## Abstract

The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the (1,∞)-RLL constraint. We derive the capacity for this setting, which can be expressed as {equation presented}, where ∈ is the erasure probability and H_{b}(.) is the binary entropy function. Moreover, we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivalent dynamic programming (DP) formulation with an optimal average-reward that is equal to the capacity. Furthermore, we obtained an optimal encoding procedure from the solution of the DP, leading to a capacity-achieving, zero-error coding scheme for our setting. DP is, thus, shown to be a tool not only for solving optimization problems, such as capacity calculation, but also for constructing optimal coding schemes. The derived capacity expression also serves as the only non-trivial upper bound known on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.

Original language | English |
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Article number | 7308065 |

Pages (from-to) | 8-22 |

Number of pages | 15 |

Journal | IEEE Transactions on Information Theory |

Volume | 62 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2015 IEEE.

## Keywords

- Binary erasure channel
- Constrained coding
- Dynamic
- Feedback capacity
- Programming
- Runlength-limited (RLL) constraints