A. J. Viterbi and J. K. Omura, Principles of diigtal communications and coding. New York: McGraw-Hill, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....difference can be used to select the signal constellations according to the outdated channel estimate. That is, letting , must guarantee (10) in order to approximately maintain the bit error probability of the nominal scheme. is the average transmitted energy. Here, is the Bhattacharyya bound [24] on the error probability of choosing when is correct for the nominal code. For example, if the nominal code is designed for a Rayleigh channel. The evaluation of the left hand side of (10) in terms of , the average transmitted SNR , and is given in [4] and [5] Making the intersubset difference ....

A. Viterbi and J. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

....Taylor series. which, in this case, is the highest slope achieved for any . Note that although convex for the AWGN channel, in general, the function need not be convex. In the case of binary quantization of both the real and imaginary components of the output of the AWGN channel, the capacity is [28], 29] 173) with and The first and second derivatives (in nats) of (173) are (174) 175) which result in 0.37 dB (176) 2.8 b s Hz (3 dB) 177) Returning to the unquantized channel, as a simple exercise we apply the formulas obtained in Theorem 10 to the Gaussian channel. Suppose we use ....

A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

.... total cost is given by (1) with if otherwise For a given , the optimal allocation minimizing the total cost has to be found subject to the buffer constraint for (2) where is the queue size at the end of time slot with if (3) We solve this optimization problem with a Viterbi like algorithm [45]. Let us first introduce some notation (cf. Fig. 1) A node is a four tuple , where denotes (discrete) time, denotes a bandwidth allocation , denotes a buffer occupancy, and denotes the weight, which equals the partial cost of the best path to this node. A branch connects a node to another node ....

A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

.... 7] and in fact, it directly arises from the peak energy constraints (3c) As a consequence, it can be easily verified that when these last constraints are absent [that is, all are set to infinite in (3c) then (7b) 8) and (9) reduce to those characterizing the standard water filling solution [2]. Remark 2: Whenever the overall available energy is assigned, we can expect that the effect of the additional constraints (3c) on is to lower the throughput conveyed by the MC system below the corresponding one computable via the standard water filling procedure [2] Although this loss may be ....

.... water filling solution [2] Remark 2: Whenever the overall available energy is assigned, we can expect that the effect of the additional constraints (3c) on is to lower the throughput conveyed by the MC system below the corresponding one computable via the standard water filling procedure [2]. Although this loss may be application dependent and it seems hard to quantify it via closed form analytical formulas, nevertheless, we can expect that the throughput loss induced by (3c) may be noticeable in application scenarios where (largely) dominates , and, in addition, the CSNRs exhibit ....

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A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

....propagation (a separation of more than symbols between error events) The effect of error propagation, however, is usually small at medium to high signal to noise ratio (SNR) VI. BOUND EVALUATION To evaluate the symbol error probability for MUDFSE, we make use of the error state diagram as in [13]. The errorstate diagram used for determining the generating function of channel codes for MLSE [13, pp. 283] has to be modified in the case of MUDFSE so that the error sequences satisfy (13) The modified diagram is shown in Fig. 1 for the case of binary signaling over an AWGN channel with memory ....

....residual interference depends on the error sequence only through the tail of the error sequence and the distance of the error sequence Note from Fig. 1 that the error state pairs that are negative of each other are indistinguishable on the basis of branch values. Thus, they can be combined as in [13]. It follows that the number of paths that terminate in the tail is the same as the number of paths that terminate in the tail Moreover, since (36) simplifies to (37) In general, the reduced error state diagram for binary signaling comprises nonzero nodes with terminating nodes. In order to ....

A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill,

....directly, but need to be estimated from a sequence of measurements depending indirectly on the states. Models of this type are often used in speech processing [8] or in digital communications for decoding convolutional codes or the deconvolution 36 of intersymbol interference [38] 39] [40]. For a detailed study of HMMs from a control perspective, see [9] Let x k be a Markov chain defined for 0 k N , taking values in a finite set X . The joint probability distribution of the chain can be expressed as p(X) q i (x 0 )q e (x N ) N Gamma1 Y k=0 (x k ; x k 1 ) 6:17) This ....

A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

....existing coding approaches. For longer codes, such as some turbo codes [6] the bounds are closer to capacity. However, even for these codes (e.g. the bounds provide a substantially tighter limit on the achievable probability of error than that provided by capacity. Other authors [7] [11] have presented even tighter lower bounds on the error probability of binary codes operating on the AWGN channel; however, these bounds have been computed only for small . The spherepacking lower bound used in this paper imposes no constraints on the symbol alphabet of the code, e.g. the ....

A. Viterbi and J. Omura, Principles of Digital Communications and Coding. New York: McGraw-Hill, 1979.

.... x = arg max x P rob(xjy) where x and y are respectively the original and the received sequences. In the fixed length code case, MAP decoding is classically achieved by searching for the optimal path in a trellis. This long known technique can be efficiently implemented via dynamic programming [5][6] and gives very good results, both in terms of performance and complexity. However, in the variable length code case, the nature of the code itself greatly complicates the decoding operation as there is no more direct relation between the information symbols and the received bits, so the ....

....graphs to be solved. The first works in the domain of such graph decoding have been those of Sayood [7] 13] and Park Miller[9] 12] The first one, introduced by Demir Sayood [7] relies on a path metric which incorporates both channel and source statistics. In the standard Viterbi de coder [5], at each step only one of the paths entering a state is kept as the survivor path and the others are pruned. It can be shown that the pruning does not affect the optimality of the sequence estimation when the applications use fixed length path labels. However, in the case of variable length path ....

A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding, New York: McGraw-Hill, 1979.

....symbol error probability of the VLC can be upper bounded by the expression P S 1 X d=d f B d P d (3) with B d the average number of symbol errors that occur when a path at Hamming distance d is selected in favor of the correct path. For the AWGN channel the probability P d can be written as [16] P d = 1 2 erfc s d E S N 0 : 4) The expressions (2) and (3) are the same as Viterbi s upper bound for error event and bit error probabilities of convolutional codes [16] To compute the coefficients B d we follow the approach in [3] and measure the symbol error rate in terms of the ....

....distance d is selected in favor of the correct path. For the AWGN channel the probability P d can be written as [16] P d = 1 2 erfc s d E S N 0 : 4) The expressions (2) and (3) are the same as Viterbi s upper bound for error event and bit error probabilities of convolutional codes [16]. To compute the coefficients B d we follow the approach in [3] and measure the symbol error rate in terms of the Levenshtein distance d L (u (i) u (j) which is defined as the minimum number of insertions deletions or substitutions to transform one symbol sequence into another [15] This ....

A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw Hill, 1979 10

....with Signal Set z l Channel Receiver Choose Signal Set b i z l Transmitter X Figure 3: The Adaptive Bit Interleaved Coded Modulation Paradigm respectively, in order to approximately maintain the bit error probability of the nominal scheme. Here, D 0 (x; v) is the Bhattacharyya bound [10] on the error probability of choosing x when v is correct for the nominal code. For example, D 0 (x; v) 1 1 d 2 E (x;v) 4Es ( Es N 0 ) 0 if the nominal code was designed for a Rayleigh channel. Define h tr l (the trellis threshold) to be the h that satisfies (4) with equality for ....

A. Viterbi and J. Omura, Principles of Digital Communication and Coding, New York: McGraw-Hill, 1979.

....s Gamma 1 )j, u l must guarantee sup aeae min Z 1 0 e Gammay 2 u l Es 8N 0 p Y jh (yjh)dy D 0 (0; u 0 E s ) 10) in order to approximately maintain the bit error probability of the nominal scheme. E s is the average transmitted energy. Here, D 0 (x; v) is the Bhattacharyya bound [24] on the error probability of choosing x when v is correct for the nominal code. For example, D 0 (x; v) 1 1 d 2 E (x;v) 4Es (SNR) 0 if the nominal code is designed for a Rayleigh channel. The evaluation of the left side of (10) in terms of h, the average transmitted SNR Es N 0 , and ....

A. Viterbi and J. Omura, Principles of Digital Communication and Coding, New York: McGraw-Hill, 1979.

..... With FE ep UWVYX Sj ] C4 , we choose M to be the largest that satisfies I N M r b R [ 0 K C KQ X C (2) This approximately maintains the bit error probability of the nominal scheme. X is the average transmitted energy. Here, 0 WC is the Bhattacharyya bound [17] on the error probability of choosing when is correct for the nominal code. For example, 0 WC E N 8 D (SNR) b if the nominal code is designed for the AWGN channel and 0v D2CE ] 8 D (SNR) b if the nominal code is designed for a Rayleigh channel; for a Rician fading ....

A. Viterbi and J. Omura, Principles of Digital Communication and Coding, New York: McGraw-Hill, 1979.

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A. Viterbi and J. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A.J. Viterbi and J.K. Omura, Principles of Digital Communication and Coding, New York McGraw-Hill, 1979.

....Reste, Zweite Abhandlung, Commentationes soc. reg. Gotting.recentiores, Vol. VII. Gottengae 1832, also contained in C. F. Gauss, Untersuchungen uber Hohere Arithmetik (German translation of the Latin Disquisitiones Arithmeticae by H. Maser, 1889) 2nd reprint. New York: Chelsea, 1981. [3] K. Huber, Codes over Gaussian integers, IEEE Trans. Inform. Theory, vol. 40, no. 1, pp. 207 216, Jan. 1994. 4] K. Huber, Codes over Eisenstein Jacobi integers, in Finite Fields: Theory, Applications and Algorithms, Contemporary Math. Las Vegas, 1993) vol 168, pp. 165 179 (American ....

A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A. J. Viterbi and J. K. Omura, Principles of diigtal communications and coding. New York: McGraw-Hill, 1979.

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A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A.J. Viterbi and J.K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A.J.Viterbi and J.K.Omura, Principles of Digital Communication and Coding. New York : McGraw-Hill, 1979.

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A. J. Viterbi and J. K. Omura, Principles of diigtal communications and coding. New York: McGraw-Hill, 1979.

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A. Viterbi and J. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding. New York: McGraw-Hill, 1979.

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