### Abstract

A general method of coding over expansions is proposed, which allows one to reduce the highly non-trivial problem of coding over continuous channels to a much simpler discrete ones. More specifically, the focus is on the additive exponential noise (AEN) channel, for which the (binary) expansion of the (exponential) noise random variable is considered. It is shown that each of the random variables in the expansion corresponds to independent Bernoulli random variables. Thus, each of the expansion levels (of the underlying channel) corresponds to a binary symmetric channel (BSC), and the coding problem is reduced to coding over these parallel channels while satisfying the channel input constraint. This optimization formulation is stated as the achievable rate result, for which a specific choice of input distribution is shown to achieve a rate which is arbitrarily close to the channel capacity in the high SNR regime. Remarkably, the scheme allows for low-complexity capacity-achieving codes for AEN channels, using the codes that are originally designed for BSCs. Extensions to different channel models and applications to other coding problems are discussed.

Original language | English (US) |
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Title of host publication | 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012 |

Pages | 1932-1936 |

Number of pages | 5 |

DOIs | |

State | Published - Oct 22 2012 |

Event | 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States Duration: Jul 1 2012 → Jul 6 2012 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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### Other

Other | 2012 IEEE International Symposium on Information Theory, ISIT 2012 |
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Country | United States |

City | Cambridge, MA |

Period | 7/1/12 → 7/6/12 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012*(pp. 1932-1936). [6283635] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2012.6283635