An iteratively optimized linear coding scheme for correlated Gaussian channels with noisy feedback

Agrawal, M. C.; Love, David J.; Balakrishnan, V.

doi:10.1109/allerton.2011.6120278

Cited by 3 publications

(16 citation statements)

References 9 publications

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“…Motivated by the advantages of incorporating the received signals into transmit signals through feedback in GOWCs, e.g., enhancing communication reliability [3]- [5], [9], we consider a linear coding framework at the users that exploits the feedback in GTWCs. In our framework, users receive some feedback information from one another and utilize that to generate their transmit signals.…”

Section: System Model In Gaussian Two-way Channelsmentioning

confidence: 99%

“…By comparing the equations in ( 8) and ( 9), we can find g 2 = (I + F2 F1 ) −1 g2 and F 2 = (I + F2 F1 ) −1 F2 . Similarly, we can rewrite the equation in (5) as…”

Section: System Model In Gaussian Two-way Channelsmentioning

confidence: 99%

“…Since the decoding is conducted at each of the users independently, we can use the same technique used in GOWC to find the optimal linear decoding scheme [4], [5]. After the N channel uses, each user aims to estimate the message of the other user.…”

Section: A Design Of Optimal Linear Decoding Schemesmentioning

confidence: 99%

“…For Gaussian one-way channels (GOWCs), the seminal work done by Schalkwijk and Kailath (S-K) in [3] introduced a simple linear encoding that can achieve doubly exponential decay in the probability of error upon having noiseless feedback information. In [4], Chance and Love proposed a linear encoding scheme for GOWCs with noisy feedback, which is further analyzed and revealed to be the optimal linear encoding scheme by [5]. In [6], Kim.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we aim to bridge the gaps between the two pieces of literature on GOWCs and GTWCs. To this end, we propose a general system model for linear coding in GTWCs by extending the existing formulations in GOWC literature [4], [5], [9] to GTWCs.…”

Section: Introductionmentioning

confidence: 99%

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Linear Coding for Gaussian Two-Way Channels

Kim¹,

Hosseinalipour²,

Kim³

et al. 2022

Preprint

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We consider linear coding for Gaussian two-way channels (GTWCs), in which each user generates the transmit symbols by linearly encoding both its message and the past received symbols (i.e., the feedback information) from the other user. In Gaussian one-way channels (GOWCs), Butman has proposed a well-developed model for linear encoding that encapsulates feedback information into transmit signals. However, such a model for GTWCs has not been well studied since the coupling of the encoding processes at the users in GTWCs renders the encoding design non-trivial and challenging. In this paper, we aim to fill this gap in the literature by extending the existing signal models in GOWCs to GTWCs. With our developed signal model for GTWCs, we formulate an optimization problem to jointly design the encoding/decoding schemes for both the users, aiming to minimize the weighted sum of their transmit powers under signal-to-noise ratio constraints. First, we derive an optimal form of the linear decoding schemes under any arbitrary encoding schemes employed at the users. Further, we provide new insights on the encoding design for GTWCs. In particular, we show that it is optimal that one of the users (i) does not transmit the feedback information to the other user at the last channel use, and (ii) transmits its message only over the last channel use. With these solution behaviors, we further simplify the problem and solve it via an iterative two-way optimization scheme. We numerically demonstrate that our proposed scheme for GTWCs achieves a better performance in terms of the transmit power compared to the existing counterparts, such as the non-feedback scheme and one-way optimization scheme.

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Section: System Model In Gaussian Two-way Channelsmentioning

confidence: 99%

“…By comparing the equations in ( 8) and ( 9), we can find g 2 = (I + F2 F1 ) −1 g2 and F 2 = (I + F2 F1 ) −1 F2 . Similarly, we can rewrite the equation in (5) as…”

Section: System Model In Gaussian Two-way Channelsmentioning

confidence: 99%

Section: A Design Of Optimal Linear Decoding Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Linear Coding for Gaussian Two-Way Channels

Kim¹,

Hosseinalipour²,

Kim³

et al. 2022

Preprint

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Linear Coding for Gaussian Two-Way Channels

Kim

Hosseinalipour

Kim

et al. 2022

2022 58th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Although user cooperation cannot improve the capacity of Gaussian two-way channels (GTWCs) with independent noises, it can improve communication reliability. In this work, we aim to enhance and balance the communication reliability in GTWCs by minimizing the sum of error probabilities via joint design of encoders and decoders at the users. We first formulate general encoding/decoding functions, where the user cooperation is captured by the coupling of user encoding processes. The coupling effect renders the encoder/decoder design non-trivial, requiring effective decoding to capture this effect, as well as efficient power management at the encoders within power constraints. To address these challenges, we propose two different two-way coding strategies: linear coding and learning-based coding. For linear coding, we propose optimal linear decoding and discuss new insights on encoding regarding user cooperation to balance reliability. We then propose an efficient algorithm for joint encoder/decoder design. For learningbased coding, we introduce a novel recurrent neural network (RNN)-based coding architecture, where we propose interactive RNNs and a power control layer for encoding, and we incorporate bi-directional RNNs with an attention mechanism for decoding. Through simulations, we show that our two-way coding methodologies outperform conventional channel coding schemes (that do not utilize user cooperation) significantly in sum-error performance. We also demonstrate that our linear coding excels at high signalto-noise ratios (SNRs), while our RNN-based coding performs best at low SNRs. We further investigate

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Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds

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An iteratively optimized linear coding scheme for correlated Gaussian channels with noisy feedback

Cited by 3 publications

References 9 publications

Linear Coding for Gaussian Two-Way Channels

Linear Coding for Gaussian Two-Way Channels

Linear Coding for Gaussian Two-Way Channels

Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds

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