### Abstract

We consider the problem of minimizing the expected distortion in the multilayer transmission of a Gaussian source using the broadcast approach with successive information enhancement. This minimization is contingent on the jointly optimal choice of the rates and power ratios of the different layers. This problem was tackled in the literature with the assumption that the fading channel has a finite number of states and the number of source layers matches the number of channel states. In this paper, we provide a more generic solution for a continuous Rayleigh fading channel, and for any predetermined number of layers. We prove that the primal optimization problem has a strong duality with the Lagrangian dual problem. Consequently, we propose a two-dimensional bisection search algorithm that can, for any number of layers, find the optimal solution of the dual problem which will be the same as the optimal solution of the primal problem. The complexity of the search algorithm has linear order with respect to the number of layers. We provide numerical results for the optimal rate and power allocation. Moreover, we show that with a small number of layers, we can approach the distortion lower bound that is achieved by transmitting an infinite number of layers.

Original language | English |
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Title of host publication | 2013 IEEE Information Theory Workshop, ITW 2013 |

DOIs | |

Publication status | Published - 1 Dec 2013 |

Event | 2013 IEEE Information Theory Workshop, ITW 2013 - Seville, Spain Duration: 9 Sep 2013 → 13 Sep 2013 |

### Publication series

Name | 2013 IEEE Information Theory Workshop, ITW 2013 |
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### Other

Other | 2013 IEEE Information Theory Workshop, ITW 2013 |
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Country | Spain |

City | Seville |

Period | 9/9/13 → 13/9/13 |

### Keywords

- Broadcast approach
- distortion minimization
- joint power and rate optimization
- multilayer transmission
- strong duality

### ASJC Scopus subject areas

- Information Systems

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## Cite this

*2013 IEEE Information Theory Workshop, ITW 2013*[6691345] (2013 IEEE Information Theory Workshop, ITW 2013). https://doi.org/10.1109/ITW.2013.6691345