### Abstract

On a discrete memoryless channel (DMC), the maximum likelihood (ML) decoding rule is not only optimal (for equiprobable messages and average error probability), but it is also linear (the metric that it maximizes is additive over the block length), which in particular, makes ML practically conceivable. On a compound DMC, the use of ML is ruled out by the channel's law ignorance. In order to account for this, the universal decoders proposed in[7],[10],[3],[9] can be employed. However, none of these decoders is linear. Hence, we consider the problem of finding good linear decoders for compound DMC's. We show that on most compound sets, when universality requires to be capacity achieving, there exists a universal decoding rule which is generalized linear, in the sense that it maximizes only a finite number of additive metrics. A local to global geometric method is developed to solve this problem. By considering very noisy channels, the global problem is reduced, in the limit, to an inner product space problem, for which insightful solutions can be found. We describe an heuristic method used, in this problem, to "lift" local results to global results.

Original language | English (US) |
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Title of host publication | Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008 |

Pages | 1098-1102 |

Number of pages | 5 |

DOIs | |

State | Published - Sep 29 2008 |

Externally published | Yes |

Event | 2008 IEEE International Symposium on Information Theory, ISIT 2008 - Toronto, ON, Canada Duration: Jul 6 2008 → Jul 11 2008 |

### Other

Other | 2008 IEEE International Symposium on Information Theory, ISIT 2008 |
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Country | Canada |

City | Toronto, ON |

Period | 7/6/08 → 7/11/08 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008*(pp. 1098-1102). [4595157] https://doi.org/10.1109/ISIT.2008.4595157