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-causality. The same technique can be applied when interference is known with given anticipation k, fixed and independent of the code blocklength n. We review the main information-theoretic results in the non-causal k = n and causal (k = 1) 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 M-PAM modulation, able to approach the rates achievable by lattice precoding ! for the AWGN dirty-tape channel. Finally, we point out some research problem 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).