Capacity of Finite-State Channels with Delayed Feedback
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916296540553216 |
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| author | Huleihel, Bashar Sabag, Oron Permuter, Haim H. Kostina, Victoria |
| author_facet | Huleihel, Bashar Sabag, Oron Permuter, Haim H. Kostina, Victoria |
| contents | In this paper, we investigate the capacity of finite-state channels (FSCs) in presence of delayed feedback. We show that the capacity of a FSC with delayed feedback can be computed as that of a new FSC with instantaneous feedback and an extended state. Consequently, graph-based methods to obtain computable upper and lower bounds on the delayed feedback capacity of unifilar FSCs are proposed. Based on these methods, we establish that the capacity of the trapdoor channel with delayed feedback of two time instances is given by $\log_2(3/2)$. In addition, we derive an analytical upper bound on the delayed feedback capacity of the binary symmetric channel with a no consecutive ones input constraint. This bound also serves as a novel upper bound on its non-feedback capacity, which outperforms all previously known bounds. Lastly, we demonstrate that feedback does improve the capacity of the dicode erasure channel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_18008 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Capacity of Finite-State Channels with Delayed Feedback Huleihel, Bashar Sabag, Oron Permuter, Haim H. Kostina, Victoria Information Theory In this paper, we investigate the capacity of finite-state channels (FSCs) in presence of delayed feedback. We show that the capacity of a FSC with delayed feedback can be computed as that of a new FSC with instantaneous feedback and an extended state. Consequently, graph-based methods to obtain computable upper and lower bounds on the delayed feedback capacity of unifilar FSCs are proposed. Based on these methods, we establish that the capacity of the trapdoor channel with delayed feedback of two time instances is given by $\log_2(3/2)$. In addition, we derive an analytical upper bound on the delayed feedback capacity of the binary symmetric channel with a no consecutive ones input constraint. This bound also serves as a novel upper bound on its non-feedback capacity, which outperforms all previously known bounds. Lastly, we demonstrate that feedback does improve the capacity of the dicode erasure channel. |
| title | Capacity of Finite-State Channels with Delayed Feedback |
| topic | Information Theory |
| url | https://arxiv.org/abs/2303.18008 |