Topic

# Trellis (graph)

About: Trellis (graph) is a research topic. Over the lifetime, 2919 publications have been published within this topic receiving 34354 citations.

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TL;DR: A simple technique for quadrature partial-response signaling (QPRS) is described that eliminates the quasicatastrophic nature of the ML trellis and shows that a good performance/complexity tradeoff can be obtained.

Abstract: A reduced-state sequence estimator for linear intersymbol interference channels is described. The estimator uses a conventional Viterbi algorithm with decision feedback to search a reduced-state subset trellis that is constructed using set-partitioning principles. The complexity of maximum-likelihood sequence estimation (MLSE) due to the length of the channel memory and the size of the signal set is systematically reduced. An error probability analysis shows that a good performance/complexity tradeoff can be obtained. In particular, the results indicate that the required complexity to achieve the performance of MLSE is independent of the size of the signal set for large enough signal sets. Simulation results are provided for two partial-response systems. A simple technique for quadrature partial-response signaling (QPRS) is described that eliminates the quasicatastrophic nature of the ML trellis. >

780 citations

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TL;DR: The definition of a new distance measure of optimization of trellis codes transmitted over Rician fading channels, guided by maximizing d/sub free, is proposed.

Abstract: It has been well established that the appropriate criterion for optimum trellis-coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. It is shown that when the trellis-coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code of optimum performance is guided by other factors, in particular, the length of the shortest error-event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along the path. Although maximum free distance (d/sub free/) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing d/sub free/. >

613 citations

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TL;DR: It is shown that soft decision maximum likelihood decoding of any (n,k) linear block code over GF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more than q^{(n-k)} states.

Abstract: It is shown that soft decision maximum likelihood decoding of any (n,k) linear block code over GF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more than q^{(n-k)} states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer than q^{n-k} . For a binary (n,n - 1) single parity check code, the Viterbi algorithm is equivalent to the Wagner decoding algorithm.

612 citations

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TL;DR: The information rate of finite-state source/channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence, followed by a forward sum-product recursion on the joint source/ channel trellis.

Abstract: The information rate of finite-state source/channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence, followed by a forward sum-product recursion on the joint source/channel trellis. This method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite-state approximations. Further upper and lower bounds can be computed by reduced-state methods

598 citations

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AT&T

^{1}TL;DR: It is concluded that there are multidimensional trellis-coded modulation schemes that perform better for the same complexity than do two-dimensional schemes.

Abstract: Trellis-coded modulation schemes using four-, eight-, or 16 -dimensional constellations have a number of potential advantages over the usual two-dimensional schemes: a smaller constituent two-dimensional constellation, easier tolerance to phase ambiguities, and a better trade-off between complexity and coding gain. A number of such schemes are presented and evaluated. Starting with a variety of multidimensional lattices, we show how to select multidimensional constellations, how to partition them into subsets, how to construct trellis codes using those subsets, and how to map hits to constellation points. Simplifications of the Viterbi decoding algorithm are presented. We conclude that there are multidimensional trellis-coded modulation schemes that perform better for the same complexity than do two-dimensional schemes.

527 citations