Signaling Over Arbitrarily Permuted Parallel Channels

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.