Low - density parity check (LDPC) code is a linear error-correcting block code, suitable for error correction in large block sizes transmitted via very noisy channels.LDPC was developed by Robert G. Gallager, in his doctoral dissertation at the Massachusetts Institute of Technology in 1960. So, these codes are also known as Gallager codes.Encoding by Low-Density Parity Check CodesA low - density parity check (LFPC) code is specified by a parity-check matrix containing mostly 0s and a low density of 1s. The rows of the matrix represent the equations and the columns represent the bits in the codeword, i.e. code symbols.A ... Read More

A challenging task in error correction is decoding the codewords that have been received via noisy channels. Before data is transmitted, the sender adds redundant bits or parity bits to the message forming codewords. The codewords are then transmitted via computer networks. The receiver checks the incoming codewords and performs the decoding or error correction process to retrieve the original data.If there are no errors, i.e. the codewords find an exact matching, then it is easy to decode the data by eliminating the parity bits. However, if a match is not found, then more complex decoding mechanisms are adopted.The two ... Read More

Convolutional CodesConvolutional codes are error correcting codes where the data streams of indefinite lengths are encoded before transmission over noisy channels. The message streams are encoded by the sliding application of Boolean functions that generate a sequence of output bits.Convolutional codes were first introduced in 1955, by Elias. After that, there were many interim researches by many mathematicians. In 1973, Viterbi developed an algorithm for maximum likelihood decoding scheme, called Viterbi scheme that lead to modern convolutional codes.Parameters in Convolutional CodesFor generating a convolutional code, the information is passed sequentially through a linear finite-state shift register. The shift register comprises ... Read More

Hamming code is a block code that is capable of detecting up to two simultaneous bit errors and correcting single-bit errors. It was developed by R.W. Hamming for error correction.In this coding method, the source encodes the message by inserting redundant bits within the message. These redundant bits are extra bits that are generated and inserted at specific positions in the message itself to enable error detection and correction. When the destination receives this message, it performs recalculations to detect errors and find the bit position that has error.Hamming Code for Single Error CorrectionThe procedure for single error correction by ... Read More

Hamming DistanceHamming distance is a metric for comparing two binary data strings. While comparing two binary strings of equal length, Hamming distance is the number of bit positions in which the two bits are different.The Hamming distance between two strings, a and b is denoted as d(a, b).It is used for error detection or error correction when data is transmitted over computer networks. It is also using in coding theory for comparing equal length data words.Calculation of Hamming DistanceIn order to calculate the Hamming distance between two strings, and , we perform their XOR operation, (a⊕ b), and then count ... Read More

Error Correcting CodesError-correcting codes (ECC) are a sequence of numbers generated by specific algorithms for detecting and removing errors in data that has been transmitted over noisy channels. Error correcting codes ascertain the exact number of bits that has been corrupted and the location of the corrupted bits, within the limitations in algorithm.ECCs can be broadly categorized into two types, block codes and convolution codes. Low - density parity check code (LDPC) is a linear error correcting block code. They are suitable for large block sizes in very noisy channels.LDPC codes were developed by Robert G. Gallager, in his doctoral ... Read More

Errors and Error Correcting CodesErrors in data occur when bits get corrupted in the data. When bits are transmitted over the computer network, they are subject to get corrupted due to interference and network problems, leading to errors.Error-correcting codes (ECC) are a sequence of numbers generated by specific algorithms for detecting and removing errors in data that has been transmitted over noisy channels. Error correcting codes ascertain the exact number of bits that has been corrupted as well as the location of the corrupted bits, within the limitations in algorithm.ECCs can be broadly categorized into two types, block codes and ... Read More

Errors and Error Correcting CodesErrors occurs when bits get corrupted while transmission over the computer network, due to interference and network problems.Error-correcting codes (ECC) are a sequence of numbers generated by specific algorithms for detecting and removing errors in data that has been transmitted over noisy channels. Error correcting codes ascertain the exact number of bits that has been corrupted and the location of the corrupted bits, within the limitations in algorithm.ECCs can be broadly categorized into two types, block codes and convolution codes.Binary Convolutional CodesIn convolutional codes, the message comprises of data streams of arbitrary length and a sequence ... Read More

Errors and Error Correcting CodesWhen bits are transmitted over the computer network, they are subject to get corrupted due to interference and network problems. The corrupted bits leads to spurious data being received by the receiver and are called errors.Error-correcting codes (ECC) are a sequence of numbers generated by specific algorithms for detecting and removing errors in data that has been transmitted over noisy channels. Error correcting codes ascertain the exact number of bits that has been corrupted and the location of the corrupted bits, within the limitations in algorithm.ECCs can be broadly categorized into two types −Block codes − ... Read More

Forward error correction (FEC) is an error correction technique to detect and correct a limited number of errors in transmitted data without the need for retransmission.In this method, the sender sends a redundant error-correcting code along with the data frame. The receiver performs necessary checks based upon the additional redundant bits. If it finds that the data is free from errors, it executes error-correcting code that generates the actual frame. It then removes the redundant bits before passing the message to the upper layers.Advantages and DisadvantagesBecause FEC does not require handshaking between the source and the destination, it can be ... Read More