### Abstract

The problem of transmission of information over arbitrarily permuted parallel channels is studied here. The transmitter does not know over which channel a certain code-sequence will actually be transmitted, however the receiver knows how the sequences are permuted. The permutation is arbitrary but constant during the (simultaneous) transmission of the code-sequences via the parallel channels. It is shown first that the sum of the capacities of each channel is achievable for such a communication system in the special case where the capacity achieving input distributions of all channels are identical. More important is that this sum-capacity can also be achieved using a single channel code for all channels combined with a sequential decoding method. The construction of a rate-matching code based on maximum distance separable (MDS) codes turns out to be crucial. Finally, the case where the parallel channels have different capacity-achieving input distributions is investigated. Also for this case the capacity is determined. Again, this capacity is achievable with a sequential decoding procedure.

Original language | English |
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Pages (from-to) | 1374-1382 |

Number of pages | 9 |

Journal | IEEE Transactions on Information Theory |

Volume | 54 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 |

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## Cite this

Willems, F. M. J., & Gorokhov, A. (2008). Signaling over arbitrarily permuted parallel channels.

*IEEE Transactions on Information Theory*,*54*(3), 1374-1382. https://doi.org/10.1109/TIT.2007.915912