Lower Bound of Rate-Reliability-Distortion Function for Generalized Channel With Side Information
Abstract
In this paper we study a generalized model of discrete memoryless channel (DMC) with finite input and output alphabets and random state sequence (side information) partially known to the encoder, channel and decoder. The study includes the family of Gel'fand-Pinsker and information hiding coding problems as special cases. Information is to be reliably transmitted through the noisy channel selected by adversary. Reasoning from applications the actions of encoder and adversary are limited by distortion constraints. The encoder and decoder depend on a random variable (RV) which can be treated as cryptographic key. Two cases are considered, when the joint distribution of this RV and side information is given or this RV is independent from side information and it's distribution can be chosen for the best code generation. We investigate the rate-reliability-distortion function for the mentioned model and derive the lower bound for it.
References
S.I. Gel'fand and M.S. Pinsker, “Coding for channel with random parameters", Problems of Control and Information Theory, vol. 9, no. 1, pp. 19-31, 1980.
R. Ahlswede, “Arbitrarily varying channels with states sequence known to the sender", IEEE Transactions on Information Theory, vol. IT-32, no. 5, pp. 621-629, 1986.
E.A. Haroutunian, M.E. Haroutunian, “Channel with random parameter", Proc. of XXII Prague conf. on Inform. Theory, Statistical Decision Functions, Random Processes, pp. 99-101, 1994.
M.E.Haroutunian, “New bounds for E-capacities of arbitrarily varying channel and channel with random parameter", Transactions of the Institute for Informatics and Automation Problems of the NAS of RA, Mathematical Problems of Computer Sciences, vol. 22, pp. 44-59, 2001.
M.E. Haroutunian, “On multiple-access channel with random parameter", Proc. of Int. conf. on Computer Science and Inform. Technologies, Armenia, Yerevan, pp. 174-178, 2003.
A. Somekh-Baruch and N. Merhav, “On the random coding error exponenets of the single-user and the multiple-access Gel'fand-Pinsker channels", Proc. of IEEE International Symposium on Information Theory, USA, Chicago, p. 448, 2004.
M.E. Haroutunian, “Estimates of E-capacity and capacity regions for multiple-access channel with random parameter", Lecture Notes in Computer Science, vol. 4123, Springer Verlag, pp. 196-217, 2006.
P. Moulin and J.A. O'Sullivan, “Information-theoretic analysis of information hiding", IEEE Transactions on Information Theory, vol. 49, no. 3, pp. 563-593, Mar. 2003.
M.E. Haroutunian, S.A. Tonoyan, “Random coding bound of information hiding E-capacity", Proc. of IEEE International Symposium on Information Theory, USA, Chicago, p. 536, 2004.
M.E. Haroutunian, S.A. Tonoyan “On estimates of rate-reliability distortion function for information hiding system", Transactions of the Institute for Informatics and Automation Problems of the NAS of RA, Mathematical Problems of Computer Science, vol. 23, pp. 20-31, 2004.
A.Somekh-Baruch, N. Merhav, “On the error exponent and capacity games of private watermarking systems", IEEE Transactions on Information Theory, vol. 49, no. 3, pp. 537-562, 2003.
A. Somekh-Baruch, N. Merhav, “On the capacity game of public watermarking systems", IEEE Transactions on Information Theory, vol. 50, no. 3, pp. 511-524, 2004.
M. Haroutunian, S. Tonoyan, O. Koval, S. Voloshynovskiy, “On reversible information hiding system", Proc. of IEEE International Symposium on Information Theory, Canada, Toronto, pp. 940-944, 2008.
T.M. Cover and M. Chiang, “Duality between channel capacity and rate distortion with two-sided state information", IEEE Transactions on Information Theory, vol. 48, no. 6, pp. 1629-1638, 2002.
M. Haroutunian, A. Muradyan, “Lower bound for E capacity of discrete memoryless channel with two-sided state information", Transactions of the Institute for Informatics and Automation Problems of the NAS of RA, Mathematical Problems of Computer Sciences, vol. 31, pp. 28-39, 2008.
P. Moulin and Y. Wang, “Capacity and random-coding exponents for channel coding with side information", IEEE Transactions on Information Theory, vol. 53, no. 4, 2007.
E.A. Haroutunian, “Upper estimate of transmission rate for memoryless channel with countable number of output signals under given error probability exponent", (in Russian), 3rd All-Union Conf. on Theory of Information Transmission and Coding, Uzhgorod, Publication house of Uzbek Academy of Sciences, Tashkent, pp. 83-86, 1967.
E.A. Haroutunian, “On bounds for E-capacity of DMC", IEEE Transactions on Information Theory, vol. 53, no. 11, pp. 4210-4220, 2007.
E.A. Haroutunian, M.E. Haroutunian and A.N. Harutyunyan, “Reliability criteria in information theory and in statistical hypothesis testing", Foundations and Trends in Communications and Information Theory, vol. 4, no 2-3, pp. 97-263, 2008.
T.M. Cover and J.A. Thomas, “Elements of Information Theory", second edition, Wiley, New York, 2006.
I. Csiszár and J.Körner, “Information Theory: Coding Theorems for Discrete Memoryless Systems", Academic Press, New York, 1981.
I. Csiszár, “The method of types", IEEE Transactions on Information Theory, vol. 44, no. 6, pp. 2505-2523, 1998.
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