Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced by Polyanskiy for the Multiple Access Channel (MAC) with a fixed, known number of transmitters, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario where neither the transmitters nor the receiver know which transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Scheduled feedback of a finite number of bits is used to synchronize the transmitters. The decoder is tasked with determining from the channel output the number of active transmitters ($k$) and their messages but not which transmitter sent which message. The decoding procedure occurs at a time $n_t$ depending on the decoder's estimate $t$ of the number of active transmitters, $k$, thereby achieving a rate that varies with the number of active transmitters. Single-bit feedback at each time $n_i, i \leq t$, enables all transmitters to determine the end of one coding epoch and the start of the next. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require $2^k - 1$ simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion.Comment: Presented at ISIT18', submitted to IEEE Transactions on Information Theor

Gaussian Multiple and Random Access in the Finite Blocklength Regime

This paper presents finite-blocklength achievabil- ity bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter’s rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to ½ log n/n + O(1/n) bits per channel use. The result then extends to a RAC model in which neither the encoders nor the decoder knows which of K possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time n t that depends on the decoder’s estimate t of the number of active transmitters k. Single-bit feedback from the decoder to all encoders at each potential decoding time n_i, i ≤ t, informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced for the Multiple Access Channel (MAC) with a fixed, known number of transmitters by Polyanskiy, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario in which neither the transmitters nor the receiver know which or how many transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Limited feedback is used to ensure that the collection of active transmitters remains fixed during each epoch. The decoder is tasked with determining from the channel output the number of active transmitters (k) and their messages but not which transmitter sent which message. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion

Gaussian Multiple and Random Access in the Finite Blocklength Regime

This paper presents finite-blocklength achievabil- ity bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a sphere and a maximum likelihood decoder, the derived MAC bound on each transmitter’s rate matches the MolavianJazi-Laneman bound (2015) in its first- and second-order terms, improving the remaining terms to ½ log n/n + O(1/n) bits per channel use. The result then extends to a RAC model in which neither the encoders nor the decoder knows which of K possible transmitters are active. In the proposed rateless coding strategy, decoding occurs at a time n t that depends on the decoder’s estimate t of the number of active transmitters k. Single-bit feedback from the decoder to all encoders at each potential decoding time n_i, i ≤ t, informs the encoders when to stop transmitting. For this RAC model, the proposed code achieves the same first-, second-, and third-order performance as the best known result for the Gaussian MAC in operation

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. As in the model recently introduced by Polyanskiy for the Multiple Access Channel (MAC) with a fixed, known number of transmitters, the channel is assumed to be invariant to permutations on its inputs, and all active transmitters employ identical encoders. Unlike the Polyanskiy model, in the proposed scenario, neither the transmitters nor the receiver knows which transmitters are active. We refer to this agnostic communication setup as the Random Access Channel (RAC). Scheduled feedback of a finite number of bits is used to synchronize the transmitters. The decoder is tasked with determining from the channel output the number of active transmitters, k, and their messages but not which transmitter sent which message. The decoding procedure occurs at a time n_t depending on the decoder’s estimate, t, of the number of active transmitters, k, thereby achieving a rate that varies with the number of active transmitters. Single-bit feedback at each time n_i, i ≤ t, enables all transmitters to determine the end of one coding epoch and the start of the next. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced for the Multiple Access Channel (MAC) with a fixed, known number of transmitters by Polyanskiy, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario in which neither the transmitters nor the receiver know which or how many transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Limited feedback is used to ensure that the collection of active transmitters remains fixed during each epoch. The decoder is tasked with determining from the channel output the number of active transmitters (k) and their messages but not which transmitter sent which message. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion

Non-Asymptotic Analysis of Single-Receiver Channels with Limited Feedback

Emerging Internet of Things, machine-type communication, and ultra-reliable low-latency communication in 5G demand codes that operate at short blocklengths, have low error probability and low energy consumption, and can handle the random activity of a large number of communicating devices. Since many of the applications have a single central device, e.g., a base station, that resolves the communication and a varying number of users, these requirements on the code design motivate interest in the non-asymptotic analysis of codes in a variety of single-receiver channels. This thesis investigates three channel coding problems with the goals of understanding the fundamental limits of channel coding under stringent requirements on reliability, delay, and power, and proposes novel coding architectures that employ constrained feedback to attain those limits. In the first part, we consider point-to-point channels without feedback, and analyze the non-asymptotic limits in the moderate deviations regime in probability theory. The moderate deviations regime is suitable for accurately approximating the maximum achievable coding rate in the operational regimes of practical interest because it simultaneously considers high rates and low error probabilities. We propose a new quantity, channel skewness, which governs the fundamental limit at short blocklengths and low error probabilities. Our approximation is the tightest among the state-of-the-art approximations for most error probability and latency constraints of interest. In the second part, we investigate rateless channel coding with limited feedback. Here, rateless means that decoding can occur at multiple decoding times. In our code design, feedback is limited both in frequency and content; it is sparse, meaning that it is available only at a few instants throughout the communication epoch; and it is stop-feedback, meaning that the receiver informs the transmitters only about whether decoding has occurred rather than what symbols it has received. Our results demonstrate that sporadically sending a few bits is almost as efficient as sending feedback at every time instant. In the third part, we focus on rateless random access channel codes, where the number of active transmitters is unknown to both the transmitters and the receiver. Our rateless code design that reserves a decoding time for each possible number of active transmitters achieves the same first two terms in the asymptotic expansion of the achievable rate as codes where the transmitter activity is known a priori. This means that, remarkably, the random transmitter activity has almost no effect on achievable rates. To obtain tight channel coding bounds, we analyze some non-asymptotic and asymptotic state-of-the-art bounds on the probability of the sum of independent and identical random variables, whose applications extend to source coding, hypothesis testing, and many others. In the scenarios where these tools are not directly applicable such as for the Gaussian channel, we propose new techniques to overcome that difficulty.</p

Variable-Length Coding for Binary-Input Channels With Limited Stop Feedback

This paper focuses on the numerical evaluation of the maximal achievable rate of variable-length stop-feedback (VLSF) codes with $m$ decoding times at a given message size and error probability for binary-input additive white Gaussian noise channel, binary symmetric channel, and binary erasure channel (BEC). Leveraging the Edgeworth and Petrov expansions, we develop tight approximations to the tail probability of length-$n$ cumulative information density that are accurate for any blocklength $n$. We reduce Yavas \emph{et al.}'s non-asymptotic achievability bound on VLSF codes with $m$ decoding times to an integer program of minimizing the upper bound on the average blocklength subject to the average error probability, minimum gap, and integer constraints. We develop two distinct methods to solve this program. Numerical evaluations show that Polyanskiy's achievability bound for VLSF codes, which assumes $m = \infty$, can be approached with a relatively small $m$ in all of the three channels. For BEC, we consider systematic transmission followed by random linear fountain coding. This allows us to obtain a new achievability bound stronger than a previously known bound and new VLSF codes whose rate further outperforms Polyanskiy's bound.Comment: 18 pages, 12 figures; submitted to IEEE Transactions on Information Theory. An earlier version of this work was accepted for presentation at ISIT 202