, "On area/depth trade-off in LUT-based FPGA technology mapping, " IEEE Trans. VLSI Syst., vol. 2, pp. 137--148, June 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....procedures that provide very useful heuristics for constructing slidingblock decodable encoders with small decoding window. They also imply useful upper bounds on the minimum size of the decoding window and on the smallest possible anticipation (or decoding delay) 12] In particular, Hollmann [92] has recently developed an approach, influenced by earlier work of Immink [103] which combines the state splitting method with a generalized look ahead encoding technique called boundeddelay encoding, originally introduced by Franaszek [61] 63] In a number of cases, it was found that this ....

....[61] 63] In a number of cases, it was found that this hybrid code design technique produced a sliding block decodable encoder with smaller window length than was achieved using other methods. Several examples of such codes for specific constraints of practical importance were constructed in [92]. For more extensive discussion of complexity measures and bounds, as well as brief descriptions of other general code construction methods, the reader is referred to [144] G. Universality of State Splitting The guarantee of a sliding block decoder when is finitetype, along with the explicit ....

, "On the construction of bounded-delay encodable codes for constrained systems," IEEE Trans. Inform. Theory, vol. 41, pp. 1354--1378, Sept. 1995.

....alodingO and presents theresuly ofsimulMOjIM on a codecalOF the hexacode.Finald Section 5concl4Oj the paper. Fig. 1. Generator matrix for a (4; 2)lOFxy binary code. 2. Background We give a very brief background onsubclFOjM ofblyf codes calsO llsO codes. Readers are referred to theclO4x texts [17,14,2]. Let F q be the #el with q elxIxIOj It is customary to de#ne l#neO codesalsOyxf4xOjM asfolMFNO De#nition 2.1. A linear block code C oflOFIF n over a#el F q is a k dimensional subspace of an n dimensional vector space over the #el F q (such a code iscalfy an (n; k) code) The most ....

R.J.McEl44MI On the BCJRtrelFf forlrOFy blOF codes, IEEE Trans. Inform. Theory 42 (1996) 1072--1092.

....quotation from John Von Neumann about entropy, which can be found for example in [ABC 00, Chap. 10] Notice that similar entropies appears with that name in a slightly di erent forms in a lot of papers related to Information Theory and Convex Analysis elds, see for example [BR82b] BR82a] BR82c] TV93] and [BTT86] and references therein. The entropy is also related to the so called (h; entropies, see for example [MMPS97] and references therein. The entropy is also known as J divergence (J stands for Jensen) See also [Csi63, Csi72] for the similar notion of divergence. The ....

....under (H1) for , the entropy functional is convex with respect to its functional argument. Alternatively, one can use directly Jensen s inequality with the bivariate function (u; v) 7 , which is convex under (H1) The convexity of entropy like functionals is well known, see for example [BR82c] BR82a, Thm. 2] and [LO00, Lem. 4] Since every convex functional is the envelope of its tangents (cf. RW98, HUL01] this gives immediately the following variational formula under (H1) f) sup (DH ) h) f h) H = sup E ( h) E (h) f h) H We ....

[Article contains additional citation context not shown here]

, On the convexity of some divergence measures based on entropy functions, IEEE Trans. Inform. Theory 28 (1982), no. 3, 489-495. MR 84d:94009

....g 4, 2002 quotation from John Von Neumann about entropy, which can be found for example in [ABC 00, Chap. 10] Notice that similar entropies appears with that name in a slightly di erent forms in a lot of papers related to Information Theory and Convex Analysis elds, see for example [BR82b] BR82a] BR82c] TV93] and [BTT86] and references therein. The entropy is also related to the so called (h; entropies, see for example [MMPS97] and references therein. The entropy is also known as J divergence (J stands for Jensen) See also [Csi63, Csi72] for the similar notion of ....

, On the convexity of higher order Jensen dierences based on entropy functions, IEEE Trans. Inform. Theory 28 (1982), no. 6, 961-963. MR 84e:94009

....from PUi must be routed to the destination processor PUd(1) and this should be done for all i (0 g i N) simultaneously. In many applications d is a permutation. A trivial way of routing permutations is by sorting on an appended destination field. Sorting algorithms for the MESH are well known, [6, 10, 3], the most efficient one requiring (8. v ff O(N 3 n) routing steps (rss) Many recent articles on routing and sorting on the MESH, 8, 2, 4] assume a MIMD machine and often have average case performance. Although these results cannot readily be compared to our results for SIMD machines, they ....

-, Bitonic sort on a MESH-connected parallel computer, IEEE Trans. Computers, C-27 (1979), pp. 2-7.

....random variable. In this paper, we study the distributions of the MAI at the output of the minimum mean square error (MMSE) receiver. Recently, there has been a substantial literature devoted to the study of linear multiuser receivers because they are practically appealing (see, e.g. 14] [16], 18] 22] 26] 27] 29] 31] We focus on the case where the MMSE receiver is employed because the MMSE receiver is optimal in the class of linear multiuser receivers in the sense of minimizing the mean square error [15] Assuming the signatures are deterministic, Poor and Verd [18] have ....

....their signatures randomly and independently. In a DS CDMA system, the signatures are binary valued. The model for binary random signatures is as follows: where the s are independent and identically distributed (i.i.d. with and This model is applicable to several scenarios (see, e.g. 8] [16], 26] 28] 31] First, consider systems where users employ Fig. 1. A simplified block diagram of the uplink of a CDMA system with MMSE receivers as a front end. Fig. 2. The block diagram of a composite waveform channel for user 1. long pseudorandom spreading sequences with periods ....

, "On the average near-far resistance for MMSE detection of directed -sequence CDMA signals with random spreading," IEEE Trans. Inform. Theory, pp. 2039.

....A system is identifiable if, for any , then In other words, the cyclic correlations are unique to the parameters To quantify which channels are identifiable, we first define the transfer function of the channel as Now, we state the indentifiability (ID) condition. ID Condition [20] 3] [24]: No subset of the zeros of lies equispaced on a circle with angle separating each zero from the next. In a blind identification problem, it is not possible to determine a priori whether the ID condition is satisfied. However, 21] gives a procedure for determining from the output spectra ....

....with angle separating each zero from the next. In a blind identification problem, it is not possible to determine a priori whether the ID condition is satisfied. However, 21] gives a procedure for determining from the output spectra whether the ID condition is satisfied. In addition, Tugnait [24] describes a class of channels that never satisfy the ID condition. For channels that do not meet the ID condition, HOS methods must be employed (see, e.g. 8] to uniquely identify the channel. D. Sample Cyclic Correlations Given the observations , the cyclic correlation at cycle and lag [see ....

, "On blind identifiability of multipath channels using fractional sampling and second-order cyclostationary statistics," IEEE Trans. Inform. Theory, vol. 41, pp. 308--311, Jan. 1995.

....smooth. These reconstructions are discussed further in Section VI. D. Methods Compared Studies were performed on the methods that are listed below along with their corresponding abbreviations by which they are referred in the rest of this paper. 1) DePierro s Algorithm (DePierro) In [8] and [9], DePierro proposed a modification to the EM algorithm for the regularized problem with convex priors. All studies were performed on DePierro s algorithm as a baseline. These reconstructions were terminated either when the optimal objective function (as determined by the interior point methods) ....

....by the interior point methods) was reached or after 1000 iterations, whichever came first. The asymptotic convergence rate of DePierro s algorithm is governed by the spectral radius of the Jacobian of its mapping function, which is slightly closer to unity than that of one step late (OSL) [9], 16] 2) One Step Late (OSL) Green s OSL algorithm [16] 17] can be written as 0 = O h W.V.f(O ) 43) q R (0 k is the EM scaling matrix. In general, the performance of Green s OSL algorithm on our studies was quite similar to that of DePierro s algorithm. For that reason, OSL ....

--', "On the convergence of an EM-type algorithm for penalized likelihood estimation in emission tomography," IEEE Trans. Med. Imag., vol. 14, pp. 762 765, Dec., 1995.

....search method used is to minimize the number of questions posed. Unlike in our case, no convergence analysis can be given due to the heuristic nature of the approach. An mathematical programming approach to model negotiations over continuous issues is to use constraint proposals methods [9] [12], 36] 39] In these methods, the mediator adjusts an artificial plane constraint until the DMs optimal choices on the plane coincide. Unlike the methods of improving directions, these methods do not produce improving agreements during the iteration. The only thing that can be guaranteed is ....

, "On distributed computation of Pareto solutions for two decision makers," IEEE Trans. Syst., Man, Cybern. A, vol. 26, pp. 498--503, July 1996.

....correction is also based on the results of test vector simulation. Therefore, since both steps of diagnosis and correction are based on information provided by test vector simulation, the method is applicable to circuits that have no global Binary Decision Diagram (BDD) representation [6] [7], 23] Next, we examine the quality of test vector simulation for the DEDC problem. Since exhaustive test vector simulation is prohibitive for most circuits, it is of interest to know the quality of a DEDC method that bases its results on a small subset of the complete input test vector space. ....

....Abadir et al. 2] are only considered, or the amount of resynthesis may not be minimal. More important, symbolic techniques that use a Fig. 1. Overview of DEDC methodology. global BDD [6] representation of the circuit are not applicable to circuits that have no such efficient representation [6] [7], 23] On the other hand, test vector simulation based methods for DEDC are applicable to all circuits. In addition, existing work shows that test vector simulation can be a computationally efficient route to DEDC for designs corrupted with one and two errors. However, just like the symbolic ....

[Article contains additional citation context not shown here]

, "On the complexity of VLSI implementation and graph representations of Boolean functions with application to integer multiplication," in IEEE Trans. Comput., vol. 40, pp. 205--213, Feb. 1991.

.... problems involving interpolation by positive real functions play an important role in circuit theory [39] 11] 25] robust stabilization and control [36] 37] 40] 30] 29] 21] 13] signal processing [18] 6] 8] 2] speech synthesis [12] and stochastic systems theory [27] [5], 4] However, in all these applications, it is important that the interpolating function be rational with a degree which does not exceed some prescribed bound. Degree constraints present some new challenges which need to be incorporated systematically into any useful enhancement of the ....

....of covariance samples , where , via some ergodic estimate such as (2.5) Knowledge of imposes certain interpolation conditions on at infinity. Finding all satisfying these is the topic which originally motivated the research programs from which the results of this paper emanated [17] 18] 6] [5], 4] 7] 8] A complete parameterization of all solutions of degree at most was provided in [6] Here we shall take a radically different approach to spectral estimation that is based on nontraditional covariance measurements. The basic idea is to determine covariance estimates after passing ....

, "On the partial stochastic realization problem," IEEE Trans. Automat. Contr., vol. 42, pp. 1049--1069, Aug. 1997.

....block interleaver can be seen in Fig. 22. This shows a comparison between turbo coders using several block interleavers with frame lengths of approximately 190 b. The block interleaver, proposed for short frame transmission systems in [37] and used by the same authors in other papers such as [34] [38], 39] clearly has a somewhat lower performance than the other block interleavers, which use an odd number of rows and columns. It is also interesting to note that of the two block interleavers with an odd number of rows and columns, the interleaver which is closer to being square (i.e. the ....

, "Results on turbo-codes for speech transmission in a joint detection CDMA mobile radio system with coherent receiver antenna diversity, " IEEE Trans. Veh. Technol., vol. 46, pp. 862--870, Nov. 1997.

....was first determined (in a different algebraic form) by Ahlswede [1] and Liao [60] The maximum probability of error criterion may give a smaller region, cf. Dueck [41] a single letter characterization of the latter is not known. For in the interior of , can be made exponentially small; Gallager [47] gave an attainable exponent everywhere positive in the interior of . Pokorny and Wallmeier [71] were first to apply the method of types to this problem. They showed the existence of (universal) codes with codewords and whose joint types with a fixed are arbitrarily given and such that the ....

, "A perspective on multiaccess channels," IEEE Trans. Inform. Theory, vol. IT-31, pp. 124--142, Mar. 1985.

....small whenever , with exponent (cf. III.3) and the remarks to Theorems IV.1 and IV.2 for notation) This exponent is best possible if the minimum is attained for some . For further results in this direction, including source channel transmission with a distortion threshold, cf. Csisz ar [24]. C. Multiterminal Source Coding Historically, the first multiuser problem studied via the method of types was that of the error exponent for the Slepian Wolf [76] problem, i.e. separate coding of (memoryless) correlated sources. Given a source pair with generic variables , the error ....

, "On the error exponent of source-channel transmission with a distortion threshold," IEEE Trans. Inform. Theory, vol. IT-28, pp. 823--828, Nov. 1982.

....bound on #(G) This is, however, not better that #: Proposition 5.6 Suppose that G has an orthonormal representation in dimension d. Then #(G) # d. On the other hand, if we consider orthogonal representations over fields of finite characteristic, the dimension may be a better bound than # [37, 5]. This, however, goes outside the ideas of semidefinite optimization. To relate # to the Shannon capacity of a graph, the following is the key observation: 20 Proposition 5.7 For any two graphs, #(G H) #(G)#(H) and #(G H) #(G)#(H) It is now easy to generalize the bound for the ....

....5.7 For any two graphs, #(G H) #(G)#(H) and #(G H) #(G)#(H) It is now easy to generalize the bound for the Shannon capacity of the pentagon, given in the introduction, to arbitrary graphs. Corollary 5. 8 For every graph, #(G) # #(G) Does equality hold here Examples by Haemers [37], and more recent much sharper examples by Alon [5] show that the answer is negative in general. But we can derive at least one interesting class of examples from the general results below. Proposition 5.9 For every graph G, #(G)#(G) # n. If G has a vertex transitive automorphism group, then ....

W. Haemers: On some problems of Lovasz concerning the Shannon capacity of a graph, IEEE Trans. Inform. Theory 25 (1979), 231--232.

....[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 variation of the channel and the error on the estimate of the channel are tightly linked. The time ....

, "A perspective on multiaccess channels," IEEE Trans. Inform. Theory, vol. IT-31, pp. 124--142, Mar. 1985.

....to lattice quantizers, which are a special but important case of tessellating quantizers. The condition is a system of partial differential equations which might not have a solution for a general . Thus as in the case of fixed rate multidimensional companding for the squared error [3] 27] [28], in general there may not exist a compressor function satisfying the above condition. The following example shows that the condition of Theorem 2 can be satisfied by an consisting of scalar compressors if is a single letter distortion measure. LINDER et al. HIGH RESOLUTION SOURCE CODING FOR ....

, "A note on optimal multidimensional companders," IEEE Trans. Inform. Theory, vol. IT-29, p. 279, Mar. 1983.

....the series parallel duality from the kineto static viewpoint. Bicchi [6] made explicit the limitations to the arbitrariness in distributing manipulation forces among cooperating limbs due to the presence of defective elements (a problem which was previously noticed by Kerr [17] and Trinkle [37]) Bicchi, Melchiorri, and Balluchi [7] studied the rigid body kinematics of WAM systems and discussed their manipulability. Dynamic analysis of manipulation systems has attracted relatively less attention so far. This is partly justified by the fact that most cooperative manipulation tasks are ....

....role in the performance of slow cooperative manipulation tasks, it is true that only a full dynamical model can explain and clarify the structural properties of complex manipulation systems. Thus, dynamic manipulation has been considered to investigate grasp stability [3] 13] 14] 22] 25] [37], to study the dualities between series and parallel manipulators [40] and to address cooperative manipulability [9] 19] 1042 296X 98 10.00 1998 IEEE 242 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 14, NO. 2, APRIL 1998 Fig. 1. Six simple examples of robotic manipulators. B. ....

[Article contains additional citation context not shown here]

, "On the stability and instantaneous velocity of grasped frictionless objects," IEEE Trans. Robot. Automat., vol. 8, pp. 560--572, Oct. 1992.

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, "On loss functions which minimize to conditional expected values and posterior probabilities," IEEE Trans. Inform. Theory, vol. 39, pp. 1404--1408, 1993.

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, "On deterministic traffic regulation and service guarantees: A systematic approach by filtering," IEEE Trans. Inform. Theory, vol. 44, pp. 1097--1110, May 1998.

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------, "Results on principal component filter banks: Colored noise suppression and existence issues," IEEE Trans. Inform. Theory, to appear.

....2: Take . Corollary 5 gives and . This is an improvement on the best previously known upper bound of , given in [31] Since a lower bound of is known [17] we conclude that this bound is in fact tight. Example 3: Corollary 5 also gives . This reproduces a well known bound which was proved in [36] through a combinatorial argument specifically devised for these parameters. See also [42, p. 530] Example 4: For , Corollary 6 yields and , a significant improvement upon the best previously known bound of , given in [8] For , Corollary 6 reduces the best known upper bound from to . C. ....

, "On upper bounds for unrestricted binary error-correcting codes," IEEE Trans. Inform. Theory, vol. IT-17, pp. 466--478, July 1971.

No context found.

, "On complexity of trellis structure of linear block codes," IEEE Trans. Inform. Theory, vol. 39, pp. 1057--1064, May 1993.

....Unfortunately, it is generally a difficult problem to determine if an arbitrary given wide function can be implemented by a PLB. This is called the Boolean matching for PLB problem. Most existing technology mapping algorithms first produce a LUT mapping solution, then pack LUTs into PLBs [9] [10], 18] 19] 21] 27] 30] 31] 39] A comprehensive survey of recent FPGA technology mapping approaches can be found in [11] In this paper, we study Boolean matching for PLB problems. We focus on two classes of (LUT based) PLBs: PLB1 and PLB2, as shown in Fig. 1(a) and (b) respectively. ....

, "On area/depth trade-off in LUT-based FPGA technology mapping, " IEEE Trans. VLSI Syst., vol. 2, pp. 137--148, June 1994.

....for the signal and noise always exist, existence of common PCFB s is not always ensured: It depends on the psd s. However, the result suggests that perhaps such a common PCFB is always optimal if it exists. This happens to be true for a particular FB class, namely the class of transform coders [3]. However, for general FB classes it is true only for certain restricted families of input psd s examples being (a) the earlier mentioned case of piecewise constant psd s, for the FB class C ; and (b) the case when the noise is white, for any FB class (all FB s are PCFB s for a white input, ....

....number of arithmetic operations needed to extract from F the FB s corresponding to points in Ev is also polynomial in N , though it is super exponential in M . It does not exceed CMN if M 2 and DN log N if M = 2, where CM = G(M ) and G; D are constants. The result is proved in full in [3]. Here in Section 3.3, we present the full proof except for the justification of a technical lemma it needs. Section 3.4 elaborates on the algorithm that extracts from F the FB s corresponding to extreme points of Sv (implied by item (3) of the theorem) 3.2. Discussion on Theorem 1 Result ....

[Article contains additional citation context not shown here]

------, "Results on principal component filter banks: Colored noise suppression and existence issues," IEEE Trans. Inform. Theory, to appear.

....upper threshold for the prior strength. DePierro s algorithm is a true MAP EM implementation that substitutes the convex function R (x) with a separable, convex, and twice continuously di erentiable function R x; x k R (x) so that separable maximizations can be performed on the variables [9, 10]. Regularization improves the convergence rate of EM, with larger prior strengths resulting in lower spectral radii. However, for reasonable prior strengths (mild to moderate smoothing) the convergence rates of OSL and DePierro s algorithm are still quite close to unity. The EM update formula on ....

On the convergence of an EM-type algorithm for penalized likelihood estimation in emission tomography, IEEE Trans. Med. Imag., 14 (1995), pp. 762-765.

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, "On a special class of broadcast channels with confidential messages," IEEE Trans. Inform. Theory, vol. 43, pp. 712--714, Mar. 1997.

.... has shown that the lower bound of Theorem 13 is tight [22] Several interesting open problems related to mismatched decoding are posed in [51] Extensions of the mismatch problem to the multiple access channel are discussed in [87] and dual problems in rate distortion theory are discussed in [89]. 6) Decoders for the Arbitrarily Varying Channel: Maximum likelihood decoders can be used to achieve the randomized code capacity of an AVC (5) without or with input or state constraints (cf. Section IV A2) passage following (86) On the other hand, fairly complex decoders are generally ....

, "On the role of mismatch in rate distortion theory," IEEE Trans. Inform. Theory, vol. 43, pp. 38--47, Jan. 1997.

....absence of any state constraint [85] is convex. Input constraints analogous to (22) are also considered in [75] The deterministic code capacity region of the multipleaccess AVC under state constraint for the average probability of error remains unresolved. For preliminary results, see [73] and [74]. Indeed, multiple access AVC counterparts of the single user discrete memoryless AVC results of Section III A2) which have not been mentioned above in this section, remain by and large unresolved issues. VII. DISCUSSION We discuss below the potential role in mobile wireless communications of ....

, "On the capacity region of the discrete additive multiple-access arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 38, pp. 1344--1346, July 1992.

....LUT resources. The algorithm is based on the cut generation for trees. Assume that the root of has fanin nodes . Let denote the subtree in rooted at . Clearly, any cut of size in induces an cut of , with , and vice versa. Let denote the set of cuts of size in , and define . It was shown in [5] that (4) where the union is on all combinations of such that . Therefore, all the cuts of size in a tree can be generated based on the recursive equation (4) and the number of cuts generated according to (4) is bounded by a constant depending only on , which is the th Catalan number [13] ....

, "On area/depth tradeoff in LUT-based FPGA technology mapping, " IEEE Trans. VLSI Syst., vol. 2, pp. 73--94, June 1994.

....emphases on universality, multiterminal models, and coding for sources modeled as random fields. Kieffer was selected for this task in considerable measure for his several contributions that proved source coding theorems with increasingly relaxed conditions in increasingly general contexts [18] [19], 20] 21] 22] 23] Kieffer s survey article also contains an invaluable bibliography of 137 items. It is not our purpose here to enter into the details of proofs of source coding theorems and information transmission theorems. Suffice it to say that at the heart of most proofs of positive ....

, "On the minimum rate for strong universal block coding of an class of ergodic sources," IEEE Trans. Inform. Theory, vol. IT-26, pp. 693--702, 1980.

....so far, plays a primary role. The availability of feedback between receiving and transmitting points on one hand, and the actual transmission demand by users, complicate the problem not only mathematically but conceptually, calling for a serious unification between information and network theory [95], 84] and so far only very rare pioneering efforts have been reported [285] 279] 17] We have not yet touched upon signaling constraints, imposed on each user which transmits several signals through the available transmitting antennas. The standard constraints are as follows. a) Average ....

....demonstrated that CDMA is inherently advantageous over FDMA in the presence of fading. Up to now we have assumed a fixed number of users transmitting to a receiver. In common models for communication (network) systems, a user accesses the channel randomly, as it gets a message to be transmitted [95], 28] 84] The random access of users is a fundamental issue which is not yet satisfactorily treated in terms of information theoretic concepts [95] 28] 84] Indeed, the out of model discussed is motivated here in a sense by random access aspects, but it does not capture the fact that the ....

[Article contains additional citation context not shown here]

,, "A perspective on multiaccess channels," IEEE Trans. Inform. Theory, vol. IT-31, pp. 124--142, Mar. 1985.

....for which #(G) cannot be computed by such elementary means is the pentagon C 5 . If we set V (C 5 ) 0, 1, 2, 3, 4 with E(C 5 ) 01, 12, 23, 34, 40 , then C 2 5 contains the stable set (0, 0) 1, 2) 2, 4) 3, 0) 4, 1) Hence #(C 5 ) # # 5. We show that equality holds here [56]. Consider an umbrella in R 3 with the unit vector e 1 as its handle, and 5 ribs of unit length. Open it up to the point when non2 consecutive ribs are orthogonal. This way we get 5 unit vectors u 0 , u 1 , u 2 , u 3 , u 4 , assigned to the nodes of C 5 so that each u i forms the same angle ....

....The angle of an orthonormal representation is the smallest half angle of a rotational cone containing the representing vectors. Proposition 5. 1 The minimum angle # of any orthogonal representation of G is given by cos 2 # = 1 #(G) In what follows we collect some properties of #, mostly from [56] (see also [50] for a survey) We start with a formula that expresses #(G) as a maximum over orthogonal representations of the complementary graph. Let the leaning of an orthonormal representation of G be defined as # i#V (e T 1 u i ) 2 . Proposition 5.2 The maximum leaning of an ....

L. Lovasz: On the Shannon capacity of graphs, IEEE Trans. Inform. Theory 25 (1979), 1--7.

....an embedding exists at all. Unlike in the case of Koebe Andre ev representations, Tutte method is easy to implement and often yields nice pictures of planar graphs. We ll see in section 3.1 how this idea leads to far reaching applications. Orthogonal representations were introduced by Lovasz [63]; a related construction was also considered by Erdos and Simonovits [28] Orthogonal representations can be viewed as versions of unit distance graphs, where the 3 underlying space is the unit sphere, and distance 1 is replaced by spherical distance # 2. The smallest dimension where these ....

....represent the nodes of a graph by unit vectors in R d so that non adjacent nodes should be represented by 6 orthogonal vectors. In the context of this paper, it would be more natural to require that adjacent nodes be represented by orthogonal vectors; other, earlier applications of this notion [63, 38] fixed the usage as given. Lovasz [61] introduced the following graph invariant #(G) Let # be the smallest half angle of a cone in R n such that the given graph G has an orthogonal representation by vectors in the cone. Let #(G) 1 cos 2 # (there are several other equivalent definitions ....

L. Lovasz: On the Shannon capacity of graphs, IEEE Trans. Inform. Theory 25 (1979), 1--7.

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A. Isidori: A remark on the problem of semiglobal nonlinear output regulation, IEEE Trans. on Autom. Cont., AC-42, pp. 1734--1738, 1997

....of the random code capacity region still holds (see the paragraph preceding [11, Remark IIA3, p. 214] By specializing our coding theorem to the unconstrained MAVC, it is clear that Jahn s characterization always holds. Further work on deterministic codes for the MAVC has appeared in [6] 8] [9]. Deterministic codes for the single user AVC have been studied by several authors, e.g. 1] 2] 5] and the references therein. 2 For the MAVC, state constraints introduce subtle problems which have no counterpart in the theory of the single user AVC or the conventional multiple access ....

....the proofs of many multiuser coding theorems. This principle, which asserts that the capacity region is a convex set, holds for the conventional MAC [3, p. 272] and even for the unconstrained MAVC [11] However, it fails for the MAVC subject to a state constraint. The difficulty arises as follows [9]. Suppose n = n 1 n 2 . Then the inequality in (1) does not imply that both 1 n 1 n 1 X k=1 (s k ) L and 1 n 2 n 2 X k=1 (s n 1 k ) L; which is a necessary condition to apply the time sharing principle to an MAVC subject to a state constraint. As a consequence of this ....

, "On the capacity region of the discrete additive multiple-access arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 38, pp. 1344-1347, July 1992.

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N. A. Svensson: On Differentially Encoded Star 16QAM with Differential Detection and Diversity, IEEE Trans. Vehic. Techn., Vol. 44, No. 3, Aug. 1995, pp. 586 - 593.

....of the random code capacity region still holds (see the paragraph preceding [11, Remark IIA3, p. 214] By specializing our coding theorem to the unconstrained MAVC, it is clear that Jahn s characterization always holds. Further work on deterministic codes for the MAVC has appeared in [6] 8] [9]. Deterministic codes for the single user AVC have been studied by several authors, e.g. 1] 2] 5] and the references therein. For the MAVC, state constraints introduce subtle problems which have no counterpart in the theory of the single user AVC or the conventional multiple access channel ....

....the proofs of many multiuser coding theorems. This principle, which asserts that the capacity region is a convex set, holds for the conventional MAC [3, p. 272] and even for the unconstrained MAVC [11] However, it fails for the MAVC subject to a state constraint. The difficulty arises as follows [9]. Suppose n = n 1 n 2 . Then the inequality in (1) does not imply that both 1 n 1 n1 X k=1 (s k ) L and 1 n 2 n2 X k=1 (s n1 k ) L; which is a necessary condition to apply the time sharing principle to an MAVC subject to a state constraint. As a consequence of this observation, we ....

, "On the capacity region of the discrete additive multipleaccess arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 38, pp. 1344--1347, July 1992.

No context found.

, On the optimality of cyclic transmission in teletext systems, IEEE Trans. Commun., 35 (1987), pp. 68--73.

No context found.

, "On area/depth trade-off in LUT-based FPGA technology mapping, " IEEE Trans. VLSI Syst., vol. 2, pp. 137--148, June 1994.

No context found.

------, "On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication," IEEE Trans. Comput., vol. 40, no. 2, pp. 205--213, Feb. 1991.

No context found.

, "A survey on fuzzy neural networks for pattern recognition: Part II," IEEE Trans. Syst., Man, Cybern. B, vol. 29, pp. 786--801, Dec. 1999.

No context found.

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