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Systematic code

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This is an old revision of this page, as edited by Oli Filth (talk | contribs) at 16:14, 25 December 2007 (rm mention of RLE - this is a source coding method, not channel encoding, so discussion of systematic/non-systematic is irrelevant). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In coding theory, a systematic code is one in which the input data are embedded in the encoded output. Similarly, a non-systematic code is one in which the output does not contain the input bits. Such codes are used to add redundant information to data; this allows errors to be detected (and possibly corrected, depending on the code used) when bits are lost or corrupted.

For example, transmitting data with a checksum is a type of systematic code: to encode the bit stream "01010110" with a simple two-bit checksum, one first calculates the checksum (01 + 01 + 01 + 10 = 01), then transmits the original stream followed by the new checksum bits: "0101011001" – note the existence of the original bits in the output.

Examples of systematic codes

Examples of non-Systematic codes

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