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

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

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Farrel be dale. , x. (i'f j), J l. = ~ {w(x. ,J l. where J e : rrodulo-2 addition, and w(x) = weight of X; = ~ l. {w (x. ) }, i f the code is linear, since the l. n'Od-2 sum of any t'NO code words is another code \\Ord. ::. e . (since correction irrplies detection first); this is partial error correct ion carbined with error detection. rations apply to ccnvoluticnal codes. The minimum distance neasure in this case is called the free distance, d free , and n is the decoding ccnstraint length. 2, d free = 3, which makes the code single-error-correcting.

Vi vor sequences need to be stored, thus reducing the amo~t of storage required.

Farrel oodes, because though non-systanatic cenvolutiooal oodes have potentially superior perfonnance, they also are liable to catastrophic behaviour. - Codes may be used to centrol randan or burst errors; and may be used to detect or correct errors. - Error correction may be achieved by maans of forward error centrol using an error-correcting code; or by maans of re-transmission error control, using an error-detecting code, and a feedback channel. The advantages of FEX:: are that no feedback channel is required, and that data flCM is ccnstant without the need for buffer storage.

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