# Dirty Paper Coding

FIELD OF STUDY

Computer Science

## ABSTRACT

Dirty paper coding is a technique that aims to maximize channel capacity. Communication channels experience a lot of interference. Through this technique, the receiver should receive the signal or message with minimal distortion. In such cases, receivers are unaware of the interference. Adoption and improvement of the technique ensure efficient data transmission with minimal power requirements.

## PRINICIPAL TERMS

• Additive white Gaussian Noise (AWGN): a model used to represent imperfections in real communication channels.
• channel capacity: the upper limit for the rate at which information transfer can occur without error.
• interference: anything that disrupts a signal as it moves from source to receiver.
• noise: interferences or irregular fluctuations affecting electrical signals during transmission.
• precoding: a technique that uses the diversity of a transmission by weighting an information channel.
• signal-to-noise ratio (SNR): the power ratio between meaningful information, referred to as “signal,” and background noise.
EFFECTIVE DATA TRANSMISSION

Data encounters interference during transmission from source to receiver on a channel. Dirty paper coding (DPC) is used in channels subjected to interference. Using DPC on such channels helps achieve efficient data transmission by ensuring channel capacity. Efficient transmission is possible despite interference because DPC uses precoding. This is a technique that minimizes data's vulnerability to distortion before reaching the receiver. The idea for DPC originated with Max Costa in 1983. Costa compared data transmission to sending a message on paper. The paper gets dirtier along the way before it reaches the intended recipient, who cannot distinguish ink from dirt. Apart from achieving channel capacity, DPC works without additional power requirements and without the receiver being aware of the interference.

ELIMINATING INTERFERENCE

Dirty paper coding is named for the conceptual analogy of deciphering writing on paper that has had known ink splotches added to it. In data transmission, the “ink splotches” are data interference, but someone who knows the interference is there can remove it to see the original data that was covered.
EBSCO illustration.

AWGN is used to simulate distortions facing a channel to make it efficient, a concept that DPC proposes. Models like AWGN have helped developers create multiuser channels with multiple-antenna transmitters. Implementing DPC techniques ensures each user encounters no interference from others in such multiuser channels.

INFORMATION INTEGRITY

In wireless infrastructures, DPC helps improve performance. Improvements have contributed to the development of multicarrier hybrid systems that combine unicast and broadcast connectivity. Implementing architectures that use DPC allows reception of interference-free signals. Thus, cellular, television, and radio signals that use unicast and broadcast connectivity are becoming clearer with each improvement.

DPC has also found its way into information hiding, or “digital watermarking.” In that process, an encoded message is sneaked into a waveform using an unknown signal. DPC ensures the receiver can decode the message. The technique also minimizes distortion to the original message and required power. Attackers with no knowledge of the encoding and signal parameters cannot decode the message. Removing the watermark also requires the hidden parameters.

Military communications apply watermarking. Parameters used in the process become classified information and are only accessible by authorized individuals. Watermarking helps safeguard information integrity.

DIRTY PAPER CODING'S CONTRIBUTION

Despite challenges in the calculations required, DPC has formed the basis for the development of new techniques for achieving efficiency in data transmission and information systems. One example is zero-forcing dirty paper coding. Efficient channels have fewer power demands, minimal message distortion, secure transmissions, and high signal-to-noise ratios (SNR). The combination of such advantages presages the development of affordable wireless infrastructures with fast and reliable data transmission rates. With the growing number of mobile devices accessing wireless networks, such infrastructure improvement might provide one of the solutions to the low battery life of the devices. Models on DPC, such as DPC with phase reshaping (PDC-PR), can help address the problem of resource allocation facing unicast and broadcast systems. However, performance comparisons between different DPC modifications can help establish the best technique to adopt.

—Melvin O

Cox, Ingemar J., Jessica Fridrich, Matthew L. Miller, Jeffrey A. Bloom, and Ton Kalker. “Practical Dirty-Paper Codes.” Digital Watermarking and Steganography. 2nd ed. Amsterdam: Elsevier, 2008. 183–212. Digital file.

Devroye, Natasha, Patrick Mitran and Vahid Tarokh. On Cognitive Graphs: Decomposing Wireless Networks. New York: Wiley Interscience, 2006. Print.

Devroye, N., P. Mitran, and V. Tarokh. “Limits on Communications in a Cognitive Radio Channel.” IEEE Communication Magazine 44.6 (2006): 4449. Inspec. Web. 9 Mar. 2016.

Kilper, Daniel C., and Tucker, Rodney S. “Energy-Efficient Telecommunications.” Optical Fiber Telecommunications. 6th ed. N.p.: Elsevier, 2013. 747–91. Digital file.

Savischenko, Nikolay V. Special Integral Functions Used in Wireless Communications Theory. N.p.: World Scientific, 2014. Digital file.

SAMPLE PROBLEM

Given a bandwidth of 10 megabytes per second (MBps) and using an acceptable signal-to-noise ratio (SNR) of 25 decibels (dB), calculate the channel capacity (C) in bits per second (bps), using the following formula:

C = B log2(1 + S/N)

where B is the bandwidth, S is the signal power, and N is the noise power.

First, convert the SNR in decibels to power, using the following equation:

Next, convert the bandwidth from megabytes per second (MBps) to bits per second (bps). Recall that 1 byte is equal to 8 bits, and ignore the seconds for now:

Then, plug in the found values for the bandwidth and S/N into the given formula, and solve: