Channel Coding over Multiple Coherence Blocks with Queueing Constraints

This paper investigates the performance of wireless systems that employ finite-blocklength channel codes for transmission and operate under queueing constraints in the form of limitations on buffer overflow probabilities. A block fading model, in which fading stays constant in each coherence block and change independently between blocks, is considered. It is assumed that channel coding is performed over multiple coherence blocks. An approximate lower bound on the transmission rate is obtained from Feintein's Lemma. This lower bound is considered as the service rate and is incorporated into the effective capacity formulation, which characterizes the maximum constant arrival rate that can be supported under statistical queuing constraints. Performances of variable-rate and fixed-rate transmissions are studied. The optimum error probability for variable rate transmission and the optimum coding rate for fixed rate transmission are shown to be unique. Moreover, the tradeoff between the throughput and the number of blocks over which channel coding is performed is identified.Comment: submitted to ICC 201

Throughput Analysis of Buffer-Constrained Wireless Systems in the Finite Blocklength Regime

In this paper, wireless systems operating under queueing constraints in the form of limitations on the buffer violation probabilities are considered. The throughput under such constraints is captured by the effective capacity formulation. It is assumed that finite blocklength codes are employed for transmission. Under this assumption, a recent result on the channel coding rate in the finite blocklength regime is incorporated into the analysis and the throughput achieved with such codes in the presence of queueing constraints and decoding errors is identified. Performance of different transmission strategies (e.g., variable-rate, variable-power, and fixed-rate transmissions) is studied. Interactions between the throughput, queueing constraints, coding blocklength, decoding error probabilities, and signal-to-noise ratio are investigated and several conclusions with important practical implications are drawn

On the Distribution of the Information Density of Gaussian Random Vectors: Explicit Formulas and Tight Approximations

Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a general formula to calculate the central moments. Using the general results we give closed-form expressions of the PDF and CDF and explicit formulas of the central moments for important special cases. Furthermore, we derive recurrence formulas and tight approximations of the general series representations, which allow very efficient numerical calculations with an arbitrarily high accuracy as demonstrated with an implementation in Python publicly available on GitLab. Finally, we discuss the (in)validity of Gaussian approximations of the information density.Comment: This extended version of the manuscript replaces the previous versions and is submitted to the journal "Problems of Information Transmission". An implementation in Python allowing efficient numerical calculations related to the main results of the paper is publicly available on GitLab: https://gitlab.com/infth/information-densit

Channels That Die

Given the possibility of communication systems failing catastrophically, we investigate limits to communicating over channels that fail at random times. These channels are finite-state semi-Markov channels. We show that communication with arbitrarily small probability of error is not possible. Making use of results in finite blocklength channel coding, we determine sequences of blocklengths that optimize transmission volume communicated at fixed maximum message error probabilities. We provide a partial ordering of communication channels. A dynamic programming formulation is used to show the structural result that channel state feedback does not improve performance

How URLLC can Benefit from NOMA-based Retransmissions

Among the new types of connectivity unleashed by the emerging 5G wireless systems, Ultra-Reliable Low Latency Communication (URLLC) is perhaps the most innovative, yet challenging one. Ultra-reliability requires high levels of diversity, however, the reactive approach based on packet retransmission in HARQ protocols should be applied carefully to conform to the stringent latency constraints. The main premise of this paper is that the NOMA principle can be used to achieve highly efficient retransmissions by allowing concurrent use of wireless resources in the uplink. We introduce a comprehensive solution that accommodates multiple intermittently active users, each with its own HARQ process. The performance is investigated under two different assumptions about the Channel State Information (CSI) availability: statistical and instantaneous. The results show that NOMA can indeed lead to highly efficient system operation compared to the case in which all HARQ processes are run orthogonally

Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback

The minimum achievable energy per bit over memoryless Gaussian channels has been previously addressed in the limit when the number of information bits goes to infinity, in which case it is known that the availability of noiseless feedback does not lower the minimum energy per bit, which is -1.59 dB below the noise level. This paper analyzes the behavior of the minimum energy per bit for memoryless Gaussian channels as a function of k, the number of information bits. It is demonstrated that in this nonasymptotic regime, noiseless feedback leads to significantly better energy efficiency. In particular, without feedback achieving energy per bit of -1.57 dB requires coding over at least k=10[superscript 6] information bits, while we construct a feedback scheme that transmits a single information bit with energy -1.59 dB and zero error. We also show that unless k is very small, approaching the minimal energy per bit does not require using the feedback link except to signal that transmission should stop.National Science Foundation (U.S.) (Grant CCF-06-35154)National Science Foundation (U.S.) (grant CNS-09-05398

The Information-Outage Probability of Finite-Length Codes over AWGN Channels

The performance of random error control codes approaches the Shannon capacity limit as the code length goes to infinity. When the code length is finite, then the code will be unable to achieve arbitrarily low error probability and a nonzero codeword error rate is inevitable. Information-theoretic bounds on codeword error rate may be found as a function of length through traditional methods such as sphere packing. Alternatively, the behavior of finite-length codes can be characterized in terms of an information-outage probability. The informationoutage probability is the probability that the mutual information, which is a random variable, is less than the rate. In this paper, a Gaussian approximation is proposed that accurately models the information-outage probability for moderately small codes. The information-outage probability is related to several previously derived bounds, including Shannon’s sphere-packing and random coding bounds, as well as a bound on maximal error probability known as Feinstein’s lemma. It is shown that the informationoutage probability is a useful predictor of achievable error rate