S. Chang and E.J. Weldon,"Coding for T-user Multiple-Access Channels", IEEE Transactions on Information Theory, Vol.25, No.6, Nov 79.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....C 4 = C1 ; C2 ; CT ) is a collection of T sets of codewords of length n, C i ae f0; 1g n . The rate of the code is R 4 = R1 ; RT ) and the sum rate is Rsum(T ) 4 = R1 R2 : RT , where R i 4 = 1=n) log 2 jC i j is the rate of the i th user s code. Chang and Weldon [1] showed that the capacity region of this channel is the set of all nonnegative rates (R1 ; RT ) satisfying 0 m X =1 R i Hm ; m = 1; T (1) Brian L. Hughes was supported by the National Science Foundation under Grant No. NCR 9217457 and by the U.S. Army Research ....

....other points in the capacity region can be approached by a similar construction. This paper presents a family of mixed rate, multiuser codes for the binary adder channel. Section 2 presents a recursive code construction. The codewords are equivalent, up to an affine transformation, to those in [1]. However, the recursions are adapted in order to distribute the codewords among as few users as possible, thus yielding codes with a wide range of information rates. Section 3 shows that these basic codes can be combined by time sharing to achieve most rates in the capacity region. Specifically, ....

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S. C. Chang and E. J. Weldon, Jr, "Coding for T - user multiple-access channels," IEEE Trans. Inform. Theory, vol. 25, pp. 684-691, Nov. 1979.

....through a common discrete time channel. At each time epoch, user i selects an input X i 2 f0; 1g for transmission. The channel output is Y 4 = T X i=1 X i (1) where summation is over the real numbers. We assume that there is no feedback and all users are synchronized. Chang and Weldon [1] showed that the capacity region of the T user binary adder channel is the set of all nonnegative rates (R1 ; RT ) satisfying 0 R i H1 ; 0 R i R j H2 ; 0 R1 Delta Delta Delta RT HT ; 2) where Hm 4 = Gamma m X i=0 m i 2 Gammam ....

.... RT HT ; 2) where Hm 4 = Gamma m X i=0 m i 2 Gammam log 2 m i 2 Gammam : 3) In particular, observe that the largest achievable sum rate, Rsum(T ) 4 = R1 Delta Delta Delta RT , is Csum(T ) 4 = HT , which is called the sum capacity. Chang and Weldon [1] also presented a family of multiuser codes which are asymptotically optimal in the sense that Rsum(T ) Csum (T ) 1 as T 1. In their construction, each user s code consists of only two codewords which are defined recursively (so R1 = R2 = Delta Delta Delta = RT ) This basic construction ....

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S. C. Chang and E. J. Weldon, Jr, "Coding for T -user multipleaccess channels," IEEE Trans. Inform. Theory, vol. 25, pp. 684691, Nov. 1979.

....Figure 1: C(2; 3) of binary adder channel Thus, C(T; M ) of the binary adder channel is f(R 1 ; RM ) 0 R S H jSj ; for all jSj Tg: For example, C(2; 3) of the binary adder channel is depicted in Fig. 1. Upon comparing this to the synchronous capacity region for T out of T users [15], we find that (R 1 ; RM ) is achievable for the T out of M frame asynchronous case if and only if any T components of the rate vector, R i 1 ; R i T ) is in the synchronous T user region. An important special case occurs when each active user transmits at the same rate. In ....

S. Chang and E. J. Weldon, Jr., "Coding for T - user multiple-access channels," IEEE Trans. Inform. Theory, vol. IT-25, pp. 684--691, November 1979.

....real adder channel, a multiple access channel that produces, at each instant of time, an output symbol which is the real sum of a set of binary input symbols, one from each of T users. A set of uniquely decodable, multiuser codes, asymptotically achieving capacity on this channel, was presented in [3]. Subsequent work [4,5] 1 A stable system is one in which the expected delay per packet is finite. COOPER, HUGHES, 19th Army Science Conference, June 1994 2 generalized the codes of [3] to have arbitrary length while retaining the recursive construction and asymptotic performance of the ....

....of uniquely decodable, multiuser codes, asymptotically achieving capacity on this channel, was presented in [3] Subsequent work [4,5] 1 A stable system is one in which the expected delay per packet is finite. COOPER, HUGHES, 19th Army Science Conference, June 1994 2 generalized the codes of [3] to have arbitrary length while retaining the recursive construction and asymptotic performance of the original codes. In Section 2, we define terms and present a family of uniquely decodable binary codes for the T user real adder channel. The codes consist of T individual codebooks, each ....

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S. C. Chang and E. J. Weldon, Jr, "Coding for T -user multiple-access channels," IEEE Transactions on Information Theory, Vol IT-25, No. 6, pp. 684-691, November 1979.

.... have been constructed to achieve all rate points in the capacity region is the collision channel without feedback studied by Massey and Mathys [5] For the M user synchronous binary input real adder channel, a family of asymptotically optimal codes with two codewords per user has been constructed [6]. The channels in [5] and [6] are noiseless. For a survey on codes for specific multiple access channels see the introduction in [7] The receiver is based on successive decoding. The key idea behind successive decoding is to decode one user at a time, using already produced codeword estimates as ....

.... all rate points in the capacity region is the collision channel without feedback studied by Massey and Mathys [5] For the M user synchronous binary input real adder channel, a family of asymptotically optimal codes with two codewords per user has been constructed [6] The channels in [5] and [6] are noiseless. For a survey on codes for specific multiple access channels see the introduction in [7] The receiver is based on successive decoding. The key idea behind successive decoding is to decode one user at a time, using already produced codeword estimates as side information to decode ....

S. C. Chang and E. J. Weldon, "Coding for T-user multiple-access channels," IEEE Trans. Inform. Theory, vol. IT--25, pp. 684--691, Nov. 1979.

....section how we can combine Theorem 1 with Harper s isoperimetric inequality and an information theoretic inequality to obtain a tighter upper bound on CZE . We note that many other variants of the above problem have been proposed and investigated in the literature. These include the T user BAC [16, 17, 18, 19, 20, 21, 22, 23, 24], ffi decodable codes [4, 15, 5, 14, 25, 10, 11] for the noisy BAC, as well as the asynchronous binary adder channel [26, 13, 27] II. Upper Bound On CZE We start by remarking that if C (n 1 ) and C (n 2 ) are two UD codes with rates (R (n 1 ) X ; R (n 1 ) Y ) and (R (n 2 ) X ; R (n 2 ....

S. C. Chang and E. J. Weldon, "Coding for T-user multiple-access channels," IEEE Trans. Inform. Theory, vol. IT-25, pp. 684--691, Nov. 1979.

.... to achieve all rate points in the capacity region is the collision channel without feedback studied by Massey and Mathys [10] For the M user synchronous binary input real adder channel (which is noiseless) a family of asymptotically optimal codes with two codewords per user has been constructed [11]. For a survey on codes for specific multiple access channels see the introduction in [12] The second approach to achieving the difficult rate tuples is time sharing between vertices. This approach can require as many as M multiple access codes, each multiple access code requiring M individual ....

S. C. Chang and E. J. Weldon, "Coding for T-user multiple-access channels," IEEE Trans. Inform. Theory, vol. IT--25, pp. 684--691, Nov. 1979.

.... to achieve all rate points in the capacity region is the collision channel without feedback studied by Massey and Mathys [10] For the M user synchronous binary input real adder channel (which is noiseless) a family of asymptotically optimal codes with two codewords per user has been constructed [11]. For a survey on codes for specific multiple access channels see the introduction in [12] The second approach to achieving the difficult rate tuples is time sharing between vertices. This approach can require as many as M multiple access codes, each multiple access code requiring M individual ....

S. C. Chang and E. J. Weldon, "Coding for T-user multiple-access channels," IEEE Trans. Inform. Theory, vol. IT--25, pp. 684--691, Nov. 1979.

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S. Chang and E.J. Weldon,"Coding for T-user Multiple-Access Channels", IEEE Transactions on Information Theory, Vol.25, No.6, Nov 79.

No context found.

S. C. Chang and E. J. Weldon, Jr., "Coding for T -user multiple-access channels," IEEE Trans. Inform. Theory, vol. IT-25, pp. 684-691, Nov. 1979.

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