Feedback Communication Systems with Limitations on Incremental Redundancy

This paper explores feedback systems using incremental redundancy (IR) with noiseless transmitter confirmation (NTC). For IR-NTC systems based on {\em finite-length} codes (with blocklength $N$) and decoding attempts only at {\em certain specified decoding times}, this paper presents the asymptotic expansion achieved by random coding, provides rate-compatible sphere-packing (RCSP) performance approximations, and presents simulation results of tail-biting convolutional codes. The information-theoretic analysis shows that values of $N$ relatively close to the expected latency yield the same random-coding achievability expansion as with $N = \infty$. However, the penalty introduced in the expansion by limiting decoding times is linear in the interval between decoding times. For binary symmetric channels, the RCSP approximation provides an efficiently-computed approximation of performance that shows excellent agreement with a family of rate-compatible, tail-biting convolutional codes in the short-latency regime. For the additive white Gaussian noise channel, bounded-distance decoding simplifies the computation of the marginal RCSP approximation and produces similar results as analysis based on maximum-likelihood decoding for latencies greater than 200. The efficiency of the marginal RCSP approximation facilitates optimization of the lengths of incremental transmissions when the number of incremental transmissions is constrained to be small or the length of the incremental transmissions is constrained to be uniform after the first transmission. Finally, an RCSP-based decoding error trajectory is introduced that provides target error rates for the design of rate-compatible code families for use in feedback communication systems.Comment: 23 pages, 15 figure

Capacity, Error Exponent, and Structural Results for Communication Networks

In various multi-terminal communication scenarios, contrary to point-to-point communication, characterization of fundamental limits such as capacity and error exponent is still an open problem. We study such fundamental limits and the structure of optimality achieving codes. This thesis consists of two parts: in the first part, we investigate the role of algebraic structures in multi-terminal communications. We show the necessity of various types of algebraic structure in capacity achieving codes and argue that the lack of such structures in the conventional random codes leads to their sub-optimality. We develop a new class of partially structured codes called quasi-structured code (QSC). Such codes span the spectrum from completely structured to completely unstructured codes. It is shown that the application of QSCs leads to improvements over the current coding strategies for many problems including distributed source coding and multiple-access channel (MAC) with feedback. In the second part of the thesis, we study the optimal error exponent in various multi-terminal communication scenarios. We derive a lower and upper bound on the error exponent of discrete memoryless MAC with noiseless feedback and variable-length codes (VLCs). The bounds increase linearly with respect to a specific Euclidean distance measure defined between the transmission rate pair and the capacity boundary. The bounds are shown to be tight for specific classes of MACs.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149959/1/mohsenhd_1.pd

Causal Sampling, Compressing, and Channel Coding of Streaming Data

With the emergence of the Internet of Things, communication systems, such as those employed in distributed control and tracking scenarios, are becoming increasingly dynamic, interactive, and delay-sensitive. The data in such real-time systems arrive at the encoder progressively in a streaming fashion. An intriguing question is: what codes can transmit streaming data with both high reliability and low latency? Classical non-causal (block) encoding schemes can transmit data reliably but under the assumption that the encoder knows the entire data block before the transmission. While this is a realistic assumption in delay-tolerant systems, it is ill-suited to real-time systems due to the delay introduced by collecting data into a block. This thesis studies causal encoding: the encoder transmits information based on the causally received data while the data is still streaming in and immediately incorporates the newly received data into a continuing transmission on the fly. This thesis investigates causal encoding of streaming data in three scenarios: causal sampling, causal lossy compressing, and causal joint source-channel coding (JSCC). In the causal sampling scenario, a sampler observes a continuous-time source process and causally decides when to transmit real-valued samples of it under a constraint on the average number of samples per second; an estimator uses the causally received samples to approximate the source process in real time. We propose a causal sampling policy that achieves the best tradeoff between the sampling frequency and the end-to-end real-time estimation distortion for a class of continuous Markov processes. In the causal lossy compressing scenario, the sampling frequency constraint in the causal sampling scenario is replaced by a rate constraint on the average number of bits per second. We propose a causal code that achieves the best causal distortion-rate tradeoff for the same class of processes. In the causal JSCC scenario, the noiseless channel and the continuous-time process in the previous scenarios are replaced by a discrete memoryless channel with feedback and a sequence of streaming symbols, respectively. We propose a causal joint sourcechannel code that achieves the maximum exponentially decaying rate of the error probability compatible with a given rate. Remarkably, the fundamental limits in the causal lossy compressing and the causal JSCC scenarios achieved by our causal codes are no worse than those achieved by the best non-causal codes. In addition to deriving the fundamental limits and presenting the causal codes that achieve the limits, we also show that our codes apply to control systems, are resilient to system deficiencies such as channel delay and noise, and have low complexities.</p

Belief Refinement Approaches to Communication and Inference Problems

This dissertation considers a problem where a single agent or a group of agents aim to estimate/learn unknown (possibly time-varying) parameters of interest despite making noisy observations. The agents take a Bayesian-like approach by maintaining a posterior probability distribution or “belief" over a parameter space conditioned on past observations. The agents aim to iteratively refine their belief over the parameter space as new information is acquired from their private observations or through collaboration with other agents. In particular, the agents aim to ensure that sufficient belief is assigned in neighborhoods centered around the true parameter with high probability or “reliability". In the context of communication problems considered in this dissertation, the agents may be active, i.e., agents may additionally take actions which provide new observations. Furthermore, agents may employ an adaptive strategy, i.e., using their past actions and the resulting observations, agents can adaptively choose actions to control the concentration of the belief. When the agents are active, we propose and analyze adaptive belief refinement approaches to obtain belief concentration on the unknown parameter with high reliability. In a different context, namely that of decentralized inference, we consider passive agents. Here, agents face an additional challenge due to the statistical insufficiency of their private observations to learn the unknown parameter. While individual agents’ observations are not informative enough, we assume that the agents’ observations are collectively informative to learn the unknown parameter. Here, we propose and analyze decentralized belief refining strategies to collaboratively obtain belief concentration on the unknown parameter. In the first part of this dissertation, we consider active strategies that are extensions of the posterior matching strategy (PM) introduced by Horstein, which is a generalization of the well-known binary search algorithm. We propose and analyze PM based strategies in the context of modern communication systems, namely the problem of establishing initial access in mm-Wave communication and spectrum sensing for Cognitive Radio. We propose and analyze channel coding strategies for real-time streaming and control applications. The second part of the dissertation investigates the belief refinement approaches for decentralized learning. In particular, it focusing on developing and analyzing a decentralized learning rule for statistical hypothesis testing and its application to decentralized machine learning