By Peter W. Hawkes (Ed.)
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Extra resources for Advances in Electronics and Electron Physics, Vol. 79
Calculating Free Euclidean Distance An error occurs in the decoder when an incorrect path becomes more likely than the correct one. Hence, to minimize the probability of error, all paths should be as “far apart” as possible. As discussed in Section ILH, the asymptotic error rate for a code is determined (primarily) by dfree,the Euclidean distance between the closest two paths. Calculating the free Euclidean distance of a code is similar to maximum likelihood decoding. To calculate drree,one must find the closest two encoder paths.
C, must be used for all other cases. IV. DESIGNING TRELLIS CODES In this section we focus on the error-correction and design aspects of trellis codes. This material is largely review. A describes the Viterbi algorithm, a form of maximum likelihood trellis decoding used to correct transmission errors. B gives an example of free Euclidean distance, a common benchmark of trellis code performance. C. The primary alternative to heuristic code design is an exhaustive search over a small, well-structured class of algebraic systems.
D). Smaller constellations are generally not useful, but larger constellations may have value. G, the number of dimensions and the location of points in the constellation have an important effect on code performance. However, bandwidth constraints, limited peak energy, and other hardware concerns often dictate constellation design. For a thorough presentation of recent advances in multidimensional constellation design, see Forney (1988). The final step in heuristic code design is the labeling of the branches of the trellis diagram with points from the constellation.
Advances in Electronics and Electron Physics, Vol. 79 by Peter W. Hawkes (Ed.)