Sequential differential optimization of incremental redundancy transmission lengths: An example with tail-biting convolutional codes

Wong, Nathan; Vakilinia, Kasra; Wang, Haobo; Ranganathan, Sudarsan V. S.; Wesel, Richard D.

doi:10.1109/ita.2017.8023481

Cited by 7 publications

(5 citation statements)

References 11 publications

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“…We apply the above analysis to the case of tail-biting convolutional codes over additive white Gaussian noise (AWGN) channels. As shown in [15] for binary inputs with a signal-tonoise ratio (SNR) of 2 dB, the Gaussian distribution closelyapproximates the ACK probability as follows:…”

Section: Case Study: Convolutional Codesmentioning

confidence: 97%

“…Optimizing the HARQ approach requires determination of the length of the initial transmission and each subsequent transmission of incremental redundancy. Sequential differential optimization (SDO) [13]- [15] identifies a sequence of HARQ transmission lengths that optimizes throughput. For a specified maximum number of feedback transmissions and a maximum probability that the decoder fails to produce a positive acknowledgement (ACK) even when all possible incremental redundancy has been received, SDO finds the transmission lengths that minimize average blocklength.…”

Section: Introductionmentioning

confidence: 99%

“…For a specified maximum number of feedback transmissions and a maximum probability that the decoder fails to produce a positive acknowledgement (ACK) even when all possible incremental redundancy has been received, SDO finds the transmission lengths that minimize average blocklength. SDO requires a known probability distribution on the probability of ACK at each cumulative blocklength, but works equally well for the variety of distributions that arise from different variable-length codes operating on different channels [15]- [17]. The original formulation of SDO minimizes the average blocklength for a fixed maximum number of feedback transmissions.…”

Section: Introductionmentioning

confidence: 99%

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Timely Transmissions Using Optimized Variable Length Coding

Arafa¹,

Wesel²

2021

Preprint

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A status updating system is considered in which a variable length code is used to transmit messages to a receiver over a noisy channel. The goal is to optimize the codewords lengths such that successfully-decoded messages are timely. That is, such that the age-of-information (AoI) at the receiver is minimized. A hybrid ARQ (HARQ) scheme is employed, in which variable-length incremental redundancy (IR) bits are added to the originally-transmitted codeword until decoding is successful. With each decoding attempt, a non-zero processing delay is incurred. The optimal codewords lengths are analytically derived utilizing a sequential differential optimization (SDO) framework. The framework is general in that it only requires knowledge of an analytical expression of the positive feedback (ACK) probability as a function of the codeword length.

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Section: Case Study: Convolutional Codesmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Timely Transmissions Using Optimized Variable Length Coding

Arafa¹,

Wesel²

2021

Preprint

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“…Later, variations of SDO were developed to improve the Gaussian model accuracy, cf. [11], [12], and SDO was applied to systems that employ incremental redundancy and hybrid automatic repeat request [13] and to the binary erasure channel [14], [15]. However, in this paper, we will show that the Gaussian model is still imprecise for small values of n. Additionally, the existing SDO procedure did not consider the gap constraint of decoding times and is only suitable for VLSF codes with sparse decoding times.…”

Section: Introductionmentioning

confidence: 94%

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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“…Later, variations of SDO were developed to improve the Gaussian model accuracy [13], [14]. The SDO algorithm is used to optimize systems that employ incremental redundancy and hybrid automatic repeat request (ARQ) [15], and to code for the binary erasure channel [16], [17]. However, in this paper, we show that the Gaussian model is still imprecise for small values of n. Additionally, the existing SDO procedure fails to consider the inherent gap constraint that two decoding times must be separated by at least one.…”

Section: Introductionmentioning

confidence: 99%

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

Yang

Yavas

Kostina

et al. 2022

2022 IEEE International Symposium on Information Theory (ISIT)

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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 channel. We first develop tight approximations on the tail probability of length-n cumulative information density. Building on the work of Yavas et al., for a given information density threshold, we formulate the integer program of minimizing the upper bound on average blocklength over all decoding times subject to the average error probability, minimum gap and integer constraints. Eventually, minimization of locally minimum upper bounds over all thresholds will yield the globally minimum upper bound and this is called the two-step minimization. For the integer program, we present a greedy algorithm that yields possibly suboptimal integer decoding times. By allowing a positive realvalued decoding time, we develop the gap-constrained sequential differential optimization (SDO) procedure that sequentially produces the optimal, real-valued decoding times. We identify the error regime in which Polyanskiy's scheme of stopping at zero does not improve the achievability bound. In this error regime, the two-step minimization with the gap-constrained SDO shows that a finite m suffices to attain Polyanskiy's bound for VLSF codes with m = ∞.

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Sequential differential optimization of incremental redundancy transmission lengths: An example with tail-biting convolutional codes

Cited by 7 publications

References 11 publications

Timely Transmissions Using Optimized Variable Length Coding

Timely Transmissions Using Optimized Variable Length Coding

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

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

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