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. 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 decoding procedure occurs at a time nt depending on the decoder's estimate t of the number of active transmitters, thereby achieving a rate that varies with the number of active transmitters. Single-bit feedback at each time ni, 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.
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 nt 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 ni, 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.Index Terms-Channel coding, random access channel, finite blocklength regime, achievability, second-order asymptotics, rateless codes. I. INTRODUCTIONAccess points like WiFi hot spots and cellular base stations are, for wireless devices, the gateway to the network. Unfortunately, access points are also the network's most critical bottleneck. As more kinds of devices become network-reliant, both the number of communicating devices and the diversity of their communication needs grow. Little is known about how to code under high variation in the number and variety of communicators.Multiple-transmitter single-receiver channels are well understood in information theory when the number and identities of transmitters are fixed and known. Unfortunately, even in this known-transmitter regime, information-theoretic solutions are too complex to implement. As a result, orthogonalization methods, such as TDMA, FDMA, and orthogonal CDMA, are
We investigate variable-length feedback (VLF) codes for the Gaussian point-to-point channel under maximal power, average error probability, and average decoding time constraints. Our proposed strategy chooses K < ∞ decoding times n1, n2, . . . , nK rather than allowing decoding at any time n = 0, 1, 2, . . . . We consider stop-feedback, which is one-bit feedback transmitted from the receiver to the transmitter at times n1, n2, . . . only to inform her whether to stop. We prove an achievability bound for VLF codes with the asymptotic1− , where ln (K) (•) denotes the K-fold nested logarithm function, N is the average decoding time, and C(P ) and V (P ) are the capacity and dispersion of the Gaussian channel, respectively. Our achievability bound evaluates a non-asymptotic bound and optimizes the decoding times n1, . . . , nK within our code architecture. Index Terms-Variable-length stop-feedback codes, Gaussian channel, second-order achievability bound.
This paper presents finite-blocklength achievability 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 secondorder terms, improving the remaining terms to 1 2 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 nt 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 ni, 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. Index Terms-Gaussian multiple access channel, Gaussian random access channel, third-order asymptotics, finite blocklength, maximum likelihood decoder, spherical distribution.
This paper presents finite-blocklength achievability 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 secondorder terms, improving the remaining terms to 1 2 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 nt 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 ni, 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. Index Terms-Gaussian multiple access channel, Gaussian random access channel, third-order asymptotics, finite blocklength, maximum likelihood decoder, spherical distribution.
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