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Also known as: Irving Reed, Irving S. Reed

Irving S. Reed (1923–2012) was an American mathematician and engineer who co-invented two of the most important families of error-correcting codes: the Reed-Muller code in 1954 and, with Gustave Solomon, the Reed-Solomon code in 1960.12 The Reed-Solomon code in particular became one of the most widely deployed pieces of forward error correction in history.

data symbols parity burst of errors corrected using parity symbols
Reed-Solomon appends parity symbols so that a burst of corrupted symbols can be located and corrected, the code Reed co-invented in 1960.

Life and work

Reed earned his PhD in mathematics from Caltech in 1949 and worked at MIT’s Lincoln Laboratory and later the RAND Corporation before joining the University of Southern California as a professor.1 He was involved in some of the earliest digital computing — he helped develop register-transfer notation used in machine design — but he is remembered chiefly for coding theory. Beyond codes, his name also attaches to the Reed–Xiaoli (RX) detector in hyperspectral imaging and to work on radar signal processing.

Contribution

Reed’s two great codes attack error correction from complementary angles.

The Reed-Muller code, introduced in 1954, is a binary block code built from multivariate Boolean polynomials. It offers a tunable trade-off between rate and error protection and has an elegant, easily analysed structure; a simple first-order variant was later used to protect telemetry from NASA’s Mariner deep-space probes.

The Reed-Solomon code, published in 1960 with Gustave Solomon, works over larger alphabets — it treats data as symbols (groups of bits) rather than single bits — and is defined by evaluating a polynomial at many points. Its defining strength is burst-error correction: because errors are counted per symbol, a run of consecutive corrupted bits damages only a few symbols, which the parity symbols can then locate and repair.2 A Reed-Solomon code that adds 2t parity symbols can correct any t symbol errors, a clean and powerful guarantee.

Legacy

Reed-Solomon coding is one of the most successful algorithms ever fielded. Its resistance to burst errors made it the natural choice for physical media and channels where damage comes in clumps — scratches on a disc, fades on a radio link. Practical decoding was made feasible by the Berlekamp–Massey algorithm and related work, building on the same block-code foundations as Richard Hamming’s earlier codes.

Relevance to SDR

Reed-Solomon is pervasive in digital radio and storage: CDs, DVDs, Blu-ray, and QR codes; DVB and ATSC digital television; deep-space telemetry; and many data-link protocols all use it. In land-mobile radio it appears inside P25, where Reed-Solomon codes protect critical trunking and header data. GopherTrunk, which decodes P25 and related trunked systems, therefore relies on Reed-Solomon decoding in its control-channel and header paths — a direct, everyday use of Reed’s 1960 invention.

Sources

  1. Irving S. Reed — Wikipedia, for biography, Reed-Muller code, and the RX detector. ↩ ↩2

  2. Reed–Solomon error correction — Wikipedia, for the symbol-based construction and burst-error correction. ↩ ↩2

See also