Block Code

In a block code, the source data is partitioned into blocks of k bits. The encoder translates each block of k input bits into n output bits where n>k. The output n-bit block is called a codeword. The codes are denoted by (n,k) and the code rate is given by k/n. Practical values of the code rate range from 1/4 to 7/8 and k can have values ranging from three to several hundred. The most well-known block codes are Hamming codes, Cyclic Redundancy Check (CRC) codes, Golay codes, BCH codes, and Reed-Solomon codes.

Usually, the transmitted block contains the original k bits of data unchanged and has (n–k) check bits added according to a defined algorithm. This code (where the original data is visible in the codeword) is called a systematic code. A non-systematic code is where the original source bits are not explicit in the codeword. The advantage of systematic codes is that the information word can be estimated by inspection.

At the receiver, the decoder recovers the data and generates a syndrome, which is a coded indication of the error state utilized in the process of correction. Syndrome is based on the medical term for the symptoms of a disease.