P. Bergmans and T. M. Cover, \Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT-20, no. 3, pp. 317-324, May 1974.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... the codeword x j (f s u;k;i : k 2 43 [m j (u) M u ] u 2 U j g) where, for each u 2 U j , forward estimates f s u;k;i : k 2 [m j (u) M u ]g are obtained by applying the encoding procedure given in Appendix B to G(s u ; d u ) Decoding: Each node decodes using successive cancellation [5, 9, 30]. Thus each node j de nes an order in which it successively decodes the signals received from di erent levels of the di erent ow graphs that it belongs. While decoding a particular level of a particular ow graph, the signal components corresponding to already decoded levels are removed from the ....

P. Bergmans and T. M. Cover, \Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT-20, no. 3, pp. 317-324, May 1974.

....where is the proportion of the total bandwidth used by the first user. Fig. 1 shows both the rate region achievable with FDMA and the Shannon capacity region. It is clear that the FDMA capacity region is strictly smaller than the Shannon capacity region and FDMA is optimal only at a single point [2]. Incidentally, this point corresponds to an FDMA strategy where each user s share of bandwidth is proportional to its respective power. The 0090 6778 02 17.00 2002 IEEE tangent line at this point is at 45 degrees and it corresponds to the maximum sum capacity point. These ideas can be ....

P. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. 20, pp. 317--324, May 1974.

....in Appendix B. Encoding: In b block i, each node j transmits the codeword J k [raj(u) Mu] U b j ) where, for each u b j, forward estimates k [raj(u) Mu] are obtained by applying the encoding procedure given in Appendix B to 6(Su, du) Decoding: Each node decodes using successive cancellation [4, 7, 25]. Thus each node j defines an order in which it successively decodes the indices Su, k [O, raj(u) u 42 While decoding a particular index su,k, the signal components corresponding to already de coded indices are removed from the received signal, and the signal components corresponding to ....

P. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Inform. The- ory, vol. IT-20, no. 3, pp. 317-324, May 1974.

.... this orthogonal signaling approach gives indeed the maximum achievable rates for the Gaussian broadcast channel [1] The optimum bandwidth allocations can be found via the techniques of the previous section. In general, higher transmission rates are achievable by means of superposition coding [2]. However, this coding scheme requires joint decoding at the mobile receivers which is too complex and hence, impractical. To minimise the average distortion D, consider the functional W k (27) over the set of non negative W k . The Lagrange multiplier , this time interpreted as cost per ....

P. M. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Info. Theory, vol. Vol. 20, no. 3, pp. 317--324, May 1974.

....orthogonal signaling approach gives indeed the maximum achievable rates for the Gaussian broadcast channel [2] The optimum bandwidth allocations can be found via the techniques of the previous section. In general however, higher transmission rates are achievable by means of superposition coding [3]. However, this coding scheme requires joint decoding at the mobile receivers which is too complex and hence, impractical. To minimise the average distortion D, consider the functional W k (24) over the set of non negative W k . The Lagrange multiplier , this time interpreted as cost per ....

P. M. Bergmans and T. M. Cover, \Cooperative broadcasting," IEEE Trans. Info. Theory, vol. Vol. 20, pp. 317-324, May 1974.

....the two power policies, the achievable rates for User j in the state n are R j (n) j (n) P j (n) j (n)B log 1 P j (n) n j B ; 53) and R j (n) 0 j (n) P 0 j (n) 0 j (n)B log 1 P 0 j (n) n j B ; 54) respectively. 53) and (54) can also be expressed as [23]: R j (n) j (n) A j (n) j (n)B log 1 A j (n) j (n)n j B ; R j (n) 0 j (n) A 0 j (n) 0 j (n)B log 1 A 0 j (n) 0 j (n)n j B ; where A j (n) P j (n) j (n) and A 0 j (n) P 0 j (n) 0 j (n) j = 1; 2; Delta Delta Delta ; M . If we define a ....

P. P. Bergmans and T. A. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. 20, no. 3, pp. 317--324, May

.... the codeword x j (f s j u;k;i : k 2 [m j (u) M u ] u 2 U j g) where, for each u 2 U j , forward estimates f s j u;k;i : k 2 [m j (u) M u ]g are obtained by applying the encoding procedure given in Appendix B to G(s u ; d u ) Decoding: Each node decodes using successive cancellation [4, 7, 25]. Thus each node j de nes an order in which it successively decodes the indices fs u;k : k 2 [0; m j (u) u 2 U j g. 42 While decoding a particular index s u;k , the signal components corresponding to already decoded indices are removed from the received signal, and the signal components ....

P. Bergmans and T. M. Cover, \Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT-20, no. 3, pp. 317-324, May 1974.

....to the two policies, the transmit power and fractions of transmission time allocated to User are and , and , respectively. Therefore, for the two power policies, the achievable rates for User in the state are (53) and (54) respectively. Equations (53) and (54) can also be expressed as [23] where and , If we define a third power policy such that in each channel state , the transmit power and fraction of transmission time allocated to User are and respectively, then LI AND GOLDSMITH: CAPACITY AND OPTIMAL RESOURCE ALLOCATION FOR FADING BROADCAST CHANNELS PART I 1099 Since we ....

P. P. Bergmans and T. A. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT-20, pp. 317--324, May 1974.

....# is the proportion of the total bandwidth used by the first user. Figure 1 shows both the rate region achievable with FDMA and the Shannon capacity region. It is clear that the FDMA capacity region is strictly smaller than the Shannon capacity region, and FDMA is optimal only at a single point [2]. Incidentally, this point corresponds to a FDMA strategy where each user s share of bandwidth is proportional to its respective power. The tangent line at this point is at 45 degrees, and it corresponds to the maximum sum capacity point. These ideas can be generalized to the Gaussian multiple ....

P. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. 20, pp. 317--324, May 1974. 18

....coded modulation schemes which provide unequal error protection (UEP) against Gaussian noise. Starting with the case of two bit streams, we consider two classes of UEP schemes: time division coded modulation (TDCM) and superposition coded modulation (SCM) The early result of Bergmanns and Cover [1] ensures the asymptotic superiority of SCM. However, accounting for the fact that practical channel codes do not achieve capacity, we show that the validity of this result depends on the prescribed degree of inequality in protection of the streams. To complement the straightforward design and use ....

....or superposition coded modulation (SCM) TDCM is a form of resource sharing in which bit streams of differing importance are transmitted on disjoint modulation intervals. In SCM, the different bit streams are transmitted on the same modulation intervals. It has been shown by Bergmanns and Cover [1] that, ideally (i.e. asymptotically) SCM always outperforms TDCM. Motivated by 0090 6778 99 10.00 1999 IEEE GADKARI AND ROSE: CODED MODULATION SCHEMES FOR UNEQUAL ERROR PROTECTION 371 that result, much of the earlier work on the design of UEP schemes focused on SCM schemes [2] 4] An ....

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P. P. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT-20, pp. 317--324, May 1974.

.... j transmits the codeword x j (f s j u;k;i : k 2 [m j (u) Mu ] u 2 U j g) where, for each u 2 U j , forward estimates f s j u;k;i : k 2 [m j (u) Mu ]g are obtained by applying the encoding procedure of Section II to G(su ; du ) Decoding: Each node decodes using successive cancellation [7, 8, 2]. Thus each node j de nes an order in which it successively decodes the indices fs u;k : k 2 [0; m j (u) u 2 U j g. While decoding a particular index s u;k , the signal components corresponding to already decoded indices are removed from the received signal, and the signal components ....

P. Bergmans and T. M. Cover, \Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT-20, no. 3, pp. 317-324, May 1974.

....the two power policies, the achievable rates for User j in the state n are R j (n) j (n) P j (n) j (n)B log 1 P j (n) n j B ; 87) and R j (n) 0 j (n) P 0 j (n) 0 j (n)B log 1 P 0 j (n) n j B ; 88) respectively. 87) and (88) can also be expressed as [17]: R j (n) j (n) A j (n) j (n)B log 1 A j (n) j (n)n j B ; R j (n) 0 j (n) A 0 j (n) 0 j (n)B log 1 A 0 j (n) 0 j (n)n j B ; where A j (n) P j (n) j (n) and A 0 j (n) P 0 j (n) 0 j (n) j = 1; 2; Delta Delta Delta ; M . Li ....

P. P. Bergmans and T. A. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. 20, pp. 317--324, May 1974. List of Figures 1 An M-user fading broadcast channel model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 An equivalent M-user fading broadcast channel model. . . . . . . . . . . . . . . . . . . . . . 4

....rate tuples that fulfill (5) with equality and vertices of the region R which have maximum sum rate. Hence, in the sequel we will refer to these rate tuples as vertices. The fact that vertices of the region R fulfill (5) with equality was first observed in the Gaussian case by Bergmans and Cover [7] and independently by Wyner [8] Another account of this idea was given in [9] For the Gaussian case the decoding procedure described above is particularly simple since decoded users can simply be subtracted from the received word. Alternative names for this decoding procedure are onion peeling, ....

P. P. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT--20, pp. 317--324, May 1974.

....the decoder of user M can decode considering the codewords of user 1; Delta Delta Delta ; M Gamma 1 as noise. The contribution of user M can then be removed from the received word, and the procedure can be repeated until each codeword has been decoded. This idea is due to Bergmans and Cover [9] and to Wyner [6] who observed that the vertices of the capacity region satisfy (2) with equality (see Appendix A for a proof of this fact) Another account of this idea was given in [4] The decoding procedure described above is known variously as onion peeling, stripping, successive ....

P. P. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT--20, pp. 317--324, May 1974.

.... is one of the challenges of code division multiple access (CDMA) A treatment of code division broadcasting (one sender and receivers) and code division multiple access ( senders and one receiver) for the bandlimited additive white Gaussian noise channel is given in Bergmans and Cover [11], where it is proved that the CDMA rate region is strictly larger than the rate regions Fig. 3. Gaussian broadcast channel. achievable by frequency division multiple access (FDMA) and time division multiple access (TDMA) We now consider the Gaussian broadcast channel where and . This is a ....

P. P. Bergmans and T. M. Cover, "Cooperative broadcasting," IEEE Trans. Inform. Theory, vol. IT-20, pp. 317--324, May 1974.

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