## Abstract

We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the long-standing open problem of finding the rate of convergence of the smallest attainable expected distortion to its asymptotic value, as a function of the blocklength n. Our main result is that in general the convergence rate is not faster than n{-1/2}. In particular, we show that for the problem of transmitting i.i.d uniform bits over a binary symmetric channels with Hamming distortion, the smallest attainable distortion (bit error rate) is at least Omega (n{-1/2}) above the asymptotic value, if the 'bandwidth expansion ratio' is above 1.

Original language | American English |
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Article number | 9046817 |

Pages (from-to) | 4722-4741 |

Number of pages | 20 |

Journal | IEEE Transactions on Information Theory |

Volume | 66 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2020 |

### Bibliographical note

Publisher Copyright:© 1963-2012 IEEE.

## Keywords

- Joint source-channel coding
- binary symmetric channel (BSC)
- broadcast channel
- finite blocklength