FECs

Forward error correction codes (FECs) are a class of error-control codes used in communications and data storage to detect and correct errors without requiring retransmission. An FEC adds redundant bits to each block of data according to a fixed encoding rule, producing a codeword that can be decoded at the receiver even in the presence of noise or impairments. The effectiveness of an FEC is described by the code rate, the ratio of data bits to total bits, and by the code’s minimum distance, which relates to its error-correcting capability.

FECs are broadly categorized as block codes and convolutional codes. Block codes encode fixed-length data blocks into longer codewords, while convolutional codes operate on sequences with memory. Decoding uses algorithms ranging from maximum-likelihood and Viterbi for convolutional codes to iterative techniques such as belief propagation for certain sparse codes. Practical systems often combine coding with interleaving and modulated signaling to handle burst errors and fading.

Notable families include Reed-Solomon codes, which are effective against burst errors and are widely used in storage media and data transmission; BCH codes, a class that generalizes many error-correcting schemes; and modern high-performance codes such as LDPC (low-density parity-check) codes and turbo codes, which provide strong protection with manageable decoding complexity for contemporary communications standards.

FECs are deployed in satellite and cellular links, fiber-optic networks, data storage devices, and even in QR codes. They improve reliability and can reduce retransmissions, but at the cost of added redundancy, possible latency, and increased decoding complexity. The field has evolved from early BCH and Reed-Solomon work to the large-scale adoption of LDPC and turbo codes in modern systems.