By A. Houghton
ISBN-10: 041279070X
ISBN-13: 9780412790706
ISBN-10: 1461304474
ISBN-13: 9781461304470
Error coding is an interesting topic as a lot, if no more so, because it is an critical a part of modem engineering structures. regrettably, in a bid to stay basic and to create a high-quality starting place upon which to construct, many books in this topic are out of the succeed in of these with extra engineering-based, or non-mathematical backgrounds. it is a pity simply because in lots of instances the math is tractable with few and easy principles. If we're content material to think that it really works, and permit others fear concerning the deeper mysteries of the way or why, then with a bit perform the layout and implementation of sensible mistakes coding platforms turns into ordinary. during this textual content i've got tried to bare the worthy kernel of the topic, removal the shell of phrases and proofs that sometimes surrounds it. Being a bit of empirical in nature ( an empiricist), and sometimes heard to cite the adage, 'if it really works two times it is a law', my factors take this way. for lots of, together with myself, summary rules are frequently greater grasped by means of sensible representation than from yards of theory.
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Additional resources for The Engineer’s Error Coding Handbook
Sample text
Probably the main strength of Hamming codes is their immediate parallel correction ability over small messages. You should now start to have some feel for orthogonality in the context of error coding. While this is not essential for implementing error control systems, it will help in the understanding of how they work, and give you ideas for creating your own systems. You should also be able to construct parity generator equations for Hamming codes to give single-bit error correction capability over certain message sizes and perform error correction using your parity bits.
5 where the bits shown bold have been inverted. 5 Decoding a message with errors 1 0 eRe Quotient GP 0 0 1 1 11 0 1 1 0 0 () 1 1 0 () () 1 () 0 0 0 0 0 JJ 0 0 1 JJ JJ 1 1 1 0 0 0 1 () 1 1 1 0 () () 1 () Remainder -:f. 0 0 1 1 0 JJ JJ 0 1 0 1 - - JJ JJ 0 0 0 1 0 0 1 0 1 0 1 1 If, however, we arrange for the error pattern to be equal to the GP, then the error will not be detected. To do this we simply line up the GP with the 20 Cyclic redundancy checking data + CRC at some arbitrary point, and XOR.
We can of course combine both of these to yield a third, 'best of both worlds' solution in some cases, but more of this later. 1 MANIPULATING FINITE FIELD ELEMENTS RS coding makes extensive use of fInite fIelds, and for simplicity we will mostly use GF(2 3) since this brings worked examples down to manageable proportions. 1 using the primitive polynomial x3 + x + 1 = O. At this point it might be useful to outline a few of the operations that we can perform on fInite fIeld elements. 1. 1 Multiplying and dividing elements For any finite field, if n = 2m - 1, uP = 1 = a O.
The Engineer’s Error Coding Handbook by A. Houghton
by Christopher
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