### Abstract

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ε is closely approximated by C - √V/n Q^{-1} (ε) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion, and Q is the complementary Gaussian cumulative distribution function.

Original language | English (US) |
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Article number | 21 |

Pages (from-to) | 2307-2359 |

Number of pages | 53 |

Journal | IEEE Transactions on Information Theory |

Volume | 56 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2010 |

### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Keywords

- Achievability
- Channel capacity
- Coding for noisy channels
- Converse
- Finite blocklength regime
- Shannon theory

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## Cite this

*IEEE Transactions on Information Theory*,

*56*(5), 2307-2359. [21]. https://doi.org/10.1109/TIT.2010.2043769