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Liu, W.; Chu, X.; Zhang, J. (2015)
Publisher: IEEE
Languages: English
Types: Other
Subjects:
The method of typical sequences is a fundamental tool in asymptotic analyses of information theory. The conditional typicality lemma is one of the most commonly used lemmas in the method of typical sequences. Recent works have generalised the definition of typicality to general alphabets or general probability distributions. However, there is still a lack of the conditional typicality lemma based on the definition of typicality with respect to general distributions on the product space. In this paper, we propose a generalised joint typicality for general alphabets and with respect to general probability distributions, and obtain the counterpart of conventional conditional and joint typicality lemmas based on the generalised typicality. As applications of the typicality lemmas, we prove the packing and coverings for the proposed generalised typicality, and then recover the direct part of the capacity theorem on the general Gelfand-Pinsker coding. We also prove a mutual covering lemma for the generalised typicality, and then obtain the Marton-type inner bound to the capacity region of the general broadcast channel.
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    • [1] C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, no. 3-4, pp. 379-423, 623-656, July-Oct. 1948.
    • [2] A. El Gamal and Y.-H. Kim, Network Information Theory. Cambridge: Cambridge University Press, 2011.
    • [3] T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley-Interscience, 2006.
    • [4] A. Orlitsky and J. R. Roche, “Coding for computing,” IEEE Trans. Inf. Theory, vol. 47, no. 3, pp. 903-917, Mar. 2001.
    • [5] A. El Gamal and E. C. van der Meulen, “A proof of Marton's coding theorem for the discrete memoryless broadcast channel (corresp.),” IEEE Trans. Inf. Theory, vol. 27, no. 1, pp. 120-122, Jan. 1981.
    • [6] K. Marton, “A coding theorem for the discrete memoryless broadcast channel,” IEEE Trans. Inf. Theory, vol. 25, no. 3, pp. 306-311, May 1979.
    • [7] S. I. Gelfand and M. S. Pinsker, “Coding for channel with random parameters,” Probl. Control Inform. Theory, vol. 9, no. 1, pp. 19-31, 1980.
    • [8] P. Mitran, “Typical sequences for Polish alphabets,” CoRR, vol. abs/1005.2321, 2010. [Online]. Available: http://arxiv.org/abs/1005.2321
    • [9] M. Raginsky, “Empirical processes, typical sequences, and coordinated actions in standard Borel spaces,” IEEE Trans. Inf. Theory, vol. 59, no. 3, pp. 1288-1301, Mar. 2013.
    • [10] A. D. Wyner, “On source coding with side information at the decoder,” IEEE Trans. Inf. Theory, vol. 21, no. 3, pp. 294-300, May 1975.
    • [11] J. Jeon, “A generalized typicality for abstract alphabets,” CoRR, vol. abs/1401.6728, 2014. [Online]. Available: http://arxiv.org/abs/1401.6728
    • [12] S. Huang and M. Skoglund, “Supremus typicality,” in Proc. IEEE Int. Symp. Inform. Theory, Honolulu, HI, USA, June 2014, pp. 2644-2648.
    • [13] M. S. Pinsker, Information and Information Stability of Random Variables and Processes, ser. Holden-Day Ser. Time Ser. Anal. San Francisco, CA, USA: Holden-Day, 1964, originally published in Russian in 1960, translated and edited by A. Feinstein.
    • [14] Y. Polyanskiy and Y. Wu, “Lecture notes on information theory,” 2014.
    • [15] T. S. Han, Information-Spectrum Methods in Information Theory, ser. Stoch. Model. Appl. Probab. Berlin: Springer-Verlag, 2003, no. 50, originally published in Japanese in 1998, translated by H. Koga.
    • [16] V. Y. F. Tan, “A formula for the capacity of the general Gel'fand-Pinsker channel,” in Proc. IEEE Int. Symp. Inform. Theory, Istanbul, Turkey, July 2013, pp. 2458-2462.
    • [17] A. Somekh-Baruch, “A general formula for the mismatch capacity,” CoRR, vol. abs/1309.7964, 2013. [Online]. Available: http://arxiv.org/abs/1309.7964
    • [18] J. Radhakrishnan, P. Sen, and N. Warsi, “One-shot Marton inner bound for classical-quantum broadcast channel,” CoRR, vol. abs/1410.3248, 2014. [Online]. Available: http://arxiv.org/abs/1410.3248
    • [19] K. Iwata and Y. Oohama, “Information-spectrum characterization of broadcast channel with general source,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci., vol. E88-A, no. 10, pp. 2808-2818, Oct. 2005.
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