A polynomial code is a linear code having a set of valid code words that comprises of polynomials divisible by a shorter fixed polynomial is known as generator polynomial.They are used for error detection and correction during the transmission of data as well as storage of data.Types of Polynomial CodesThe types of polynomial codes are:Cyclic Redundancy CodeBose–Chaudhuri–Hocquenghem (BCH) CodesReed–Solomon CodesRepresentation of Bit Strings with PolynomialsThe code words, which are essentially bit strings, are represented by polynomials whose coefficients are either 0 or 1. A 𝑘 – bit word is represented by a polynomial ranging from 𝑥0 to 𝑥𝑘−1. The order ... Read More

Fletcher checksum is an error – detection technique that uses two checksums to determine single-bit errors in a message transmitted over network channels. It is a block code technique that was devised by John G. Fletcher in 1970s at Lawrence Livermore Labs, USA.The checksums are created based on the data values in the data blocks to be transmitted and appended to the data. When the receiver gets this data, the checksums are re-calculated and compared with the existing checksums. A non-match indicates an error.The error-detection capabilities of this method is nearly same as that of Cyclic Redundancy Check (CRC) but ... Read More

Interleaving is a tool that is used to enhance existing error correcting codes so that they can be used to perform burst error corrections as well.Most error correcting codes (ECCs) are designed to correct random errors, i.e. error caused by additive noise that is independent of each other. Burst error are the errors that occur in a sequence or as groups. They are caused due to defects in storage media or disruption in communication signals due to external factors like lightning etc. Interleaving modifies the ECC or does some processing on the data after they are encoded by ECCs.Interleaving ProcedureDuring ... Read More

A parity bit is a check bit, which is added to a block of data for error detection purposes. It is used to validate the integrity of the data. The value of the parity bit is assigned either 0 or 1 that makes the number of 1s in the message block either even or odd depending upon the type of parity. Parity check is suitable for single bit error detection only.The two types of parity checking areEven Parity − Here the total number of bits in the message is made even.Odd Parity − Here the total number of bits in ... Read More

Errors and Error DetectionWhen 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 detection techniques are responsible for checking whether any error has occurred or not in the frame that has been transmitted via network. It does not take into account the number of error bits and the type of error.For error detection, the sender needs to send some additional bits along with the data bits. The receiver performs necessary checks based upon the ... Read More

Errors and Error DetectionWhen 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 detection techniques are responsible for checking whether any error has occurred or not in the frame that has been transmitted via network. It does not take into account the number of error bits and the type of error.For error detection, the sender needs to send some additional bits along with the data bits. The receiver performs necessary checks based upon the ... Read More

Errors and Error DetectionWhen 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 detection techniques are responsible for checking whether an error has occurred or not in the frame that has been transmitted via the network. It does not take into account the number of error bits and the type of error.For error detection, the sender needs to send some additional bits along with the data bits. The receiver performs necessary checks based upon ... Read More

Error-detecting codes are a sequence of numbers generated by specific procedures for detecting errors in data that has been transmitted over computer networks.When 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 – detecting codes ensures messages to be encoded before they are sent over noisy channels. The encoding is done in a manner so that the decoder at the receiving end can detect whether there are errors in the incoming signal with high ... Read More

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