By P. G. Farrell (auth.), G. Longo (eds.)
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Additional resources for Algebraic Coding Theory and Applications
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). (iv) The considerable mathenatical structure of cyclic codes makes it possible to find sirrplifying algorithms for ccnverting the syndrare into the corresponding error pattern.
T of ccrrputation required to decode each segrrent is a Pareto distributed variable, so that there is a finite (a1dnon-trivial) probabili ty of deccrler storage over-flON, with consequent failure to deccrle 67 ,68. lith the code constraint length (Le. een the received sequence and the paths being searched frc::rn a given node in the, tree is exceeded, then the decoder must return to the previous node, and search branches fran that node. C. Farrel leads to excessive carputation and overload, as indicated above.
1 exactly, there is a polynanial H(x) such that G(x) H(x) = >l? + 1 H(x) is the parity check polynania1 of the cyclic co:le (carpare the above equation with the previously quoted equation for a general linear code [GJ. [H] t = [OJ). , the [H] matrix above). '1en converting to SEF. This corresponds to the fact that the parity check equations of a cyclic code are also cyclic. 7 Codes for Random Errors and for Burst Errors Information (data) protected by encoding into code \\1Ords or sequences is usually transmitted (or stored) by means of an analogue baseband or modulated carrier signal.
Algebraic Coding Theory and Applications by P. G. Farrell (auth.), G. Longo (eds.)