Download Advances in Electronics and Electron Physics, Vol. 79 by Peter W. Hawkes (Ed.) PDF

By Peter W. Hawkes (Ed.)

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Extra info for Advances in Electronics and Electron Physics, Vol. 79

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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. Coset codes, as defined by Calderbank and Sloane (1987), are a generalization of finite input memory LSCs that operate over rings rather than fields. The encoder outputs are cosets of a lattice of signal points, with several uncoded bits selecting a particular point from the chosen coset. As with FIM LSCs, coset codes can be efficiently enumerated.

A minimal code is the “smallest” of all equivalent codes; a minimal realization of a code is often the simplest 24 HOWARD J. CHIZECK AND MITCHELL D. TROTT u=o (a 10. Finite and infinite input memory trellis diagrams: (a) IIM (three horizontal branches), (b) IIM (two horizontal branches with same label), (c) FIM, (d) IIM (a zero input can cause periodic behavior). FIG. realization to analyze and construct. D). For efficient enumeration, only one representative from each set of equivalent codes should be examined.

A code with an TIM inverse is said to be catastrophic. Catastrophic codes are avoided in practice. The trellis code in Fig. 1Oc is catastrophic. A received sequence {a,a, c, a, a, a,. . } decodes into { 1,1,0,0,0,0,. } while a received sequence {a,a, b,a, a , a . } decodes into {O,O, 1, I , I , 1,. }. The decoder’s inability to 28 HOWARD J. CHIZECK AND MITCHELL D. TROTT find the correct initial state allows a single transmission error converting ‘c’ to ‘b’ to cause an infinite number of decoding errors.

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