By P. G. Farrell (auth.), G. Longo (eds.)

ISBN-10: 3662387522

ISBN-13: 9783662387528

ISBN-10: 3662396416

ISBN-13: 9783662396414

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**Additional info for Algebraic Coding Theory and Applications**

**Example text**

G. v rate at high error rates) of pure ARQ systems. A feedback cna"'L'1el can also be used to optimise the operation of the forward link demcilulator-detector or of the deccrler. l) M2rTDry48. variable block lenq'"J-. bu~ ' . le red uncancy 5S' , have also been studied. Incremental (Le. l. jcY" ~yp'-2S ,. + 6(: protocols of these networks 51 of~en e~bedded . trcriucec. in this sectior; are A Survey of Error-Control Codes 31 summarised in Figs. 2 - 4. - Codes may be binCL,), or multi-level (q-nary); rrost practical codes are binary, though applications for multi-level codes are opening up because of the increasing use of m-ary signalling, and the advent of CCD multi-level processors.

If a t-error-correcting code, to just the error patterns of ~ight ~ (iii) t). By implementing a canbinatorial log-ic circuit to convert the syndrare into its error pattern. This rrethod (nonnally 37 A Survey of Error-Control Codes bounded distance) is inpractical for t > 3, but is applicable to both block and cO"lVolutianal codes. It is CCl'lSiderably sUtplified i f the code is a cylcic block code, because the partial syndrate which determines whether a particular digit is in error or not is the sane for all cyclic shifts of the received sequence (Meggitt56 decx:xllng).

It is, however, the only q>timum decoding algorithm awlicable to non-linear block codes. algorithm. codes. It is an q>timum (Le. maximum likelihood) de<:xxling It is not often ccnsidered for use with burst-error-correcting Ccrrputatioo with this algorithm may be halved i f the code is transparent; that is, when the logical carplerrent (inverse) of every code \\lOrd (or sequence) is also in the code. described below. Further siITplification will be Sare of the siITplified versions are fully equivalent to the basic algorithm, in the sense of still being optimum, and so are saretimes also called minimum distance decoding algorithms.

### Algebraic Coding Theory and Applications by P. G. Farrell (auth.), G. Longo (eds.)

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