## Abstract

We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The number of data symbols is chosen according to the Robust Soliton distribution. XOR and cyclic shift operations establish a unitary commutative ring if data symbols have a length of p - 1 bits, for some prime number p. We consider the graph given by code symbols combining two data symbols. If n/2 such random pairs are given for n data symbols, then a giant component appears, which can be resolved in linear time. We can extend Cyclone codes to data symbols of arbitrary even length, provided the Goldbach conjecture holds. Applying results for this giant component, it follows that Cyclone codes have the same encoding and decoding time complexity as LT codes, while the overhead is upper-bounded by those of LT codes. Simulations indicate that Cyclone codes significantly decreases the overhead of extra coding symbols.

Original language | 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 | 156-160 |

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

Funding Information:∗supported by the Sustainability Center Freiburg, supported by BW Ministry of Economics and BW Ministry of Science, Research and the Arts.

Publisher Copyright:

© 2017 IEEE.