Simple parity checking or one-dimension parity check
Coding Theory Online Course https://giladjames.com Section: Polynomials in Error Detection and Correction in Data Communication System Lesson: Simple parity checking or one-dimension parity check Coding Theory. This course is brought to you by Gilad James Mystery School. Learn more at Gilad James.com. Introduction Different types of errors are encountered during data transmission because of physical defects in the communication medium as well as environmental interference. Environmental interference and physical defects in the communication medium can cause random bit errors during data transmission. Error coding is a method of detecting and correcting these errors to ensure that there are no errors in the information when it is sent from source to destination. Error coding is used for error-free communication in the primary and secondary memory devices such as RAM, ROM, hard disk, CD’s, and DVDs, as well as in different digital data communication systems such as network communication, satellite, and cellular communication and deep space combination. Data transmission errors occur in terrestrial mobile communication due to multipath fading, diffractions or scattering in cellular wireless communications, low signal-to-noise ratio, and limited transmitted power and energy resources in satellite communication . Error coding uses mathematical formulae to encode data bits at the source into longer bit words for transmission. The “code word” is then decoded at the destination to retrieve the information. The code word consists of extra bits, which provide redundancy, and at the destination, it will decode the data to find out whether the communication channel introduced any error and some schemes can even correct the errors so that there is no need to resend the data. There are two ways to deal with errors. One way is to introduce redundant information along with the data to be transmitted, which will enable the receiver to deduce the information that has been transmitted. The second way is to include only enough redundancy to allow the receiver to detect that error has occurred, but not which error and the receiver makes a request for retransmission. The first method uses Error-Correcting Codes and the second uses Error-detecting Codes. Consider a frame having mdata bits (message to be sent) and rredundant bits (used for checking). The total number of bits in the frame will be n(m + r), which is referred as n-bit code word. Consider two code-words, 11,001,100 and 11,001,111, and perform Exclusive OR and then count number of 1’s in the result. The number of bits in which the codewords are different is called Hamming distance. Suppose the code words are Hamming distance d- apart, it will require d single-bit errors to connect one code word to another. The properties of error detection and error correction depend on the Hamming distance. A distance (d + 1) code is required to detect d errors because d-single bit errors cannot change a valid codeword into another valid code. Thus the error is detected at the receiver. A distance (2d + 1) code is required to correct d errors because the codewords will be so apart that the transmitted codeword will be still closer than any other valid codeword, and thus the error can be determined. A distance (d + 1) code is required to detect d errors because d-single bit errors cannot change a valid codeword into another valid code. Thus the error is detected at the receiver. A distance (2d + 1) code is required to correct d errors because the codewords will be so apart that the transmitted codeword will be still closer than any other valid codeword, and thus the error can be determined. When the data travels from the sender to receiver, different types of errors are encountered in the communication channel . When the data travel through a conductor, there are different influences such as sound waves, electrical signals, noise such as electricity from motors, power switches, impulse noise, because of which data can be corrupted or destroyed. Old conductors are unable to handle these types of interference and heavy data traffic, hence the data transmission suffers. Burst er #coding #theory
Coding Theory Online Course https://giladjames.com Section: Polynomials in Error Detection and Correction in Data Communication System Lesson: Simple parity checking or one-dimension parity check Coding Theory. This course is brought to you by Gilad James Mystery School. Learn more at Gilad James.com. Introduction Different types of errors are encountered during data transmission because of physical defects in the communication medium as well as environmental interference. Environmental interference and physical defects in the communication medium can cause random bit errors during data transmission. Error coding is a method of detecting and correcting these errors to ensure that there are no errors in the information when it is sent from source to destination. Error coding is used for error-free communication in the primary and secondary memory devices such as RAM, ROM, hard disk, CD’s, and DVDs, as well as in different digital data communication systems such as network communication, satellite, and cellular communication and deep space combination. Data transmission errors occur in terrestrial mobile communication due to multipath fading, diffractions or scattering in cellular wireless communications, low signal-to-noise ratio, and limited transmitted power and energy resources in satellite communication . Error coding uses mathematical formulae to encode data bits at the source into longer bit words for transmission. The “code word” is then decoded at the destination to retrieve the information. The code word consists of extra bits, which provide redundancy, and at the destination, it will decode the data to find out whether the communication channel introduced any error and some schemes can even correct the errors so that there is no need to resend the data. There are two ways to deal with errors. One way is to introduce redundant information along with the data to be transmitted, which will enable the receiver to deduce the information that has been transmitted. The second way is to include only enough redundancy to allow the receiver to detect that error has occurred, but not which error and the receiver makes a request for retransmission. The first method uses Error-Correcting Codes and the second uses Error-detecting Codes. Consider a frame having mdata bits (message to be sent) and rredundant bits (used for checking). The total number of bits in the frame will be n(m + r), which is referred as n-bit code word. Consider two code-words, 11,001,100 and 11,001,111, and perform Exclusive OR and then count number of 1’s in the result. The number of bits in which the codewords are different is called Hamming distance. Suppose the code words are Hamming distance d- apart, it will require d single-bit errors to connect one code word to another. The properties of error detection and error correction depend on the Hamming distance. A distance (d + 1) code is required to detect d errors because d-single bit errors cannot change a valid codeword into another valid code. Thus the error is detected at the receiver. A distance (2d + 1) code is required to correct d errors because the codewords will be so apart that the transmitted codeword will be still closer than any other valid codeword, and thus the error can be determined. A distance (d + 1) code is required to detect d errors because d-single bit errors cannot change a valid codeword into another valid code. Thus the error is detected at the receiver. A distance (2d + 1) code is required to correct d errors because the codewords will be so apart that the transmitted codeword will be still closer than any other valid codeword, and thus the error can be determined. When the data travels from the sender to receiver, different types of errors are encountered in the communication channel . When the data travel through a conductor, there are different influences such as sound waves, electrical signals, noise such as electricity from motors, power switches, impulse noise, because of which data can be corrupted or destroyed. Old conductors are unable to handle these types of interference and heavy data traffic, hence the data transmission suffers. Burst er #coding #theory