### Abstract

We address the rate of transmission attainable on a given channel when the decoding rule is specified, perhaps suboptimally. We concentrate on decoders, termed d-decoders, which accept the codeword x 'closest' to the received sequence y in the sense of a metric d(x,y), defined for sequences as an additive extension of a single-letter metric. We provide a simple sufficient condition for C_{d}(W) = C(W), and more generally, for the equality of the d-capacities for two different decoding metrics d and d̄. This is followed by a sufficient condition for C_{eo} (W) = C(W). We then show that the lower bound on d-capacity given previously by past studies, is not tight in general but C_{d}(W) > iff this bound is positive. The 'product space' improvement of the lower bound is considered, and a 'product space characterization' of C_{eo}(W) is obtained. We also determine the e.o. capacity of a deterministic arbitrarily varying channel defined by a bipartite graph, and show that it equals capacity.

Original language | English |
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Publication status | Published - Dec 1 1994 |

Event | Proceedings of the 1994 IEEE International Symposium on Information Theory - Trodheim, Norw Duration: Jun 27 1994 → Jul 1 1994 |

### Other

Other | Proceedings of the 1994 IEEE International Symposium on Information Theory |
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City | Trodheim, Norw |

Period | 6/27/94 → 7/1/94 |

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### ASJC Scopus subject areas

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

### Cite this

*Channel capacity for a given decoding metric*. Paper presented at Proceedings of the 1994 IEEE International Symposium on Information Theory, Trodheim, Norw, .