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(5.15) Shannon entropy. (Computer science) Natural languages are highly redundant; the number of intelligible fifty-letter English sentences is many fewer than 2^650, and the number of distinguishable ten-second phone conversations is far smaller than the number of sound signals that could be generated with frequencies up to 20,000 Hz.59 This immediately suggests a theory for signal compression. If you can recode the alphabet so that common letters and common sequences of letters are abbreviated, while infrequent combinations are spelled out in lengthy fashion, you can dramatically reduce the channel capacity needed to send the data. (This is lossless compression, used in zip, gz, and gif file formats.) An obscure language A'bç! for long-distance communication has only three sounds: a hoot represented by A, a slap represented by B, and a click represented by C. In a typical message, hoots and slaps occur equally often (p= 1/4), but clicks are twice as common (p = 1/2). Assume the messages are ot

          (5.15) Shannon entropy. (Computer science) Natural languages are highly redundant; the number of intelligible fifty-letter English sentences is many fewer than 2^650, and the number of distinguishable ten-second phone conversations is far smaller than the number of sound signals that could be generated with frequencies up to 20,000 Hz.59 This immediately suggests a theory for signal compression. If you can recode the alphabet so that common letters and common sequences of letters are abbreviated, while infrequent combinations are spelled out in lengthy fashion, you can dramatically reduce the channel capacity needed to send the data. (This is lossless compression, used in zip, gz, and gif file formats.) An obscure language A'bç! for long-distance communication has only three sounds: a hoot represented by A, a slap represented by B, and a click represented by C. In a typical message, hoots and slaps occur equally often (p= 1/4), but clicks are twice as common (p = 1/2). Assume the messages are ot

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