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1-3-3 Error Control Method

Error control refers to controlling the bit errors that occur on the communication channel when data is transmitted. Shannon recommends the two encodings that are described below as

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the coding theory for improving reliability, efficiency, and safety in the course of information transmission.

(1) Source coding

Source coding refers to encoding (.i.e., data compression) of the information source to reduce the amount of transmission data (i.e., number of bits). This is a concept according to which, if the bit error rate of the communication channel, etc. is a fixed value, the lower the number of transmission bits the more difficult it is for an error to occur. There are two typical methods of source coding as described below.

(2) Channel Coding

Channel coding refers to appending a single or multiple redundant bits that are different from the information source to perform encoding. This is a concept that can detect an error that has occurred in the communication channel and can correct the error by using the appended redundant bit. It is generally called the error detection and correction method. The typical kinds of the error detection and correction method are as described below.

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(1) Parity check This is a method that detects an error by appending a redundant bit (i.e., parity bit) for checking to the bit string to be transmitted. This method can be classified into several techniques as shown below depending on the regularity of the redundant bit and the target to which the redundant bit is to be appended.

In the parity check, while an odd number of bit errors can be detected, an even number of bit errors cannot be detected. By using the horizontal/vertical parity check technique, it is

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possible to identify one bit error and its position (i.e., intersection point of the column and row in which the error has occurred). However, since the error may occur in several bits, the error correction function is generally not made available in the parity check.

(2) Checksum This is a method that detects an error by appending redundant bits (e.g., a total value) that is determined through a simple calculation in units of blocks.

(3) CRC (Cyclic Redundancy Check) This is a method in which transmission data is represented by a polynomial, the polynomial of the transmission data is divided by a predetermined generating polynomial, and then a checking code (CRC code) that is obtained by converting the remainder to a bit string is appended. At the receiving side, the reception data that is represented by a polynomial is divided by a generating polynomial, and the existence of an error is detected depending on the divisibility. This is a highly accurate error detection method by which continuous bit errors (i.e., burst error) can be detected. · 1 question

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(4) Hamming code This is a method that enables the detection and correction of bit errors. A code like the Hamming code that has the purpose of correcting errors is called an ECC (Error Correcting Code). The ECC is also used for correcting errors in memory. · 1 question

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The number of bits that can be detected or corrected by the Hamming code is decided by the Hamming distance (i.e., the number of different elements (i.e., bits) in the information bits of the same bit length). · 1 question

• • If the hamming distance is “m+1” or more, m bit errors can be detected.
  
• • If the hamming distance is “2n+1” or more, n bit errors can be corrected.
  In the Hamming code that is created in example 1, three redundant bits are added to the four-bit data. Therefore, it is called the (7, 4) Hamming code. Since the Hamming distance becomes three or more, it is possible to correct one bit error and detect two bit errors.