TY - JOUR

T1 - On the Capacity of the Carbon Copy onto Dirty Paper Channel

AU - Rini, Stefano

AU - Shitz, Shlomo Shamai

PY - 2017/9/1

Y1 - 2017/9/1

N2 - The 'carbon copy onto dirty paper' (CCDP) channel is the compound 'writing on dirty paper' channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: 1) the state sequences are independent and identically distributed; and 2) the state sequences are scaled versions of the same sequence. In the first scenario, we show that a combination of superposition coding, time-sharing, and Gel'fand-Pinsker binning is sufficient to approach the capacity to within 3 bits per channel use for any number of possible state realizations. In the second scenario, we derive capacity to within 4 bits per channel use for the case of two possible state sequences. This result is extended to the CCDP channel with any number of possible state sequences under certain conditions on the scaling parameters, which we denote as 'strong fading' regime. We conclude by providing some remarks on the capacity of the CCDP channel in which the state sequences have any jointly Gaussian distribution.

AB - The 'carbon copy onto dirty paper' (CCDP) channel is the compound 'writing on dirty paper' channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: 1) the state sequences are independent and identically distributed; and 2) the state sequences are scaled versions of the same sequence. In the first scenario, we show that a combination of superposition coding, time-sharing, and Gel'fand-Pinsker binning is sufficient to approach the capacity to within 3 bits per channel use for any number of possible state realizations. In the second scenario, we derive capacity to within 4 bits per channel use for the case of two possible state sequences. This result is extended to the CCDP channel with any number of possible state sequences under certain conditions on the scaling parameters, which we denote as 'strong fading' regime. We conclude by providing some remarks on the capacity of the CCDP channel in which the state sequences have any jointly Gaussian distribution.

KW - Gel'fand-Pinsker channel

KW - carbon copying onto dirty paper

KW - compound channels with side information at the transmitter

KW - compound statedependent channel

KW - costa pre-coding

KW - quasi-static fading

UR - http://www.scopus.com/inward/record.url?scp=85029505773&partnerID=8YFLogxK

U2 - 10.1109/TIT.2017.2708112

DO - 10.1109/TIT.2017.2708112

M3 - Article

AN - SCOPUS:85029505773

SN - 0018-9448

VL - 63

SP - 5907

EP - 5922

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 9

M1 - 7934034

ER -