Finite-State Channel with Feedback and Causal State Information Available at the Encoder

Shemuel, Eli; Sabag, Oron; Permuter, Haim H.

doi:10.1109/allerton.2018.8636094

Cited by 3 publications

(4 citation statements)

References 21 publications

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“…There are some additional special cases of FSCs where the feedback capacity is known explicitly. One method to compute an explicit feedback capacity expression is by formulating it as a dynamic programming (DP) optimization problem, as was first introduced in Tatikonda's thesis [36] and then in [25], [27], [37]- [40]. This is beneficial in estimating the feedback capacity using efficient algorithms such as the value iteration algorithm [41], which, in turn, can help in generating a conjecture for the exact solution of the corresponding Bellman equation [42].…”

Section: Introductionmentioning

confidence: 99%

“…This side information may generally be beneficial for increasing the feedback capacity of channels with memory. The capacity problem of discrete memoryless channels (DMCs) with states known at the encoder dates back to Shannon's early work [55], followed by works of Kusnetsov and Tsybakov [56], Gel'fand and Pinsker [57], and Heegard and El Gamal [58], which paved the way to various recent works such as [40], [59]- [67]. Since Shannon showed in [17] that feedback does not increase the capacity of a DMC, his setting in [55], where the state process is i.i.d.…”

Section: Introductionmentioning

confidence: 99%

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The Feedback Capacity of Noisy Output Is the STate (NOST) Channels

Shemuel

Sabag

Permuter

2022

IEEE Trans. Inform. Theory

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We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels. We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder. If CSI is unavailable, the feedback capacity is C FB = max P (x|y ′ ) I(X; Y |Y ′ ), while if it is available at the encoder, the feedback capacity is C FB-CSI = max P (u|y ′ ),x(u,s ′ ) I(U ; Y |Y ′ ), where U is an auxiliary RV with finite cardinality. In both formulas, the output process is a Markov process with stationary distribution. The derived formulas generalize special known instances from the literature, such as where the state is i.i.d. and where it is a deterministic function of the output. C FB and C FB-CSI are also shown to be computable via convex optimization problem formulations. Finally, we present an example of an interesting NOST channel for which CSI available at the encoder does not increase the feedback capacity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Feedback Capacity of Noisy Output Is the STate (NOST) Channels

Shemuel

Sabag

Permuter

2022

IEEE Trans. Inform. Theory

Self Cite

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show abstract

“…There are some additional special cases of FSCs where the feedback capacity is known explicitly. One method to compute explicit feedback capacity expression is by formulating it as a dynamic programming (DP) optimization problem, as was first introduced in Tatikonda's thesis [38] and then in [25], [27], [30], [39]- [41]. This is beneficial in estimating the feedback capacity using efficient algorithms such as the value iteration algorithm [42], which, in turn, can help in generating a conjecture for the exact solution of the corresponding Bellman equation [43].…”

Section: Introductionmentioning

confidence: 99%

“…Gel'fand and Pinsker [58], and Heegard and El Gamal [59], which paved the way to various recent works such as [30], [31], [60]- [63]. Since Shannon showed in [17] that feedback does not increase the capacity of a DMC, his setting in [56], where the state process was distributed i.i.d.…”

Section: Introductionmentioning

confidence: 99%

The Feedback Capacity of Noisy Output is the STate (NOST) Channels

Shemuel¹,

Sabag²,

Permuter³

2021

Preprint

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We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels. We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder. If CSI is unavailable, the feedback capacity iswhile if it is available at the encoder, the feedback capacity iswhere U is an auxiliary random variable with finite cardinality. In both formulas, the output process is a Markov process with stationary distribution. The derived formulas generalize special known instances from the literature, such as where the state is distributed i.i.d. and where it is a deterministic function of the output. C FB and C FB-CSI are also shown to be computable via concave optimization problem formulations. Finally, we give a sufficient condition under which CSI available at the encoder does not increase the feedback capacity, and we present an interesting example that demonstrates this.

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