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

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

ISBN-10: 3662387522

ISBN-13: 9783662387528

ISBN-10: 3662396416

ISBN-13: 9783662396414

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Xi can be used for efficient randati error correction provided n/k > t; thus it is best applied only to low rate and/or small t codes. ability of rrore ~rful decoding is used. cyclically ~ft A great deal of the error-correcting In practice it is not necessary to the received sequence, but only the contents . fter shifting. · ve. on ue g m1.. S used . o t errors I Suppose that a cyc li c code can but it cannot be guaranteed that rrore than t-l errors can be trapped (i. , the syndrare weight threshold is t-l).

Ighted rrajority, or threshold gates, in a one-step This is threshold decodinl 4 ,65,66. G. Farrel 46 useful for cyclic codes in particular, and for convolutional codes; unfortunately, the threshold function may in general involve all the 2c parity check sums, though in same cases of practical interest this number can be reduced 65 . The tenn "threshold decoding" is alsC' often . . ty 1oglC . 5 Sequential Decoding The complexity of a minimum distance decoder grows exponentially with block or constraint length.

The capacity of the feedback link can new be IlUlch less than that of the forward link. decision feedback, or ARQ (Autanatic request for a repeat This is 39 40 ' ). If each block is acknewledged by B before transmission of the next block fran A begins, operation is revertive . ,"1C of the block currently being does not take place until after the tran~tted. Tne use of a feedback link does not increase the capacity of the forward link, but error control can be achieved rrore efficiently, and wi th less canplexi ty, if one is available, because of the existence of pawe=ful yet simple error detection codes.

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


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