Abstract
Some elementary concepts of block codes are introduced in Chapter 1. In general, it is known that the encoding and decoding of 2k codewords of length n can be quite complicated when n and k are large unless the encoder has certain special structures. In this chapter, a class of block codes, called linear block codes, is discussed. Such codes have a linear algebraic structure that provides a significant reduction in the encoding and decoding complexity, relative to that of arbitrary block codes. It might be asked whether restricting our attention to linear codes is limiting in an information-theoretic sense. The Shannon random coding bound shown in Chapter 1 pertains to general block codes. However, it is known [1] that some linear codes can also provide an excellent error-correcting capability. In fact, there is a sequence of linear codes with increasing block length and a fixed rate that is only slightly smaller than channel capacity and has an error probability which approaches zero exponentially as the block length increases.
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© 1999 Springer Science+Business Media New York
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Reed, I.S., Chen, X. (1999). Linear Block Codes. In: Error-Control Coding for Data Networks. The Springer International Series in Engineering and Computer Science, vol 508. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5005-1_3
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DOI: https://doi.org/10.1007/978-1-4615-5005-1_3
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