{{Short description|Coding technique that can compensate for a known interference}} In [[telecommunication]]s, '''dirty paper coding''' ('''DPC''') or '''Costa precoding''' is a technique for efficient transmission of [[Digital data|digital]] [[data]] through a [[communications channel|channel]] subjected to some [[interference (communication)|interference]] known to the transmitter. The technique consists of [[precoding]] the data in order to cancel the interference. Dirty-paper coding achieves the [[channel capacity]] without a power penalty and without requiring the receiver to know the interfering signal.
The term ''dirty paper coding'' was coined by Max Costa<ref name="costa"> {{cite journal |author=M. Costa |title=Writing on dirty paper |journal=IEEE Transactions on Information Theory |pages=439–441 |volume=29 |date=May 1983 |doi=10.1109/TIT.1983.1056659 |issue=3 |url=http://faculty.cua.edu/regalia/EE572/costa_dirty_paper.pdf |url-status=dead |archive-url=https://web.archive.org/web/20150121063414/http://faculty.cua.edu/regalia/EE572/costa_dirty_paper.pdf |archive-date=2015-01-21 }} </ref> who compared the technique to writing a message on a piece of paper which is partially soiled with random ink strokes or spots. By erasing and adding ink in the proper places, the writer can convey just as much information as if the paper were clean, even though the reader does not know where the dirt was. In this analogy, the paper is the channel, the dirt is interference, the writer is the transmitter, and the reader is the receiver.
Note that DPC at the encoder is an [[information theory|information-theoretic]] [[dual (information theory)|dual]] of [[Distributed source coding#Wyner–Ziv coding – lossy distributed coding|Wyner–Ziv coding]] at the decoder.{{Citation needed|date=December 2010}}
== {{Anchor|Costa precoding|Tomlinson–Harashima precoding}} Variants == Instances of dirty paper coding include Costa precoding (1983).<ref name="costa"/> Suboptimal approximations of dirty paper coding include Tomlinson–Harashima precoding (THP) published in 1971<ref> {{cite journal |author=M. Tomlinson |title=New automatic equalizer employing modulo arithmetic |journal=Electron. Lett. |pages=138–139 |volume=7 |date=March 1971 |doi=10.1049/el:19710089 |issue=5–6|bibcode=1971ElL.....7..138T }} </ref><ref> {{cite journal |author1=H. Harashima |author2=H. Miyakawa |title=Matched-transmission technique for channels with intersymbol interference |journal=IEEE Trans. Commun. |pages=774–780 |volume=COM-20 |date=August 1972|issue=4 |doi=10.1109/TCOM.1972.1091221 }} </ref> and the vector perturbation technique of Hochwald et al. (2005).<ref> {{cite journal |author1=B. M. Hochwald |author2=C. B. Peel |author3=A. L. Swindlehurst |title=A vector-perturbation technique for near-capacity multiantenna multiuser communication - Part II: Perturbation |journal=IEEE Trans. Commun. |pages=537–544 |volume=53 |date=March 2005 |doi=10.1109/TCOMM.2004.841997 |issue=3|citeseerx=10.1.1.3.9687 |s2cid=2384238 }} </ref>
== Design considerations ==
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.
== Applications == In 2003, Caire and Shamai<ref>{{cite journal|last=Caire|first=Guissepe|author2=Shamai, Shlomo|title=On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel|journal=IEEE Transactions on Information Theory|date=July 2003|volume=49|issue=3|pages=1691–1706 |doi=10.1109/TIT.2003.813523 |s2cid=13926433 }}</ref> 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 network]]s<ref> {{cite conference |author1=C. T. K. Ng |author2=A. Goldsmith |title=Transmitter Cooperation in Ad-Hoc Wireless Networks: Does Dirty-Paper Coding Beat Relaying? |book-title=IEEE Information Theory Workshop |date=October 2004 |pages=277–282 |location=San Antonio, Texas}} </ref> and into an interference aware coding technique for dynamic wireless networks.<ref> {{cite conference |author1=Momin Uppal |author2=Zhixin Liu |author3=Vladimir Stankovic |author4=Anders Høst-Madsen |author5=Zixiang Xiong |title=Capacity Bounds and Code Designs for Cooperative Diversity |book-title=Information theory and applications |date=February 2007}} </ref>
Recently, DPC has also been used for "informed [[digital watermarking]]" and is the modulation mechanism used by [[10GBASE-T]].
== See also == * [[Cognitive radio]] * [[Multiple-input multiple-output communications]] * [[Multi-user MIMO]] * [[Palimpsest]] * [[Reed-Solomon error correction]]
== References == {{Reflist}}
== External links == * [https://web.archive.org/web/20150121063414/http://faculty.cua.edu/regalia/EE572/costa_dirty_paper.pdf "Writing on Dirty Paper"], the original publication by Max Costa
[[Category:Encodings]]