Let us first discuss some issues related, directly ,indirectly, to error detection and correction. Types of Errors Redundancy Detection Versus Correction Forward Error Correction Versus Retransmission Coding Modular Arithmetic | Chapter 10 Error Detection and Correction Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10. Data can be corrupted during transmission. Some applications require that errors be detected and corrected. Note 10. 10-1 INTRODUCTION Let us first discuss some issues related, directly or indirectly, to error detection and correction. Types of Errors Redundancy Detection Versus Correction Forward Error Correction Versus Retransmission Coding Modular Arithmetic Topics discussed in this section: 10. In a single-bit error, only 1 bit in the data unit has changed. Note 10. Figure Single-bit error 10. A burst error means that 2 or more bits in the data unit have changed. Note 10. Figure Burst error of length 8 10. To detect or correct errors, we need to send extra (redundant) bits with data. Note 10. Figure The structure of encoder and decoder 10. In this book, we concentrate on block codes; we . | Chapter 10 Error Detection and Correction Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10. Data can be corrupted during transmission. Some applications require that errors be detected and corrected. Note 10. 10-1 INTRODUCTION Let us first discuss some issues related, directly or indirectly, to error detection and correction. Types of Errors Redundancy Detection Versus Correction Forward Error Correction Versus Retransmission Coding Modular Arithmetic Topics discussed in this section: 10. In a single-bit error, only 1 bit in the data unit has changed. Note 10. Figure Single-bit error 10. A burst error means that 2 or more bits in the data unit have changed. Note 10. Figure Burst error of length 8 10. To detect or correct errors, we need to send extra (redundant) bits with data. Note 10. Figure The structure of encoder and decoder 10. In this book, we concentrate on block codes; we leave convolution codes to advanced texts. Note 10. In modulo-N arithmetic, we use only the integers in the range 0 to N −1, inclusive. Note 10. Figure XORing of two single bits or two words 10. 10-2 BLOCK CODING In block coding, we divide our message into blocks, each of k bits, called datawords. We add r redundant bits to each block to make the length n = k + r. The resulting n-bit blocks are called codewords. Error Detection Error Correction Hamming Distance Minimum Hamming Distance Topics discussed in this section: 10. Figure Datawords and codewords in block coding 10. The 4B/5B block coding discussed in Chapter 4 is a good example of this type of coding. In this coding scheme, k = 4 and n = 5. As we saw, we have 2k = 16 datawords and 2n = 32 codewords. We saw that 16 out of 32 codewords are used for message transfer and the rest are either used for other purposes or unused. Example 10. Figure Process of error detection in block coding .
