Transmission over arbitrarily permuted parallel Gaussian channels

We address the problem of communication over arbitrarily permuted parallel Gaussian channels, where the permutation is known only to the receiver. We present a practical transmission scheme, that allows to transmit over this channel using off-the-shelf codes, in conjunction with linear processing and successive interference cancellation. The scheme is based on the approach of joint matrix triangularization. Explicit precoding matrices are derived for up to six parallel channels.