## Abstract

The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the (0, k)-runlength limited (RLL) constraint, i.e., no more than k consecutive zeros are allowed. The feedback capacity of this channel is derived for all k≥1 C^{fn}_{(0, k)}(ϵ) = max ϵH_{2}(δ_{0})+Σ^{k-1}_{i=1}(ϵ^{i+1}H_{2})(δ_{i})Π^{i-1}_{m=0}δ_{m})/1+Σ^{k-1}_{i=0}(ϵ^{i+1}Π^{i}_{m=0}δ_{m}) where ϵ is the erasure probability, ϵ=1-ϵ, H_{2}(·) is the binary entropy function and the maximization is only over δ_{k-1}, while the other parameters δ_{0},..., δ_{k-2} are simple functions of δ_{k-1}. A simple coding scheme is constructed for all k, establishing that the feedback capacity can be achieved using variable length zero-error coding. In addition, it is shown that non-causal knowledge of the erasures at the encoder does not increase the feedback capacity.

Original language | American English |
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Title of host publication | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1783-1787 |

Number of pages | 5 |

ISBN (Electronic) | 9781509040964 |

DOIs | |

State | Published - 9 Aug 2017 |

Externally published | Yes |

Event | 2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: 25 Jun 2017 → 30 Jun 2017 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Conference

Conference | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
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Country/Territory | Germany |

City | Aachen |

Period | 25/06/17 → 30/06/17 |

### Bibliographical note

Publisher Copyright:© 2017 IEEE.