Writing on dirty tape with LDPC codes

We consider channels with interference known to the transmitter but unknown
to the receiver. A precoding technique based on lattice quantization is capable of achieving Costa’s “Dirty-Paper” limit for arbitrary interference signals, when interference is known non-causally. The same technique can be applied when interference is known with given anticipation, fixed and independent of the code blocklength. We review the main information-theoretic results in the non-causal-- and causal -- settings, and provide specific examples for a modulo-2 additive-noise binary channel with binary interference and for an AWGN channel with additive interference. Then, we turn to coding design for the AWGN case with causally-known interference (nicknamed “Dirty-Tape” channel, in analogy with Costa’s “Dirty-Paper”). We provide explicit code constructions based on Low-Density Parity-Check codes and on-PAM modulation, able to approach the rates achievable by lattice precoding for the AWGN Dirty-Tape channel. Finally, we point out some research problems such as the wideband limit of the causally-known interference channel (and the related optimal signaling) and the extension of our coding technique to the case of non-causally known interference (AWGN Dirty- Paper channel).