A network unit includes a non-linear precoder for jointly pre-processing transmit samples to be transmitted over respective communication channels for crosstalk mitigation. The non-linear precoder includes a first non-linear precoding stage configured to operate according to a first triangular precoding matrix and including a modulo function, followed by a second linear precoding stage configured to operate according to a second precoding matrix. The network unit further includes a first pilot signal generator configured to generate first pilot signals for pre-processing by the second precoding stage only to yield partially-precoded pilot signals for further transmission over the respective communication channels, and a controller configured to update the second precoding matrix based on first error measurements performed during the transmission of the partially-precoded pilot signals over the respective communication channels while keeping the first precoding matrix unaltered.