On the multiple access channel model: overview of capacities and ...

On the multiple access channel model: overview of capacities and coding" A.J. Han Vinck

Institute for Experimental Mathematics, University of Essen, Germany [email protected] In Information Theory literature, several interesting channel models are used for Multi-Access communications. Research considered coding for these channels and also calculations of channel capacity were performed. In calculating capacity, we show the difference between the conditions posed by Information Theory where a fixed set of users always transmit information and the networking counterpart where a particular set of unknown transmitters try to communicate with their respective receivers. We give some concluding results on the following models: M-ary Pulse Position Modulation channel as used by Cohen et al. in frequency hopping random access[1]. We give superimposed code constructions in [9]. These codes are to be used in a multi-user concept where the set of active users is small compared to the total amount of potential users.; M-user T-frequency channel as for instance described by Chang and Wolf.[2]. This channel model detects the presence of input frequencies (with or without intensity)We extended the calculations to the networking “unsynchronized” situation [7]; Adder channel with and without intensity information, see [8]; XOR channel. Especially, coding aspects were considered in [5,6, 8]; Switching channel, introduced at the Swedish-Soviet workshop as a non-trivial two access channel, constructions are given in [11].

[10]. Code

[1] A. Cohen, J. Heller and A. Viterbi, "A New Coding Technique for Asynchronous Multiple Access Communication," IEEE Trans. on Comm., vol. COM-19, pp. 849-855, October 1971. [2] Shin-Chun Chang and J.K. Wolf, "On the T-User M-Frequency Noiseless Multiple-Access Channel with and without Intensity Information," IEEE Trans. on Inform. theory, vol. IT-27, pp. 41-48, January 1981. [3] A.J. Han Vinck and Jeroen Keuning, „On the Capacity of the Asynchronous T-user M-frequency Noiseless Multiple Access Channel without Intensity Information,“ IEEE Trans. on Inform. theory, November 1996. [4] F.R.K. Chung, J.A. Salehi and V.K. Wei, „optical orthogonal codes: Design, analysis and applications,“ IEEE Trans. on Inform. theory, vol. 35, pp. 595-604, May 1989. [5] G. Poltyrev and J. Snyders, “Linear Codes for the Sum-2 Multiple-Access Channel with Restricted Access,” IEEE IT Trans., 794-799, May 1995 [6] T. Ericson and V. Levenshtein, “Superimposed Codes in the Hamming Space,” IEEE IT Trans.m pp. 1882-1893, Nov. 1994 [7] P. Gober and A. J. Han Vinck , ”Note on “On the Asymptotic Capacity of a Multiple-Access Channel” by L. Wilhelmsson and K. Sh. Zigangirov,” pp. 19–22, Pr. of Inf. Tr., 2000 [8] A.J. Han Vinck and Peter Gober, “On the Capacity of Two Uncoordinated Multiple Access Channels,” CISS2002, Princeton, USA, March 20-22 (CD-ROM), 2002. [9] A. J. Han Vinck and S. Martirosyan, “On Superimposed Codes,” in Numbers, Information and Complexity, Ingo Althöfer, Ning Cai, Gunter Dueck, Levon Khachatrian,Mark S. Pinsker, Andras Sarkozy, Ingo Wegenerand Zhen Zhang (eds.), Kluwer Academic Publishers, February 2000, pp. 325-331. [10] A.J. Han Vinck, On the Multi-Access Channel, Proceedings 2nd Joint Swedish-Soviet Int. Workshop on Information theory, pages 24-29, Gränna, Sweden, April 1985. [11] P. Vanroose, „Code Constructions for the Noiseless Binary Switching Multiple-Access Channel,” IEEE Trans. on Information theory, pp. 100-1106, 1988.