A New Capacity Theorem for the Gaussian Channel with Two-sided Input and Noise Dependent State Information
Subject Areas : Communication Systems & DevicesNima S. Anzabi-Nezhad 1 * , Ghosheh Abed Hodtani 2
1 - Quchan University of Technology, Iran
2 - Ferdowsi University of Mashhad
Keywords: Communication channel capacity, , Gaussian channel capacity, , correlated side information, , two sided state information, , interference cancellation, , dirty paper coding, , , ,
Abstract :
Gaussian interference known at the transmitter can be fully canceled in a Gaussian communication channel employing dirty paper coding, as Costa shows, when interference is independent of the channel noise and when the channel input designed independently of the interference. In this paper, a new and general version of the Gaussian channel in presence of two-sided state information correlated to the channel input and noise is considered. Determining a general achievable rate for the channel and obtaining the capacity in a non-limiting case, we try to analyze and solve the Gaussian version of the Cover-Chiang theorem mathematically and information-theoretically. Our capacity theorem, while including all previous theorems as its special cases, explains situations that can not be analyzed by them; for example, the effect of the correlation between the side information and the channel input on the capacity of the channel that can not be analyzed with Costa’s “writing on dirty paper" theorem. Meanwhile, we try to exemplify the concept of “cognition" of the transmitter or the receiver on a variable (here, the channel noise) with the information-theoretic concept of “side information" correlated to that variable and known at the transmitter or at the receiver. According to our theorem, the channel capacity is an increasing function of the mutual information of the side information and the channel noise.
[1] C. E. Shannon, “Channels with side information at the transmitter,” IBM Journal of Research and Development, vol. 2, no. 4, pp. 289 –293, oct. 1958.
[2] A. V. Kosnetsov and B. S. Tsybakov, “Coding in a memory with defective cells,” Probl. Pered. Inform., vol. 10, no. 2, pp. 52–60, Apr./Jun. 1974.Translated from Russian.
[3] S. I. Gel’fand and M. S. Pinsker, “Coding for channel with random parameters,” Probl. Contr. Inform. Theory, vol. 9, no. 1, pp. 19–31, 1980.
[4] C. Heegard and A. El Gamal, “On the capacity of computer memory with defects,” Information Theory, IEEE Transactions on, vol. 29, no. 5, pp. 731 – 739, sep 1983.
[5] M. Costa, “Writing on dirty paper (corresp.),” Information Theory, IEEE Transactions on, vol. 29, no. 3, pp. 439 – 441, may 1983.
[6] T. M. Cover and M. Chiang, “Duality between channel capacity and rate distortion with two-sided state information,” Information Theory, IEEE Transactions on, vol. 48, no. 6, pp. 1629 –1638, jun 2002.
[7] S. Jafar, “Capacity with causal and noncausal side information: A unified view,” Information Theory, IEEE Transactions on, vol. 52, no. 12, pp. 5468 –5474, dec. 2006.
[8] G. Keshet, Y. Steinberg, and N. Merhav, “Channel coding in the presence of side information,” Found. Trends Commun. Inf. Theory, vol. 4, pp. 445–586, June 2008.
[9] N. Merhav and S. Shamai, “Information rates subject to state masking,” Information Theory, IEEE Transactions on, vol. 53, no. 6, pp. 2254 –2261, june 2007.
[10] I. Bergel, D. Yellin, and S. Shamai, “A lower bound on the data rate of dirty paper coding in general noise and interference,” IEEE Wireless Communications Letters, vol. 3, no. 4, pp. 417–420, 2014.
[11] Y. Steinberg, “Coding for the degraded broadcast channel with random parameters, with causal and noncausal side information,” Information Theory, IEEE Transactions on, vol. 51, no. 8, pp. 2867 –2877, aug. 2005.
[12] S. Sigurjonsson and Y.-H. Kim, “On multiple user channels with state information at the transmitters,” in Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on, sept. 2005, pp. 72 –76.
[13] Y. H. Kim, A. Sutivong, and S. Sigurjonsson, “Multiple user writing on dirty paper,” in Information Theory, 2004. ISIT 2004. Proceedings. International Symposium on, june-2 july 2004, p. 534.
[14] T. Philosof and R. Zamir, “On the loss of single-letter characterization: The dirty multiple access channel,” Information Theory, IEEE Transactions on, vol. 55, no. 6, pp. 2442 –2454, june 2009.
[15] Y. Steinberg and S. Shamai, “Achievable rates for the broadcast channel with states known at the transmitter,” in Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on, sept. 2005, pp. 2184 –2188.
[16] R. Duan, Y. Liang, and S. Shamai, “State-dependent gaussian interference channels: Can state be fully canceled?” IEEE Transactions on Information Theory, vol. 62, no. 4, pp. 1957–1970, 2016.
[17] Y. Sun, Y. Liang, R. Duan, and S. S. Shitz, “State-dependent z-interference channel with correlated states,” in 2017 IEEE International Symposium on Information Theory (ISIT), 2017, pp. 644–648.
[18] Y. Sun, R. Duan, Y. Liang, and S. Shamai Shitz, “State-dependent interference channel with correlated states,” IEEE Transactions on Information Theory, vol. 65, no. 7, pp. 4518–4531, 2019.
[19] Y.-C. Huang and K. R. Narayanan, “Joint source-channel coding with correlated interference,” in Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on, 2011, pp. 1136 – 1140.
[20] N. S. Anzabi-Nezhad, G. A. Hodtani, and M. Molavi Kakhki, “Information theoretic exemplification of the receiver re-cognition and a more general version for the Costa theorem,” IEEE Communication Letters, vol. 17, no. 1, pp. 107–110, 2013.
[21] ——, “A more general version of the costa theorem,” Journal of Communication Engineering, vol. 2, no. 4, pp. 1–19, Autumn 2013.
[22] B. Chen, S. C. Draper, and G. Wornell, “Information embedding and related problems: Recent results and applications,,” in Allerton Conference, USA, 2001.
[23] A. Rosenzweig, Y. Steinberg, and S. Shamai, “On channels with partial channel state information at the transmitter,” Information Theory, IEEE Transactions on, vol. 51, no. 5, pp. 1817 – 1830, may 2005.
[24] A. Zaidi and P. Duhamel, “On channel sensitivity to partially known two-sided state information,” in Communications, 2006. ICC ’06. IEEE International Conference on, vol. 4, june 2006, pp. 1520 –1525.
[25] L. Gueguen and B. Sayrac, “Sensing in cognitive radio channels: A theoretical perspective,” Wireless Communications, IEEE Transactions on, vol. 8, no. 3, pp. 1194–1198, march 2009.
[26] G. A. Hodtani, “The effect of transceiver recognition on the gaussian channel capacity,” in 2015 Iran Workshop on Communication and Information Theory (IWCIT), May 2015, pp. 1–3.
[27] A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed. 1em plus 0.5em minus 0.4em McGraw-Hill, 2002