Figure10.6 Process of error detection in block coding.块编码的差错检测过程 Sender Receiver Encoder Decoder k bits Dataword Dataword k bits Extract Generator Checker Discard Unreliable transmission n bits Codeword Codeword bits 10.16
10.16 Figure 10.6 Process of error detection in block coding块编码的差错检测过程
Example 10.2 只能检测一比特的检错码例子 Let us assume that k=2 and n=3.Table 10.1 shows the list of datawords and codewords.Later,we will see how to derive a codeword from a dataword. Assume the sender encodes the dataword 01 as 011 and sends it to the receiver.Consider the following cases: 1.The receiver receives 011.It is a valid codeword.The receiver extracts the dataword 01 from it. 2.The codeword is corrupted during transmission,and 111 is received.This is not a valid codeword and is discarded. 3.The codeword is corrupted during transmission,and 000 is received.This is a valid codeword.The receiver incorrectly extracts the dataword 00.Two corrupted bits have made the error undetectable. 10.17
10.17 只能检测一比特的检错码例子 Let us assume that k = 2 and n = 3. Table 10.1 shows the list of datawords and codewords. Later, we will see how to derive a codeword from a dataword. Assume the sender encodes the dataword 01 as 011 and sends it to the receiver. Consider the following cases: 1. The receiver receives 011. It is a valid codeword. The receiver extracts the dataword 01 from it. 2. The codeword is corrupted during transmission, and 111 is received. This is not a valid codeword and is discarded. 3. The codeword is corrupted during transmission, and 000 is received. This is a valid codeword. The receiver incorrectly extracts the dataword 00. Two corrupted bits have made the error undetectable. Example 10.2
Table 10.1 A code for error detection (Example 10.2) Datawords Codewords 00 000 01 011 10 101 11 110 10.18
10.18 Table 10.1 A code for error detection (Example 10.2)
Note An error-detecting code can detect only the types of errors for which it is designed;other types of errors may remain undetected. 检错码是为某些类型的差错而设计的，因此 只能检测这些类型的差错；其它类型的差错 就无法检测到。 10.19
10.19 An error-detecting code can detect only the types of errors for which it is designed; other types of errors may remain undetected. 检错码是为某些类型的差错而设计的，因此 只能检测这些类型的差错；其它类型的差错 就无法检测到。 Note
Figure 10.7 Structure ofencoder and decoder in error correction 纠错码的编码器和译码器的结构 Sender Receiver Encoder Decoder k bits Dataword Dataword k bits Correct Generator Checker Unreliable transmission n bits Codeword Codeword n bits 10.20
10.20 Figure 10.7 Structure of encoder and decoder in error correction 纠错码的编码器和译码器的结构