Second-order resolvability, intrinsic randomness, and fixed-length source coding for mixed sources: Information spectrum approach

IEEE Transactions on Information Theory

Volumn 59, Issue 1, 2013, Pages 1-16

  Nomura, Ryo ^a   Han, Te Sun ^b  

^a SENSHU UNIVERSITY   (Japan)

^b NATIONAL INSTITUTE OF INFORMATION AND COMMUNICATIONS TECHNOLOGY   (Japan)

Author keywords

Asymptotic normality; mixed source; random number generation; second order achievability; source coding

Indexed keywords

ACHIEVABILITY; ASYMPTOTIC NORMALITY; ASYMPTOTICS; COMPUTATION PROBLEMS; CONTINUOUS MIXTURES; FIRST-ORDER; GENERAL SOURCE; INFORMATION SPECTRUM; INTRINSIC RANDOMNESS; MARKOV SOURCES; MIXED SOURCE; SECOND ORDERS; SOURCE-CODING;

COMPUTER APPLICATIONS; INFORMATION THEORY;

RANDOM NUMBER GENERATION;

EID: 84871796514     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2012.2215836     Document Type: Article

References (19)

1. T. S. Han and S. Verdú, "Approximation theory of output statistics," IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 752-772, May 1993.
2. S. Vembu and S. Verdú, "Generating random bits from an arbitrary source: Fundamental limits," IEEE Trans. Inf. Theory, vol. 41, no. 5, pp. 1322-1332, Sep. 1995.
3. T. S. Han, "Folklore in source coding: Information-spectrum approach," IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 747-753, Feb. 2005. (Pubitemid 40211082)
4. K. Visweswariah, S. R. Kulkarni, and S. Verdú, "Source codes as random number generators," IEEE Trans. Inf. Theory, vol. 44, no. 2, pp. 462-471, Mar. 1998. (Pubitemid 128737615)
5. T. S. Han, Information-Spectrum Methods in Information Theory. New York: Springer-Verlag, 2003.
6. Y. Steinberg and S. Verdú, "Simulation of random processes and ratedistortion theory," IEEE Trans. Inf. Theory, vol. 42, no. 1, pp. 63-86, Jan. 1996. (Pubitemid 126775658)
7. I. Kontoyiannis, "Second-order noiseless source coding theorems," IEEE Trans. Inf. Theory, vol. 43, no. 4, pp. 1339-1341, Jul. 1997. (Pubitemid 127828068)
8. I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems. New York: Academic, 1981.
9. M. Hayashi, "Information spectrum approach to second-order coding rate in channel coding," IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 4947-4966, Nov. 2009.
10. Y. Polyanskiy, H. Poor, and S. Verdú, "Channel coding rate in the finite blocklength regime," IEEE Trans. Inf. Theory, vol. 56, no. 5, pp. 2307-2359, May 2010.
11. M. Hayashi, "Second-order asymptotics in fixed-length source coding and intrinsic randomness," IEEE Trans. Inf. Theory, vol. 54, no. 10, pp. 4619-4637, Oct. 2008.
12. R. Nomura and T. Matsushima, "Achievable condition in resolvability problem for mixed sources," in Proc. 33rd Symp. Inf. Theory Appl., 2010, pp. 138-143.
13. Y. Polyanskiy, H. V. Poor, and S. Verdú, "Dispersion of the Gilbert-Elliott channel," IEEE Trans. Inf. Theory, vol. 57, no. 4, pp. 1829-1848, Apr. 2011.
14. K. L. Chung, Markov Chains with Stationary Transition Probabilities, 2nd ed. New York: Springer-Verlag, 1966.
15. P. Billingsley, Probability and Measure. Hoboken, NJ: Wiley, 1995.
16. P. C. Shields, The Ergodic Theory of Discrete Sample Paths. Providence, RI: Amer. Math. Soc., 1996.
17. A. J. Goldsmith and P. P. Varaiya, "Capacity, mutual information, and coding for finite-state Markov channels," IEEE Trans. Inf. Theory, vol. 42, no. 3, pp. 868-886, May 1996. (Pubitemid 126770540)
18. B. D. Fritchman, "A binary channel characterization using partitioned Markov chain," IEEE Trans. Inf. Theory, vol. IT-13, no. 2, pp. 221-227, Apr. 1967.
19. R. Nomura and T. S. Han, Capacity theorems for the Fritchman channel, in preparation.