By Peter W. Hawkes (Ed.)
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Extra info for Advances in Electronics and Electron Physics, Vol. 79
Trellis codes with unusual sizes, although unlikely to produce great performance gains, may allow more finely tuned tradeoffs between complexity and performance. Calderbank and Mazo (1984) define trellis codes as arbitrary finite input memory systems (see Fig. 9) with binary inputs and one- or two-dimensional constellations. ). )and M ( - ) simultaneously. , 1985). The most significant limitations of sliding window codes are their restriction to binary-valued inputs and their inability to represent any encoders with infinite input memory.
15, assuming a 4-AM constellation with a H 3, d H 1,c H - 1 and b H -3. For this example, $,,,= ( I ~ c - ~ 1 1 ’ = (42 + Ild - c1I2 + Ild - b112)”2 + 2 * + 42)”* (37) (38) = 6. (39) a b (-3) FIG. 15. A free Euclidean distance path for Fig. 6. 32 HOWARD J. CHIZECK AND MITCHELL D. TROTT Several other paths achieve the same (minimum) Euclidean distance. The average energy of the 4-AM constellation is - 3)’ + (- 1)’ + 1’ + 3’) = 5. For comparison, an uncoded system would transmit the same one bit per symbol using a 2-AM constellation with the same average energy.
E addresses catastrophic error propagation, a type of decoder failure related to the structure of the encoder’s inverse. A. Trellis Codes A trellis code is a finite state machine whose outputs select points from a finite constellation of points in n-dimensional Euclidean space. We refer to the finite state machine alone as the encoder, while the combination of the encoder and constellation is the trellis code. D) followed by a mapping onto a specified constellation. Calderbank and Mazo (1984) expanded this definition to include all discrete-time sequential systems with a finite input memory.