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Also known as: Gustave Solomon, Gus Solomon

Gustave Solomon (1930–1996) was an American mathematician who, with Irving S. Reed, co-invented the Reed-Solomon code in 1960 — an algebraic error-correcting code that went on to protect data on compact discs, deep-space links, QR codes, and digital broadcasting.12 Reed-Solomon is one of the most widely deployed forms of forward error correction ever devised.

data = one polynomial, sampled at many points
Reed-Solomon treats a message as the coefficients of a polynomial and transmits its values at many points; extra samples let a receiver recover the polynomial despite errors.

Life and work

Solomon earned his PhD in mathematics from MIT in 1956 and worked at MIT’s Lincoln Laboratory, where he and Reed collaborated, and later at the Jet Propulsion Laboratory and in the aerospace industry.1 A gifted algebraist with wide interests — he was also an accomplished singer and music theorist — he brought a pure-mathematics sensibility to the practical problem of protecting digital data. His 1960 paper with Reed, only a few pages long, defined the code that carries both their names.

Contribution

The insight behind the Reed-Solomon code is to treat a block of data symbols as the coefficients of a polynomial over a finite field, and to transmit that polynomial’s values at many points rather than the coefficients themselves.2 A polynomial of degree k−1 is fixed by any k of its values, so sending n > k values builds in redundancy: even if several transmitted values are corrupted, enough correct ones remain to reconstruct the original polynomial, and hence the data.

Because the symbols are drawn from a large alphabet (typically 8-bit bytes), the code excels at burst errors — a long run of damaged bits corrupts only a handful of symbols, which the code can locate and correct. A Reed-Solomon code with 2t parity symbols corrects up to t symbol errors, and it is a maximum-distance-separable code, meaning it achieves the best possible error protection for its amount of redundancy.

Legacy

Solomon and Reed’s short paper defined a code whose practical importance grew for decades. Efficient decoding methods — notably the Berlekamp–Massey algorithm and the Forney and Chien search procedures — turned the elegant construction into fielded hardware. Reed-Solomon now stands beside the earlier block codes of Richard Hamming and Reed’s own Reed-Muller code as a cornerstone of coding theory.

Relevance to SDR

Reed-Solomon coding is ubiquitous wherever digital data crosses an unreliable channel: optical discs, QR codes, DSL, DVB and ATSC digital television, and deep-space telemetry all use it. In land-mobile radio it appears inside P25, where Reed-Solomon codes guard trunking control messages and header words against burst corruption. GopherTrunk decodes P25 and related systems, so Reed-Solomon decoding is part of its control-channel and header processing — a direct legacy of Solomon’s 1960 work.

Sources

  1. Gustave Solomon — Wikipedia, for biography and his role in the code. ↩ ↩2

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

See also