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Distributed Source Coding Using Constrained-Random-Number Generators (2401.13232v3)
Published 24 Jan 2024 in cs.IT and math.IT
Abstract: This paper investigates the general distributed lossless/lossy source coding formulated by Jana and Blahut. Their multi-letter rate-distortion region, an alternative to the region derived by Yang and Qin, is characterized by entropy functions for arbitrary general correlated sources. Achievability is shown by constructing a code based on constrained-random number generators.
- R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography — Part II: CR capacity,” IEEE Trans. Inform. Theory, vol. IT-44, no.1, pp. 225–240, Jan. 1998.
- R. Ahlswede and J. Körner, “Source coding with side information and a converse for degraded broadcast channels,” IEEE Trans. Inform. Theory, vol. IT-21, no. 6, pp. 629–637, Nov. 1975.
- T. Berger, “Multiterminal source coding,” The Information Theory Approach to Communications, pp. 171–231, Springer-Verlag, New York, 1978.
- J. L. Carter and M. N. Wegman, “Universal classes of hash functions,” J. Comput. Syst. Sci., vol. 18, pp. 143–154, 1979.
- T. M. Cover, “A proof of the data compression theorem of Slepian and Wolf for ergodic source,” IEEE Trans. Inform Theory, vol. IT-21, no. 2, pp. 226–228, Mar. 1975.
- I. Csiszár, “Linear codes for sources and source networks: Error exponents, universal coding,” IEEE Trans. Inform. Theory, vol. IT-28, no. 4, pp. 585–592, Jul. 1982.
- S. I. Gelfand and M. S. Pinsker, “Source coding with incomplete side information,” (in Russian) Probl. Pered. Inform., vol. 15, no. 2, pp. 45–57, 1979.
- T.S. Han and K. Kobayashi, “A unified achievable rate region for a general class of multiterminal source coding systems,” IEEE Trans. Inform. Theory, vol. IT-26, no. 3, pp. 277–288, May 1980.
- T.S. Han and S. Verdú, “Approximation theory of output statistics,” IEEE Trans. Inform. Theory, vol. IT-39, no. 3, pp. 752–772, May 1993.
- R. Impagliazzo and D. Zuckerman, “How to recycle random bits,” 30th IEEE Symp. Fund. Computer Sci., Oct. 30–Nov. 1, 1989, pp. 248–253.
- K. Iwata and J. Muramatsu, “An information-spectrum approach to rate-distortion function with side information,” IEICE Trans. Fundamentals, vol. E85-A, No. 6, pp. 1387–1395, Jun. 2002.
- S. Jana and R. Blahut, “Canonical description for multiterminal source coding,” Proc. 2008 IEEE Int. Symp. Inform. Theory, Toronto, Canada July 6–11, pp. 697–701, 2008.
- W. Kang and S. Ulukus, “A new data processing inequality and its applications in distributed source and channel coding,” IEEE Trans. Inform. Theory, vol. 57, no. 1, pp. 56–69, Jan. 2011.
- H. Koga, “Coding theorems on the threshold scheme for a general source,” IEEE Trans. Inform. Theory, vol. IT-54, no. 6, pp. 2658–2677, Jun. 2008.
- J. Körner and K. Marton, “How to encode the modulo-two sum of binary sources,” IEEE Trans. Inform. Theory, vol. IT-25, no. 2, pp. 219-–221, Mar 1979.
- S. Miyake and F. Kanaya, “Coding theorems on correlated general sources,” IEICE Trans. Fundamentals, vol. E78-A, No. 9, pp. 1063–1070, Sept. 1995.
- J. Muramatsu, “Channel coding and lossy source coding using a generator of constrained random numbers,” IEEE Trans. Inform. Theory, vol. IT-60, no. 5, pp. 2667–2686, May 2014.
- J. Muramatsu, “Variable-length lossy source code using a constrained-random-number generator,” IEEE Trans. Inform. Theory, vol. IT-61, no. 6, pp. 3574–3592, Jun. 2015.
- J. Muramatsu, “On the achievability of interference channel coding,” Proceedings of the 2022 International Symposium on Information Theory and its Applications, Tsukuba, Japan, Oct. 17–19, pp. 39–43, 2022. Extended version is available at arXiv:2201.10756[cs.IT].
- J. Muramatsu, “Channel codes for relayless networks with general message access structure,” Proceedings of the 2023 IEEE Information Theory Workshop, Saint-Malo, France, Apr. 23–28, 2023. Extended version is available at arXiv:2206.00792[cs.IT].
- J. Muramatsu and S. Miyake, “Hash property and coding theorems for sparse matrices and maximal-likelihood coding,” IEEE Trans. Inform. Theory, vol. IT-56, no. 5, pp. 2143–2167, May 2010. Corrections: vol. IT-56, no. 9, p. 4762, Sep. 2010, vol. IT-59, no. 10, pp. 6952–6953, Oct. 2013.
- J. Muramatsu and S. Miyake, “Construction of broadcast channel code based on hash property,” Proc. 2010 IEEE Int. Symp. Inform. Theory, Austin, U.S.A., June 13–18, pp. 575–579, 2010. Extended version is available at arXiv:1006.5271[cs.IT], 2010.
- J. Muramatsu and S. Miyake, “Construction of strongly secure wiretap channel code based on hash property,” Proc. of 2011 IEEE Int. Symp. Inform. Theory, St. Petersburg, Russia, Jul. 31–Aug. 5, 2011, pp.612–616.
- J. Muramatsu and S. Miyake, “On the error probability of stochastic decision and stochastic decoding,” Proc. 2017 IEEE Int. Symp. Inform. Theory, Aachen, Germany, Jun. 25–30, 2017, pp. 1643–1647. Extended version is available at arXiv:1701.04950[cs.IT].
- J. Muramatsu and S. Miyake, “Multi-terminal codes using constrained-random-number generator,” Proc. 2018 International Symposium on Information Theory and its Applications, Singapore, Oct. 28–31, 2018, pp. 612–616. Extended version is available at arXiv:1801.02875v2[cs.IT].
- J. Muramatsu and S. Miyake, “Channel code using constrained-random number generator revisited,” IEEE Trans. Inform. Theory, vol. IT-65, no. 1, pp. 500–510, Jan. 2019.
- F. Shirani and S. S. Pradhan, “A new achievable rate-distortion region for distributed source coding,” IEEE Trans. Inform. Theory, vol. IT-67, no. 7, pp. 4485–4503, Jul. 2021.
- D. Slepian and J. K. Wolf, “Noiseless coding of correlated information sources,” IEEE Trans. Inform. Theory, vol. IT-19, no. 4, pp. 471–480, Jul. 1973.
- Y. Steinberg and S. Verdú, “Simulation of random process and rate-distortion theory,” IEEE Trans. Inform. Theory, vol. IT-42, pp. 63–86, 1996.
- A. B. Wagner and V. Anantharam, “An improved outer bound for multiterminal source coding,” IEEE Trans. Inform. Theory, vol. 54, no. 5, pp. 1919–1937, May. 2008.
- A. B. Wagner, B. G. Kelly, and Y. Altuğ, “Distributed rate-distortion with common components,” IEEE Trans. Inform. Theory, vol. 57, no. 7, pp. 4035–4057, Jul. 2011.
- A. D. Wyner, “On source coding with side information at the decoder,” IEEE Trans. Inform. Theory, vol. IT-21, no. 3, pp. 294–300, May. 1975.
- A. D. Wyner and J. Ziv, “The rate-distortion function for source coding with side information at the decoder,” IEEE Trans. Inform. Theory, vol. IT-22, no. 1, pp. 1–10, Jan. 1976.
- M. H. Yassaee, M. R. Aref, and A. Gohari, “Achievability proof via output statistics of random binning,” IEEE Trans. Inform. Theory, vol. IT-60, no. 11, pp. 6760-6786, Nov. 2014.
- S. Yang and P. Qin, “An information-spectrum approach to multiterminal rate-distortion theory,” available at arXiv:cs/0605006v1[cs.IT].
- S. Yang and P. Qin, “An enhanced covering lemma for multiterminal source coding,” Proceedings of the 2006 IEEE Information Theory Workshop, Chengdu, China, Oct. 22–26, pp. 303–307, 2006.