By Barnes J.R.

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**Example text**

Output equivalence is a very general concept. For example, adding a unit delay to the input of a code markedly changes its input-output behavior (see 26 HOWARD J. CHIZECK AND MITCHELL D. 12. Input-output minimality. (a) Minimal trellis. (b) Nonminimal; D and E indistinguishable. (c) Input-output minimal; D and E distinguishable. (d) Nonminimal; {A, B, C, D} and {E} do not communicate. (e) Nonminimal; {E} does not communicate with other states. Fig. 1l), but does not affect the set of reachable output sequences.

X , - ~ , X , - 1,x,) (54) Y", u H (To(u), . . , T,- l(u)) (55) Y, (xo,.. , X n - (56) d : U -+ Y, H xo u H D(u). 20: The periodicity of FGH weighting patterns. (57) 42 HOWARD J. CHIZECK AND MITCHELL D. TROTT We call this the standard observable (SO)realization of a weighting pattern: It’s analogous to the standard observable realization of a linear system. We construct SO-realizations from weighting patterns in Section VII when searching for new codes, and we also use the SO-realization in proofs.

A(( C . Heuristic Code Design As pioneered by Ungerboeck (1982,1987), good trellis codes can often be designed heuristically. The free Euclidean distance of a trellis code is a function of its output labeling, allowed state transitions, and constellation. , 1984). For example, the state transition diagrams in Fig. 16 are optimal (in the sense of maximizing d,,,,) for most symmetric constellations. The number of states IS( in the encoder is determined by the maximum acceptable decoder complexity.

### Designing electronic systems for ESD immunity by Barnes J.R.

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