R. Ahlswede, "Multi-way communication channels,," ISIT, 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of the single user channel is the multiple access channel which models the channel with several transmitters that share the same transmission medium and a single receiver. The capacity region and coding theorems for such a channel were established independently by R.Ahlswede and H. Liao in [6], 7] and [8] They showed that the capacity region of a multiple access channel is a convex hull of a union of pentagons. Shortly after that, A.Wyner [9] and T.Cover [10] gave a simplified version of these results for memoryless channels. Another important information theoretic parameter, the ....

....cellular environments and there is a need to extend the usual single cell model to multiple cells. This has been accomplished in [16] where a simple model that describes the cellular environment has been introduced and respective information theoretic parameters analyzed. Extending the results of [6], 7] 8] to the case of CDMA the capacity region of synchronous CDMA multiple access AWGN channel has been derived in [3] and later reformulated in [17] as 1 (P,G) ju (R,R2, Ra: Ri logliji H: JC 1, K iEJ (1.6) where matrix H = W 2) SS T (W ) and Ii I is [J[ x [J[ dimensional ....

R. Ahlswede, "Multi-way communication channels," in Proc. 2nd Int. Symp. Information Theory, pp. 103 135, 1971.

....j;u;k 1: Proof See Appendix D. 2 It is worth noting that the achievable rate vector regions given by Theorem 4. 1 for the U user Gaussian multiple access channel and the U user Gaussian broadcast channel are 18 exactly the capacity de ning achievable rate regions given for these channels in [1, 21] and [4, 14] respectively. We next extend Theorems 3.1 and 4.1 so as to allow di erent information to be sent over di erent ow graphs between a source destination pair (s; d) The basic idea is to colocate virtual source destination pairs at the same pair of nodes s and d, in the above scheme. ....

R. Ahlswede, \Multi-way communication channels," in Proc. 2nd Intl. Symp. Information Theory, pp. 23-52, Prague, 1971.

....each user are Gaussian distributed when underlying Markov process for that user is in active state. As for passive state, code symbols have a degenerate Gaussian distribution with a = 0, i.e. only one symbol is transmitted. The capacity region of K user multiple access channel has been derived in [11], 12] We shall focus our analysis on finding the sum capacity and exploring its dependence of E No. The sum capacity is given by [6] page 401 5 = i=1 where N is a random variable corresponding to Gaussian channel noise process and Y is the channel output, Y = Ei= Xi N. Since noise is ....

R.Ahlswede,"Multi-way communication channels," in Proc. 2nd Int. Symp. Information Theory, 1971, pp.103- 135.

....each user are Gaussian distributed when underlying Markov process for that user is in active state. As for passive state, code symbols have a degenerate Gaussian distribution with , i.e. only one symbol is transmitted. The capacity region of user multiple access channel has been derived in [5]. We focus our analysis on finding the sum capacity and exploring its dependence of . The sum capacity is given by [3] page 401 (8) N### where N is a random variable corresponding to Gaussian 853 channel noise process and Y is the channel output, Y N. ....

R.Ahlswede, "Multi-way communication channels," in Proc. 2nd Int. Symp. Information Theory, 1971, pp.103-135. -854-

....Then the signal received by node 1 at the end of the i th transmission is given by Yll;i hl, l Xl, i ] Zl;i , 6) E[ where h, is the channel gain from node 1 to node and Z = Z; Z; Z;b) is a sequence of i.i.d. Gaussian random variables with mean 0 and variance N, for 1 [1, . An example of the channel gain term , is to model the signal power path loss from node 1 to 1, i.e. rl,l where r, is the distance between nodes 1 and 1 and a is the signal power path loss exponent. This is the Physical model studied in [14] For this model of the channel gain, X;i, i, ....

.... 1. q 1 uELij(q) k mq) u) Proof See Appendix D. It is worth noting that the achievable rate vector regions given by Theorem 4. 1 for the U user Gaussian multiple access channel and the U user Gaussian broadcast channel are exactly the capacity defining achievable rate regions given in [1, 17] and [3, 12] respectively for these channels. We next extend Theorems 3.1 and 4.1 so as to allow different information to be sent over different flow graphs between a source destination pair (s, d) The basic idea is to colocate virtual source destination pairs at the same pair of nodes s and d, ....

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R. Ahlswede, "Multi-way communication channels," in Proc. 2nd Intl. $ymp. Informa- tion Theory, pp. 23-52, Prague, 1971.

....simple situation where the users locations are fixed and the signal of user is attenuated by a factor of when received at the base station, i.e. for all time . The characterization of the capacity region of the multiaccess memoryless channel with probability transitions is well known (Ahlswede [1], Liao [13] it is the set of all rate vectors satisfying for some independent input distribution . In this paper, for any vector we use the notation to denote . Note that is any subset of users in . The right hand side of each of the above inequalities is the mutual information between the ....

R. Ahlswede, "Multi-way communication channels," in Proc. 2nd. Int. Symp. Information Theory (Armenian S.S.R., 1971), pp. 23--52.

.... the question: How much information can wireless networks transport It is a triumph of information theory that the capacity regions for some systems have been characterized, as for example the Gaussian broadcast channel [10, 11, 12, 13] shown in Figure 1, and the Gaussian multiple access channel [14, 15] shown in Figure 2. Recently, for a network with a single source destination pair, the asymptotic rate has been characterized as the number of nodes in a bounded domain is increased, while excluding them from open neighborhoods of the source and destination; see [16] Y Y 2 m Figure ....

R. Ahlswede, \Multi-way communication channels," in Proceedings of the 2nd Int. Symp. Inform. Theory (Tsahkadsor, Armenian S.S.R.), (Prague), pp. 23-52, Publishing House of the Hungarian Academy of Sciences, 1971.

....The issue of network capacity has generally been considered in the context of networks of links exhibiting ergodic error processes. Channel coding theorems and capacity regions can be found for certain networks of this type, such as broadcast channels [1, 2, 3] multiple access channels [4, 5] and relay channels [6, 7, 8] Recently, some renewed attention has been paid to the capacity of error free networks. In particular, coding over error free networks for the purpose of transmitting multicast connections has been considered [9, 10, 11] For a further, recent discussion of network ....

R. Ahlswede,\Multi-way Communication Channels", Proceedings of the

....k=m (q) j (u) q) j;u;k 1: Proof See Appendix D. 2 It is worth noting that the achievable rate vector regions given by Theorem 4. 1 for the U user Gaussian multiple access channel and the U user Gaussian broadcast channel are exactly the capacity de ning achievable rate regions given in [1, 17] and [3, 12] respectively for these channels. We next extend Theorems 3.1 and 4.1 so as to allow di erent information to be sent over di erent ow graphs between a source destination pair (s; d) The basic idea is to colocate virtual source destination pairs at the same pair of nodes s and d, in ....

R. Ahlswede, \Multi-way communication channels," in Proc. 2nd Intl. Symp. Information Theory, pp. 23-52, Prague, 1971.

....in the tradeoff of coding rate versus distortion, thereby making the theory of sliding block codes practically significant. Seeing that Slepian and Wolf [93] had conducted seminal research on lossless multiterminal source coding problems analogous to the multiple access channel models of Ahlswede [90] and Liao [91] Berger and Wyner agreed that research should be done on a lossy source coding analog of the novel Cover Bergmans [88] 89] theory of broadcast channels. Gray and Wyner were the first to collaborate successfully on such an endeavor, authoring what proved to be the first of many ....

R. Ahlswede, "Multi-way communication channels," in Proc. 2nd. Int. Symp. Information Theory (Tsahkadsor, Armenian SSR), 1971, pp. 23--52.

....coding theorems, which use information stability results [50] 68] have been established [31] 49] The last issue we have mentioned, the multiple access problem, has been well studied in the memoryless case. The capacity region in the memoryless case was established with synchronicity ( 41] [1]) and asynchronicity ( 9] 51] Overviews of the multiple access problem are given in [16] 20] 71] and [45] In this paper, we consider the issues of ISI, time variation, and multiple access in the context of an error about the channel measurement available at the receiver. The time ....

R. Ahlswede, "Multi-way communication channels," in 2nd Int. Symp. Information Theory, 1971, pp. 23--52.

....users (thereby requiring feedback) This paper considers the limits imposed by information theory on the T out of M coding problem for the multiple access channel with static assignment. The first information theoretic result for the multiple access channel was obtained independently by Ahlswede [2] and Liao [3] who determined the capacity region for two synchronized users. Some extensions of this work appear in [4] 8] Cover, McEliece and Posner [9] have shown that the same capacity region is valid for a mildly frameasynchronous multiple access channel in which the relative delays ....

R. Ahlswede, "Multi-way communication channels, " in Proc. 2nd Int. Symp. Information Theory, Tsahkadsor, USSR, pp. 103--135, 1971.

....he may or may not collide with user 2. In the absence of multi user interference, each user sees an AWGN channel with noise variance oe 2 N . We have average power constraints of oe 2 1 and oe 2 2 for users 1 and 2, respectively. 2 We combine concepts from multi access communications ( 13] [1]) rate splitting ( 9] 18] and broadcast channels ( 6] 7] The rationale behind our approach springs from the following observation. In multi access channels, rate splitting achieves capacity by creating virtual users and decoding all users using interference cancellation. Thus, a set of ....

R. Ahlswede, "Multi-way Communication Channels", Proc. 2nd ISIT, pp. 23-52, 1971.

....practical network design problems that has contributed to the creation of an anti intellectual bias in parts of the networking community. At the same time, information theory has not done much to dispel that bias. During its early development, information theory did consider multiuser systems [1], 2] and much of the subsequent work on such systems tried to capture (and did) many of the fundamental differences between the classical, stand alone, single channel case and that of the shared channel in multiuser systems. For example, it was realized that although feedback from the receiver to ....

R. Ahlswede, "Multiway communication channels," Proceedings 2nd International Symposium on Information Theory, Tsahkadsor, Armenia, 1971.

....been the subject of extensive research and development in the past few decades. Essentially, multiuser communication is a method of communication in which all or some of the users transmit simultaneously over a common channel in a way that allows the proper receiving of the transmitted messages [1,2]. A major consideration in devising codes and designing access scheme is clearly the nature of the channel over which this communication takes place. Two types of channels have been most popular: the Collision Channel [3] and the Binary Adder Channel [4] The latter is the subject of this paper. ....

....0 , 1 X M 0 , 1 Figure 1: The M User Binary Adder Channel (BAC) reliable communication can be assured. The users are independent of one another, and P i denotes the probability that the i th user transmits a 1 at any given time unit, i.e. P i = D Prob[X i = 1 ] Ahlswede and Liao [2,5], proved that for any discrete time and memoryless multiple access channel with independent inputs (of which our BAC is a special case) 1) C SUM (M) max I(X 1 , X 2 , X M ; Y) where the maximum is taken over all possible probability distributions P(X 1 , X 2 , X M ) of the ....

R. Ahlswede, Multi-Way Communication Channels, in Proc. 2nd Int. Symp. Information Theory, Tsahkadsor, Armenian S.S.R., Hungarian Acad. Sc., pp. 23-52, 1973.

....for several classes of regular sources. An attempt is made to discuss the methods of the subject systematically. 1. Introduction The study of channels with several senders and receivers was initiated in 1961 by Shannon [1] and the first multi user coding theorem was proved ten years later in [2]. This led to a great research activity during the seventies in an area, which is usually called Multi user Information Theory. On the source coding side a strong impetus came in 1973 from the paper [3] which concerns a probabilistic model of correlated sources. In the same year, independently ....

R. Ahlswede, "Multi--way communication channels", Proc. of 2nd Inf. Symp. on Inform. Theory, Tsakkadsor, Armenian SSR, pp. 23--52, 1971.

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R. Ahlswede, "Multi-way communication channels,," ISIT, 1971.

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R. Ahlswede, "Multiway communication channels," in Proc. 2nd Int. Symp. Information Theory (Tsahkadsor, Armenia, 1971).

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R. Ahlswede, "Multi-way communication channels," ISIT, pp. 23--52, 1971.

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R. Ahlswede, "Multi-way Communication Channels," Proceedings of 2nd International Symposium on Information Theory (Tsahkadsor, Armenian S.S.R.), pp. 23-52, Prague, 1971.

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R. Ahlswede, Multi-way Communication Channels. Proceedings of ISIT, pp. 23--52, 1971.

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R.Ahlswede,"Multi-waycommunicationchannels,"inProc.2ndIEEE Int.Symp.InformationTransmission,U.S.S.R.,1971.

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R. Ahlswede, Multi-way Communication Channels. Proceedings of ISIT, pp. 23--52, 1971.

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R. Ahlswede, "Multi-way communication channels," in Proc. 2nd Int. $ymp. Inform. Theory, Tsahkadsor, Armenian S.S. R., 1971.

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R. Ahlswede, "Multi-way communication channels," in Proc. 2nd Int. Symp. Inform Theory (Tsahkadsor, Armenian S.S.R.,

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