The information bottleneck channel (or the oblivious relay channel) concerns a channel coding setting where the decoder does not directly observe the channel output. Rather, the channel output is relayed to the decoder by an oblivious relay (which does not know the codebook) via a rate-limited link. The capacity is known to be given by the information bottleneck. We study finite-blocklength achievability results of the channel, where the relay communicates to the decoder via fixed-length or variable-length codes. These two cases give rise to two different second-order versions of the information bottleneck. Our proofs utilize the nonasymptotic noisy lossy source coding results by Kostina and Verdú, the strong functional representation lemma, and the Poisson matching lemma. Moreover, we also give a novel nonasymptotic variable-length noisy lossy source coding result.

The information bottleneck channel (or the oblivious relay channel) concerns a channel coding setting where the decoder does not directly observe the channel output. Rather, the channel output is relayed to the decoder by an oblivious relay (which does not know the codebook) via a rate-limited link. The capacity is known to be given by the information bottleneck. We study finite-blocklength achievability results of the channel, where the relay communicates to the decoder via fixed-length or variable-length codes. These two cases give rise to two different second-order versions of the information bottleneck. Our proofs utilize the nonasymptotic noisy lossy source coding results by Kostina and Verdú, the strong functional representation lemma, and the Poisson matching lemma. Moreover, we also give a novel nonasymptotic variable-length noisy lossy source coding result. A full version of this paper is accessible at [1].

We present a unified one-shot coding framework designed for the communication and compression of messages among multiple nodes across a general acyclic noisy network. Our setting can be seen as a one-shot version of the acyclic discrete memoryless network studied by Lee and Chung, and noisy network coding studied by Lim, Kim, El Gamal and Chung. We design a proof technique, called the exponential process refinement lemma, that is rooted in the Poisson matching lemma by Li and Anantharam, and can significantly simplify the analyses of one-shot coding over multi-hop networks. Our one-shot coding theorem not only recovers a wide range of existing asymptotic results, but also yields novel one-shot achievability results in different multi-hop network information theory problems, such as compress-and-forward and partial-decode-and-forward bounds for a one-shot (primitive) relay channel, and a bound for one-shot cascade multiterminal source coding. In a broader context, our framework provides a unified one-shot bound applicable to any combination of source coding, channel coding and coding for computing problems.

We present a unified one-shot coding framework designed for communication and compression of messages among multiple nodes across a general acyclic noisy network. Our setting can be seen as a one-shot version of the acyclic discrete memoryless network studied by Lee and Chung, and noisy network coding studied by Lim, Kim, El Gamal and Chung. We design a proof technique, called the exponential process refinement lemma, that is rooted in the Poisson matching lemma by Li and Anantharam, and can significantly simplify the analyses of one-shot coding over multi-hop networks. Our one-shot coding theorem not only recovers a wide range of existing asymptotic results, but also yields novel one-shot achievability results in different multi-hop network information theory problems. In a broader context, our framework provides a unified one-shot bound applicable to any combination of source coding, channel coding and coding for computing problems.

We present a one-shot information-theoretic analysis of the information hiding problem, which has a wide range of applications including watermarking, fingerprinting, steganogra-phy and copyright protection. The problem can be viewed as a game: one party includes an information hider and a decoder, where the former embeds a message into a host data source and introduces some tolerable distortion, and the latter wishes to reconstruct the message; another party is an attacker that is modeled as a noisy channel which aims at removing the hidden information. We derive a one-shot achievability result using the Poisson matching lemma. Unlike previous asymptotic results, our result applies to any distribution of the host data, and any class of attack channels (not necessarily memoryless or ergodic).

To reduce the communication cost of differential privacy mechanisms, we introduce a novel construction, called Poisson private representation (PPR), designed to compress and simulate any local randomizer while ensuring local differential privacy. Unlike previous simulation-based local differential privacy mechanisms, PPR exactly preserves the joint distribution of the data and the output of the original local randomizer. Hence, the PPR-compressed privacy mechanism retains all desirable statistical properties of the original privacy mechanism such as unbiasedness and Gaussianity. Moreover, PPR achieves a compression size within a logarithmic gap from the theoretical lower bound. Using the PPR, we give a new order-wise trade-off between communication, accuracy, central and local differential privacy for distributed mean estimation. Experiment results on distributed mean estimation show that PPR consistently gives a better trade-off between communication, accuracy and central differential privacy compared to the coordinate subsampled Gaussian mechanism, while also providing local differential privacy.

The literature provides evidence that considering signal propagation delays can significantly enhance the scheduling rate region of wireless networks. This paper focuses on the link scheduling problem in networks where signal delays between nodes are multiples of a time interval. To model such networks, a directed hypergraph is employed, along with an integer matrix that specifies the delays. The link scheduling problem is closely connected to the independent sets of the periodic hypergraph induced by the network model. However, due to the infinite number of vertices, it is impractical to enumerate the independent sets of the periodic hypergraph using generic graph algorithms. To tackle this challenge, a graphical approach is proposed in this paper. The link scheduling rate region is characterized using a finite directed graph called a scheduling graph, which is derived from the network model. A collision-free schedule of the network corresponds to a path in the scheduling graph, and the rate region is determined by the convex hull of the rate vectors associated with the cycles in the scheduling graph. Although existing cycle enumeration algorithms can be employed to calculate the rate region, their computational complexity becomes prohibitively high as the size of the scheduling graph grows exponentially with the number of network links. To address this issue, the dominance property of a special scheduling graph called the step-$T$scheduling graph is investigated. This property allows the utilization of specific subgraphs of the step-$T$scheduling graph to characterize the scheduling rate region, achieving a reduction in both the number of cycles and their lengths. For common problems such as calculating the rate region and maximizing a weighted sum of the scheduling rates, algorithms leveraging the dominance property are developed. These algorithms can be more efficient than using generic graph algorithms directly on the scheduling graphs.

In this paper, we introduce a new class of codes, called weighted parity-check codes, where each parity-check bit has a weight that indicates its likelihood to be one (instead of fixing each parity-check bit to be zero). It is applicable to a wide range of settings, e.g. asymmetric channels, channels with state and/or cost constraints, and the Wyner-Ziv problem, and can provably achieve the capacity. For the channel with state (Gelfand-Pinsker) setting, the proposed coding scheme has two advantages. First, it achieves the capacity of any channel with state (e.g. asymmetric channels). Second, simulation results show that the proposed code achieves a smaller error rate compared to the nested linear codes. We also discuss a sparse construction where the belief propagation algorithm can be applied to improve the coding efficiency.

We consider a generalized collision channel model for general multi-user communication systems, an extension of Massey and Mathys’ collision channel without feedback for multiple access communications. In our model, there are multiple transmitters and receivers sharing the same communication channel. The transmitters are not synchronized and arbitrary time offsets between transmitters and receivers are assumed. A "collision" occurs if two or more packets from different transmitters partially or completely overlap at a receiver. Our model includes the original collision channel as a special case.This paper focuses on reliable throughputs that are approachable for arbitrary time offsets. We consider both slot-synchronized and non-synchronized cases and characterize their reliable throughput regions for the generalized collision channel model. These two regions are proven to coincide. Moreover, it is shown that the protocol sequences constructed for multiple access communication remain "throughput optimal" in the generalized collision channel model. We also identify the protocol sequences that can approach the outer boundary of the reliable throughput region.

We study the link scheduling problem of wireless networks with signal propagation delays into consideration. Recently, when the propagation delays are integers, the rate region using slotted scheduling with a proper timeslot size has been characterized explicitly. We study the general case that the propagation delays can be real values and the scheduling can be unslotted. As a practical communication device cannot transmit signals in arbitrarily short time intervals, we focus on scheduling where an active interval’s length is bounded below by a given value. We first reveal some properties of continuity of the scheduling rate region concerning the propagation delays. We then show that for a network with rational propagation delays, the continuous (unslotted) scheduling rate region is the same as that of slotted scheduling with a proper timeslot size when the bound on the active interval length is sufficiently small. Moreover, for a network with possibly irrational propagation delays, we provide an approximation of the network by Dirichlet’s theorem so that the continuous scheduling rate region of the original network can be approximated by the slotted scheduling rate region for a network with integer delays.

In this paper, we introduce a new class of codes, called weighted parity-check codes, where each parity-check bit has a weight that indicates its likelihood to be one (instead of fixing each parity-check bit to be zero). It is applicable to a wide range of settings, e.g. asymmetric channels, channels with state and/or cost constraints, and can provably achieve the capacity. For the channel with state (Gelfand-Pinsker) setting, the proposed coding scheme has two advantages compared to the nested linear code. First, it achieves the capacity of any channel with state (e.g. asymmetric channels). Second, simulation results show that the proposed code achieves a smaller error rate compared to the nested linear code.

We study the link scheduling problem of wireless networks where signal propagation delays are multiples of certain time interval. The problem can be modeled as a character of the independent sets of periodic graphs, which have infinitely many vertices. We show that the rate region of scheduling a network can be achieved using collision-free, periodic schedules, and derive a graphical approach to explicitly characterize the rate region. In particular, a collision-free schedule can be equivalent to a path in a graph called the scheduling graph induced by the network collision profile and the propagation delays, and hence the rate region is equal to the convex hull of the rate vectors associated with the cycles of the scheduling graph, which have bounded length. With the maximal independent set problem as a special case, calculating the whole rate region is NP hard and also hard to approximate. By exploring a partial order on the paths, we derive an algorithm to calculate a subset of the rate region more efficiently. Our results are also of independent interest for periodic graphs.