A New Method for Employing Feedback to Improve Coding Performance

Wagner, Aaron B.; Shende, Nirmal V.; Altug, Yucel

doi:10.1109/tit.2020.2997385

Cited by 16 publications

(18 citation statements)

References 35 publications

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“…Furthermore, for = 10 −3 , P = 1, and N = 1000, 83.6% of the -capacity is achieved with K = 1, 85.3% with K = 2, 92.2% with K = 3, and 95.4% with K = 4. The achievability bounds for K ∈ [4] and the converse bound (17) are illustrated in Fig. 1.…”

Section: Related Workmentioning

confidence: 99%

“…Feedback simplifies coding in Horstein's scheme for the binary symmetric channel [2] and Schalkwijk and Kailath's scheme [3] for the Gaussian channel. Wagner et al [4] show that feedback improves the second-order achievable rate for any discrete memoryless channel (DMC) with multiple capacity-achieving input distributions giving distinct dispersions.…”

Section: Introductionmentioning

confidence: 99%

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Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel

Yavas

Kostina

Effros

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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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.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel

Yavas

Kostina

Effros

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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“…In the variable-length regime, feedback has been shown to simplify the transmission scheme [2], [3] and to significantly improve the optimal error exponent [4]. In the fixedlength regime, feedback is shown to improve the second-order coding rate for the compound-dispersion discrete memoryless channels [5].…”

Section: Introductionmentioning

confidence: 99%

Variable-Length Stop-Feedback Codes With Finite Optimal Decoding Times for BI-AWGN Channels

Yang¹,

Yavas²,

Kostina³

et al. 2022

Preprint

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In this paper, we are interested in the performance of a variable-length stop-feedback (VLSF) code with m optimal decoding times for the binary-input additive white Gaussian noise (BI-AWGN) channel. We first develop tight approximations on the tail probability of length-n cumulative information density. Building on the work of Yavas et al., we formulate the problem of minimizing the upper bound on average blocklength subject to the error probability, minimum gap, and integer constraints. For this integer program, we show that for a given error constraint, a VLSF code that decodes after every symbol attains the maximum achievable rate. We also present a greedy algorithm that yields possibly suboptimal integer decoding times. By allowing a positive real-valued decoding time, we develop the gap-constrained sequential differential optimization (SDO) procedure. Numerical evaluation shows that the gap-constrained SDO can provide a good estimate on achievable rate of VLSF codes with m optimal decoding times and that a finite m suffices to attain Polyanskiy's bound for VLSF codes with m = ∞.

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“…Note that we are comparing the RAC achievable rate with rate-0 feedback to the MAC capacity without feedback. Wagner et al[37] show that if a discrete, memoryless, point-to-point channel has at least two capacityachieving input distributions and their dispersions V 1 (13) are distinct, then using one-bit feedback improves the achievable second-order term. Although rate-0 feedback does not change the capacity region of a discrete memoryless MAC[29], in light of[37] it is plausible that even one-bit feedback can improve the achievable second-order term for some MACs 7.…”

mentioning

confidence: 99%

“…Wagner et al[37] show that if a discrete, memoryless, point-to-point channel has at least two capacityachieving input distributions and their dispersions V 1 (13) are distinct, then using one-bit feedback improves the achievable second-order term. Although rate-0 feedback does not change the capacity region of a discrete memoryless MAC[29], in light of[37] it is plausible that even one-bit feedback can improve the achievable second-order term for some MACs 7. As noted previously, focusing on scenarios with decoding times ordered as n 1 < n 2 < • • • < n K simplifies the exposition but is not critical to the approach.Authorized licensed use limited to: CALIFORNIA INSTITUTE OF TECHNOLOGY.…”

mentioning

confidence: 99%

Random Access Channel Coding in the Finite Blocklength Regime

Yavas

Kostina

Effros

2021

IEEE Trans. Inform. Theory

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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

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A New Method for Employing Feedback to Improve Coding Performance

Cited by 16 publications

References 35 publications

Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel

Variable-length Feedback Codes with Several Decoding Times for the Gaussian Channel

Variable-Length Stop-Feedback Codes With Finite Optimal Decoding Times for BI-AWGN Channels

Random Access Channel Coding in the Finite Blocklength Regime

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