Carbon Copying Onto Dirty Paper

• Published in: IEEE transactions on information theory Vol. 53; no. 5; pp. 1814 - 1827
• Main Authors: Khisti, A., Erez, U., Lapidoth, A., Wornell, G.W.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Additives; Antennas; Applied sciences; Broadcasting; Codes; Coding; Common information; Data transmission; dirty paper coding; Exact sciences and technology; Gaussian; Gel'fand- Pinsker channels; Information theory; Information, signal and communications theory; Interference; MIMO; multiple-input/multiple-output (MIMO) broadcast channel; Multiuser channels; Noise robustness; Optimization; Propagation losses; Radiocommunications; Receivers; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Time sharing computer systems; Transmission and modulation (techniques and equipments); Transmitters; Transmitters. Receivers; Wireless communications; Writing; writing on dirty paper; Additive noise; Availability; MIMO system; Addition; dirty paper coding; Gaussian channel; Wireless telecommunication; Transmitter; Common information; Gel'fand- Pinsker channels; multiple-input/multiple-output (MIMO) broadcast channel; Data broadcast; Information dissemination; Multicast; Memoryless channel; Signal interference; Time sharing system; writing on dirty paper; Coding; Broadcast channels; Antenna array; Message transmission
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2007.894693

A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multiple-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we establish the capacity when there are two receivers. When there are many receivers, we show that the transmitter side information provides a vanishingly small benefit. When the interference is large and independent across the users, we show that time sharing is optimal. For the Gaussian case, we present a coding scheme and establish its optimality in the high signal-to-interference-plus-noise limit when there are two receivers. When the interference power is large and independent across all the receivers, we show that time-sharing is again optimal. Connections to the problem of robust dirty paper coding are also discussed