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Консультация № 177867
16.04.2010, 11:10
41.04 руб.
0
1
1
Доброго времени суток, уважаемые эксперты!
Предмет называется "Теория передачи информации и сигналов". Помогите пожалуйста решить такую задачу: построить код Шеннона-Фано для шести сообщений A, B, C, D, E, F, появляющихся с вероятностями 0.4; 0.25; 0.15; 0.1; 0.05; 0.05. Вычислить среднюю длину кодовой комбинации и сравнить ее с энтропией сообщений.
С уважением, Анатолий.
Предмет называется "Теория передачи информации и сигналов". Помогите пожалуйста решить такую задачу: построить код Шеннона-Фано для шести сообщений A, B, C, D, E, F, появляющихся с вероятностями 0.4; 0.25; 0.15; 0.1; 0.05; 0.05. Вычислить среднюю длину кодовой комбинации и сравнить ее с энтропией сообщений.
С уважением, Анатолий.
Обсуждение
Неизвестный
16.04.2010, 14:06
общий
это ответ
Здравствуйте, Иванов Анатолий Николаевич.
Дерево построения кода Шеннона-Фано приведено на рисунке. В скобках указана суммарная вероятность группы символов.
Согласно дереву имеем следующие кодовые комбинации:
A: 1
B: 01
C: 001
D: 0001
E: 00001
F: 00000
Средняя длина кодовой комбинации: 1*0.4 + 2*0.25 + 3*0.15 + 4*0.1 + 5*0.05 + 5*0.05 = 2.25
Энтропия сообщения: -[0.4*log2(0.4) + 0.25*log2(0.25) + 0.15*log2(0.15) + 0.1*log2(0.1) + 2*0.05*log2(0.05)] = 2.20 бит
Дерево построения кода Шеннона-Фано приведено на рисунке. В скобках указана суммарная вероятность группы символов.
Согласно дереву имеем следующие кодовые комбинации:
A: 1
B: 01
C: 001
D: 0001
E: 00001
F: 00000
Средняя длина кодовой комбинации: 1*0.4 + 2*0.25 + 3*0.15 + 4*0.1 + 5*0.05 + 5*0.05 = 2.25
Энтропия сообщения: -[0.4*log2(0.4) + 0.25*log2(0.25) + 0.15*log2(0.15) + 0.1*log2(0.1) + 2*0.05*log2(0.05)] = 2.20 бит
5
Отлично!!!<br>Благодарю за решение задачи и за картинку.<br>С уважением, Анатолий.
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