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Консультация № 198317
20.04.2020, 23:01
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
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Обсуждение
30.04.2020, 18:32
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это ответ
Здравствуйте, Areomoy!
Декодирование систематического кода (n, k) состоит в вычислении т.н. синдрома - двоичного вектора разрядности n-k, i-й бит которого является результатом сложения по модулю 2 тех битов принятого кодового сообщения, которым соответствуют единицы в i-й строке проверочной матрицы. В данном случае для систематического кода (7, 3) имеем:
Синдром S = S[sub]1[/sub]S[sub]2[/sub]S[sub]3[/sub]S[sub]4[/sub] однозначно определяет, какой бит переданного сообщения был искажён, а именно - присутствующий в выражениях для единичных разрядов вычисленного синдрома. Например, синдрому 0001 соответствует искажение бита a[sub]7[/sub] (он присутствует только в выражении для S[sub]4[/sub]), синдрому 1011 - искажение бита a[sub]1[/sub] (присутствующего в выражениях для S[sub]1[/sub], S[sub]3[/sub] и S[sub]4[/sub]) и т.д. Соответствие значений синдрома и искажённых битов определяется таблицей:
Декодирование систематического кода (n, k) состоит в вычислении т.н. синдрома - двоичного вектора разрядности n-k, i-й бит которого является результатом сложения по модулю 2 тех битов принятого кодового сообщения, которым соответствуют единицы в i-й строке проверочной матрицы. В данном случае для систематического кода (7, 3) имеем:
Синдром S = S[sub]1[/sub]S[sub]2[/sub]S[sub]3[/sub]S[sub]4[/sub] однозначно определяет, какой бит переданного сообщения был искажён, а именно - присутствующий в выражениях для единичных разрядов вычисленного синдрома. Например, синдрому 0001 соответствует искажение бита a[sub]7[/sub] (он присутствует только в выражении для S[sub]4[/sub]), синдрому 1011 - искажение бита a[sub]1[/sub] (присутствующего в выражениях для S[sub]1[/sub], S[sub]3[/sub] и S[sub]4[/sub]) и т.д. Соответствие значений синдрома и искажённых битов определяется таблицей:
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