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Notes 1: Introduction, linear codes

Introduction to Coding TheoryCMU: Spring 2010 Notes 1: Introduction, linear codesJanuary 2010 Lecturer: Venkatesan GuruswamiScribe: Venkatesan GuruswamiThe theory of error-correcting codes and more broadly, information theory , originated in ClaudeShannon s monumental work A mathematical theory of communication, published over 60 yearsago in 1948. Shannon s work gave a precise measure of the information content in the output of arandom source in terms of itsentropy. Thenoiseless coding theoremor the source coding theoreminformally states random variables each with entropyH(X) can be compressed inton(H(X) + ) bits with negligible probability of information loss, and conversely compression inton(H(X) ) bits would entail almost certain infor

The theory of error-correcting codes and more broadly, information theory, originated in Claude ... the early uses of the probabilistic method; it asserted the existence of good coding schemes at all ... De nition 2 (Hamming weight) The Hamming weight of a string xover alphabet is de ned as the number of non-zero symbols in the string. More ...

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