Dirty paper coding

In telecommunications, dirty paper coding (DPC) or Costa precoding is a technique for efficient transmission of digital data through a channel subjected to some interference known to the transmitter. The technique consists of precoding the data in order to cancel the effect caused by the interference.

The term dirty paper coding comes from Max Costa who imagined a paper which is partially covered with dirt that is indistinguishable from ink. The theorem says that if the writer knows where the dirt is to start with, she can convey just as much information by writing on the paper as if it were clean, even though the reader does not know where the dirt is. In this case the dirt is interference, the paper is the channel, the writer on the paper is the transmitter, and the reader is the receiver. In information-theoretic terms, dirty-paper coding achieves the channel capacity, without a power penalty and without requiring the receiver to gain knowledge of the interference state.

Note that DPC at the encoder is an information-theoretic dual of Wyner-Ziv coding at the decoder.

Instances of dirty paper coding include Costa precoding (1983). Suboptimal approximations of dirty paper coding include Tomlinson-Harashima precoding (THP) published in 1971 and the vector perturbation technique of Hochwald et al. (2005).

DPC and DPC-like techniques require knowledge of the interference state in a non causal manner, such as channel state information of all users and other user data. Hence, the design of a DPC-based system should include a procedure to feed side information to the transmitters.

In 2003, Caire and Shamai applied DPC to the multi-antenna multi-user downlink, which is referred to as the 'broadcast channel' by information theorists. Since then, there has been widespread use of DPC in wireless networks and into an interference aware coding technique for dynamic wireless networks.

Recently, DPC has also been used for "informed digital watermarking" and is the modulation mechanism used by 10GBASE-T.

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