergodic processes, we prove that the Rényi entropy rate always exists and can be approximated by its defining sequence at most polynomially; moreover, using the Markov approximation method, we show that the Rényi entropy rate can be exponentially approximated by that of the Markov approximating sequence, as the Markov order goes to infinity. For the general case, by constructing a counterexample, we disprove the conjecture that the Rényi entropy rate of a general stationary ergodic process always converges to its Shannon entropy rate as$\alpha $goes to 1.

Regular testing and quantitative evaluation of hydraulic concrete has become the key to ensure the safe operation of hydropower projects. However, the underwater environment poses difficulties and challenges for data collection and quantitative analysis of flatness inspection. Traditional detection methods such as physical contact measurement, acoustic measurement, and image measurement have limitations in measurement accuracy and collection density, making it difficult to efficiently detect and objectively evaluate the flatness of hydraulic concrete. This paper proposes a flatness inspection method based on underwater laser scanning technology. It contains three parts: flatness data collection, data processing and data analysis. The inspection method uses underwater 3D laser scanning technology for 3D data acquisition. The 3D data processing algorithm of data filtering, point cloud cropping, and plane fitting is designed. The Unflatness Area Ratio (Unflatness Area Ratio, UAR) index was proposed for the quantitative evaluation of flatness. Field application and validation in a power station in Sichuan on the guide wall of the stilling basin. Engineering application device is designed to acquire point cloud data of guide walls. The data processing algorithm is implemneted by 3D point colud processing library. The validity of the detection method is verified by data analysis and comparison of unflatness area ratio data. This method has the significance of engineering guidance, and has the value of popularization and application in major infrastructure such as hydropower station.

In this paper, we consider a novel$M$-ary sequential hypothesis testing problem in which an adversary is present and perturbs the distributions of the samples before the decision maker observes them. This problem is formulated as a sequential adversarial hypothesis testing game played between the decision maker and the adversary. This game is a zero-sum and strategic one. We assume the adversary is active under all hypotheses and knows the underlying distribution of observed samples. We adopt this framework as it is the worst-case scenario from the perspective of the decision maker. The goal of the decision maker is to minimize the expectation of the stopping time to ensure that the test is as efficient as possible; the adversary’s goal is, instead, to maximize the stopping time. We derive a pair of strategies under which the asymptotic Nash equilibrium of the game is attained. We also consider the case in which the adversary is not aware of the underlying hypothesis and hence is constrained to apply the same strategy regardless of which hypothesis is in effect. Numerical results corroborate our theoretical findings.

We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in expectation or with high probability. We show that, by using adaptive strategies for the discrimination problem, both types of error probabilities decrease to zero exponentially fast and the rates are characterized by the measured relative entropy between two quantum channels. Allowing for quantum memory, we see that the optimal rates are given by the regularized channel relative entropy. We also characterize the error exponents in the discrimination problem if non-adaptive strategies are used.

Shaping codes are used to generate code sequences in which the symbols obey a prescribed probability distribution. They arise naturally in the context of source coding for noiseless channels with unequal symbol costs. Recently, shaping codes have been proposed to extend the lifetime of flash memory and reduce DNA synthesis time. In this paper, we study a general class of shaping codes for noiseless finite-state channels with cost and i.i.d. sources. We establish a relationship between the code rate and minimum average symbol cost. We then determine the rate that minimizes the average cost per source symbol (total cost). An equivalence is established between codes minimizing average symbol cost and codes minimizing total cost, and a separation theorem is proved, showing that optimal shaping can be achieved by a concatenation of optimal compression and optimal shaping for a uniform i.i.d. source.

In this paper, we formulate the sequential binary hypothesis testing problem in which an adversary is active under both hypotheses. This problem is formulated as a sequential adversarial hypothesis testing game played between the decision maker and the adversary and it is a zero-sum and strategic one. The goal of the decision maker is to minimize the expectation of stopping time to make the test more efficient, while the adversary’s goal is to maximize it. We obtain the pair of strategies under which the asymptotic Nash equilibrium of the game is attained.

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set$\Gamma $. We would like to design a test to decide which hypothesis is in effect. Under the constraints that the probabilities that the length of the test, a stopping time, exceeds$n$are bounded by a certain threshold$\epsilon $, we obtain certain fundamental limits on the asymptotic behavior of the sequential test as$n$tends to infinity. Assuming that$\Gamma $is a convex and compact set, we obtain the set of all first-order error exponents for the problem. We also prove a strong converse. Additionally, we obtain the set of second-order error exponents under the assumption that the alphabet of the observations$\mathcal {X}$is finite. In the proof of second-order asymptotics, a main technical contribution is the derivation of a central limit-type result for a maximum of an uncountable set of log-likelihood ratios under suitable conditions. This result may be of independent interest. We also show that some important statistical models satisfy the conditions.

In this work we show that for a stationary and ergodic source$X$, stationary and ergodic test channels achieve the rate-distortion function for the lossy source coding problem with feed-forward. As a by-product, we prove that the upper bound for the feed-forward rate-distortion function derived by Venkataramanan and Pradhan (2007) is tight. In addition, we derive an upper bound on the rate-distortion function by proving a Shannon-McMillan-Breiman theorem for the causally conditional entropy rate for the class of asymptotic mean stationary and ergodic processes.

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set$\Gamma$. We would like to design a test to decide which hypothesis is in effect. Under the constraints that the probabilities that the length of the test, a stopping time, exceeds$n$are bounded by a certain threshold$\epsilon$, we obtain certain fundamental limits on the asymptotic behavior of the sequential test as$n$tends to infinity. Assuming that$\Gamma$is a convex and compact set, we obtain the set of all first-order error exponents for the problem. We also prove a strong converse. Additionally, under the assumption that$\Gamma$is a finite set, we obtain the set of second-order error exponents.

We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of the two hypotheses is made after each test. Under the constraint that the number of samples is bounded, either in expectation or with high probability, we exhibit adaptive strategies that minimize both types of misidentification errors. Namely, we show that these errors decrease exponentially (in the stopping time) with decay rates given by the measured relative entropies between the two states. Moreover, if we allow joint measurements on multiple samples, the rates are increased to the respective quantum relative entropies. We also fully characterize the achievable error exponents for non-adaptive strategies and provide numerical evidence showing that adaptive measurements are necessary to achieve our bounds.

We consider the class of channels formed from the concatenation of a deletion channel and a finite-state channel. For this class of channels, we show that the operationally-defined capacity is equal to the stationary capacity. We also show that the stationary capacity can be approached by a sequence of Markov processes with increasing Markovian orders. As a by-product, we show that the polar coding scheme proposed by Tal, Pfister, Fazeli, and Vardy [arxiv: 1904.13385 (2019)] achieves the capacity of the binary deletion channel.

We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions P0and P1and we would like to decide which hypothesis is true using a sequential test. It is known from the work of Wald and Wolfowitz that as the expectation of the length of the test grows, the optimal typeI and type-II error exponents approach the relative entropies D(P1||P0) and D(P0||P1). We refine this result by considering the optimal backoff from the corner point of the achievable exponent region (D(P1||P0),D(P0||P1)) under the expectation constraint on the length of the test (or the sample size). We consider the expectation constraint in which the expectation of the sample size is bounded by n, and under mild conditions, characterize the backoff, also coined second-order asymptotics, precisely. Examples are provided to illustrate our results.

We consider the class of channels formed from the concatenation of a deletion channel and a finite-state channel. For this class of channels, we show that the operationally-defined capacity is equal to the stationary capacity. We also show that the stationary capacity can be approached by a sequence of Markov processes with increasing Markovian orders. As a byproduct, we show that the polar coding scheme constructed by Tal, Pfister, Fazeli, and Vardy [arxiv: 1904.13385 (2019)] achieves the capacity of the binary deletion channel.

We consider the problem of detecting one of M signals corrupted with white Gaussian noise. Conventionally, to minimize the probability of error, one uses matched filters to obtain a set of M sufficient statistics. In practice, M may be prohibitively large; this motivates the design and analysis of a reduced set of statistics which we term approximate sufficient statistics. By considering a sequence of sensing matrices that possesses suitable coherence and orthogonality properties, we bound the error exponent of the approximate sufficient statistics and compare it to that of the sufficient statistics. Additionally, we show that lower bound on the error exponent increases linearly for small compression rates.

We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions P0and P1and we would like to decide which hypothesis is true using a sequential test. It is known from the work of Wald and Wolfowitz that as the expectation of the length of the test grows, the optimal type-I and type-II error exponents approach the relative entropies D(P1∥P0) and D(P0∥P1). We refine this result by considering the optimal backoff-or second-order asymptotics-from the corner point of the achievable exponent region (D(P1∥P0), D(P0∥P1)) under two different constraints on the length of the test (or the sample size). First, we consider a probabilistic constraint in which the probability that the length of test exceeds a prescribed integer n is less than a certain threshold 0 <; ε <; 1. Second, the expectation of the sample size is bounded by n. In both cases, and under mild conditions, the second-order asymptotics is characterized exactly. Numerical examples are provided to illustrate our results.

In this paper, we consider a discrete channel with inter-cell interference (ICI) as a model for NAND flash memory. We derive an explicit formula for the mutual information rate when the input is Markovian. Using this formula, we obtain the asymptotics of the channel capacity in the high signal-to-noise (SNR) regime.

For a 2-dimensional (2D) Gaussian inter-symbol interference (ISI) channel with discrete input and a 2D discrete memoryless channel with a special class of irreducible constraints, we show that the information capacity is equal to the stationary capacity. As a byproduct, these capacities are shown to be equal to the operational capacity.

In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formula of its mutual information rate; and for a binary erasure channel with its first-order Markovian input supported on the$(1, \infty )$-RLL constraint based on the concavity of its mutual information rate with respect to some parameterization of the input, we numerically evaluate its first-order Markov capacity and further derive its full asymptotics. The asymptotics obtained in this paper, when compared with the recently derived feedback capacity for a binary erasure channel with the same input constraint, enable us to draw the conclusion that feedback may increase the capacity of an input-constrained channel, even if the channel is memoryless.

In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as the order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels.

In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels [2] with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as its order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels.

Principal component analysis (PCA) is an important method for feature extraction of hyperspectral remote sensing image. With the development of hyperspectral sensors, the magnitude of hyperspectral data grows quickly, and it is a challenging task to efficiently reduce the data dimension and compress massive data volumes in hyperspectral imaging. In this paper, a distributed parallel optimization of PCA algorithm (PCA_DP) is presented on cloud computing architecture. The realization of the proposed method using Apache Hadoop and MapReduce model is described and evaluated. The experiments conducted on real hyperspectral images of different sizes, demonstrate significant acceleration factor of PCA_DP. It is efficient for massive hyperspectral data processing.

In this paper, we derive an explicit formula for the entropy rate of a hidden Markov chain, observed when the Markov chain passes through a memoryless erasure channel. This result naturally leads to an explicit formula for the mutual information rate of memoryless erasure channels with Markovian inputs. Moreover, if the input Markov chain is of first-order and supported on the (1,∞)-run length limited (RLL) constraint, we show that the mutual information rate is strictly concave with respect to a chosen parameter. Then we apply a recent algorithm [1] to approximately compute the first-order noisy constrained channel capacity and the corresponding capacity-achieving distribution.

The computation of the capacity of a finite-state channel (FSC) is a fundamental and long-standing open problem in information theory. The capacity of a memoryless channel can be effectively computed via the classical Blahut-Arimoto algorithm (BAA), which, however, does not apply to a general FSC. Recently Vontobel et al. [1] generalized the BAA to compute the capacity of a finite-state machine channel with a Markovian input. Their proof of the convergence of this algorithm, however, depends on the concavity conjecture posed in their paper. In this paper, we confirm the concavity conjecture for some special FSCs. On the other hand, we give examples to show that the conjecture is not true in general.