MY CAREER IN COMMUNICATION SYSTEMS (THE EARLY YEARS)

1. MY CAREER IN COMMUNICATION SYSTEMS(THE EARLY YEARS) SOLOMON W. GOLOMB (VITERBI PROFESSOR OF COMMUNICATIONS IN THE VITERBI SCHOOL OF ENGINEERING) CSSE TUESDAY, OCTOBER 24, 2006 AT USC

2. MY CAREER IN COMMUNICATION SYSTEMS(THE EARLY YEARS) In June, 1951, having just celebrated my 19th birthday and received a B.A. degree in Mathematics from the Johns Hopkins University, I started the first of four successive summers at the Martin Co. (now part of Lockheed-Martin) at its original location just east of Baltimore.

3. I worked in the “systems engineering” division, a term I hadn’t heard before, and whose meaning I absorbed by osmosis. My first summer was with the Controls Group, and thereafter (while I was a grad student at Harvard in “Pure Mathematics”) with the Communications Group. In retrospect, I’ve spent the past 50-plus years applying all the areas of math that my professors assured me couldn’t possibly have any applications, to problems in communication technology.

4. Communications is a great place to learn “systems thinking”. Every communications system has a block diagram, usually containing several subsystems. Sometimes a subsystem will itself have a complex block diagram; and the entire comm. system is usually part of a much bigger system. The aerospace industry, decades ago, created “pert charts” for scheduling system development. My own research focus has been to look for techno/math hurdles, that if overcome, will allow a superior system to be configured, and then solve the tech/math problem.

5. By the summer of 1954, at the Martin Co., I was developing the mathematical model for binary linear feedback shift registers, which in a “mysterious” way could sometimes produce long “pseudo-random” sequences of 1’s and 0’s. Already in 1954, this was of interest to a number of organizations for a variety of applications: • for secure telemetry to guide missiles (Martin Co.; JPL) • for cryptographic “key streams” (NSA) • for coded radar signals (Lincoln Labs)

6. My work had come to the attention of Dr. Eberhardt Rechtin at JPL, who actually came to meet me at my Harvard office in Jan. 1955, while I was continuing my work for Martin as a consultant. I spent academic 1955-56 in Norway (where I finished my Ph.D. thesis for Harvard), and on my return to the U.S. I interviewed at several organizations (including Lincoln and NSA), but I decided to work for Eb Rechtin in his telecommunications section at JPL.

7. At JPL we concluded that signals using linear shift register sequences could easily be broken by a “sophisticated jammer”; so I turned my attention to nonlinear sequences. This turned out to be intimately related to properties of boolean functions, and I developed the theory of the cryptanalysis of sequences obtained either from shift registers with nonlinear feedback, or by the nonlinear modification of linear sequences, or by the nonlinear combination of two or more sequences.

8. My cryptanalytic approach involved multi-dimensional correlations, and I developed a theory of “correlation immunity” based on a set of invariants for boolean functions of n binary variables. In 1957-1959 all this was of course classified, even though the flow of information between me and NSA was always one way (from me to them). However, I presented a talk, “On the Classification of Boolean Functions”, at a large IEEE meeting at UCLA in 1959, which was printed in the IEEE Trans. on Information Theory; and I included this paper as a chapter in my 1967 book Shift Register Sequences, in the section on nonlinear sequences! I just didn’t mention the application, explicitly, that motivated it.

9. On October 4, 1957, Sputnik I was launched. Less than four months later, on Jan. 31, 1958, Explorer I was successfully launched. Wernher von Braun’s Huntsville group provided the first stage rocket, a modified Redstone missile. JPL developed stages two, three, four, and the payload, some of which was assembled in my lab at JPL. This complicated structure had never been tested, but it succeeded on the first try, only 88 days after the U.S. Army (which funded JPL and Huntsville) was told it could proceed with a satellite project.

10. Later in 1958, NASA was created, and became JPL’s main source of funding. I turned my attention from secure missile guidance to satellite and space communication. There was interest at JPL in creating a ranging system, for accurate determination of the distance between a space probe and earth. I had a number of discussions with Eb Rechtin about this.

11. A typical problem: We could probably develop a system with precision to 100 nanoseconds. Light travels about one foot per nanosecond, but over distances of millions of miles, how accurately could we express the range in meters, given the imprecision in our knowledge of the propagation velocity? Also, the precise location of our large tracking antenna at Goldstone hadn’t been surveyed to tie it into any standard grid to better than ±100 meters.

12. Here’s how we “solved” these problems. We would measure distance in “light-seconds”, and put the origin of our coordinate system at our antenna at Goldstone. Any future improvements in refining the propagation velocity of our radio signal could be used to improve our range measurement in meters. We knew exactly where our antenna was if we defined it to be at the origin of our coordinate system — we just didn’t know where Pasadena was! Future surveying could reduce that uncertainty.

13. Our ranging system would be based on binary modulation of an RF-signal, which was already a JPL signalling approach to missile guidance. The modulation would be based on a very long, random-looking binary signal, and we would correlate the incoming signal against “all” the shifts of the binary-modulated signal, and the correlation peak would indicate how long the signal traveled, and hence the range. However, if we used a periodic binary signal, there would be a big-range-ambiguity corresponding to multiples of the period.

14. Here is the solution that Eb and I came up with. We would have a number of relatively short-period sequences, of relatively prime period, where each short sequence would have an impulse-like autocorrelation function. We would combine these short sequences using a boolean function which would be “worst possible” for cryptographic purposes! Instead of resisting a “correlation attack” to separate the short “components sequences”, it would make it easy to extract the component sequences by correlation.

15. Here is an example. Suppose we had 9 binary short-period sequences, all generated at the same “chip rate”, and we combined them, term-by-term, using the majority-decision boolean function, where maj(x1, x2, x3, x4, x5, x6, x7, x8, x9) = 1 if at least 5 of the xi’s are 1, and =0 otherwise. This majority-decision sequence is positively correlated with each of its input sequences, and its period is the product of the nine individual (relatively prime) periods. If the “short” periods average around 80, the combined period will be ≈1.44 x 1017, easily enough to avoid a gross-ambiguity problem.

16. We used ranging on several groundbreaking experiments. In April, 1961, we had a successful radar (radio detection and ranging) contact with Venus, the first with another planet. (The U.S. Army had bounced a radar signal off the moon in 1946.) Several other groups in the U.S. and abroad reported detecting Venus at the same 1961 conjunction (or even, in the case of Lincoln Labs, at a conjunction a few years earlier). The problem was, Venus wasn’t where any of those other groups claimed to have detected her!

17. The “astronomical unit” (A.U) is the average value of the semi-major axis of the earth’s elliptical orbit around the sun, and is the basic scale factor for the solar system. The International Astronomical Union (the same folks who recently decided that Pluto is no longer a planet) had established an “official value” of the A.U., I guess by majority vote, based on a collection of indirect measurements. Our Venus radar measurement gave a direct answer. The astronomers were wrong by one part in 103, a huge error. Our measurement refined the A.U. to better than one part in 106.

18. JPL was only authorized to do “engineering”, not “science”. What were we doing in the planetary radar business, and in refining the value of the A.U.? Eb Rechtin had provided an irrefutable justification. JPL was soon to launch a space probe (“Mariner 2”) to Venus, and it was important to know where Venus really was! If we had relied on the “official” value of the astronomical unit, we could have missed Venus by 100,000 miles!

19. The JPL ranging system had another major scientific achievement — the most accurate test, by far, up to that time, of the predictions of general relativity. I explained how this would work in a talk I gave in 1960, in Washington, D.C., at a meeting of the International Union of Radio Science (U.R.S.I.), titled “The Role of Ranging in Space Exploration”. Here is how it works:

20. RF-Signal E Sun SPACE PROBE When a space probe is on the other side of the Sun from Earth, Einstein predicts that the RF-signal is bent by the Sun’s gravitational field. Ordinary matter would accelerate toward the Sun (as comets do), but since photons are already travelling at the speed of light, when they gain energy from a gravitational field, they can’t speed up. Instead, their frequency increases.

21. The JPL ranging system is coherent, that is, it actually counts RF-cycles. The two relativistic effects — bending the propagation path, and increasing the frequency (I.e., shortening the wavelength) both increase the number of RF-cycles, compared to a non-relativistic model. (An accurate calculation involves both special- and general-relativity effects.) When Mariner 9 was heading toward Mars, around 1969, this experiment was conducted as I had proposed it, and Einstein was verified to an accuracy of about 99%.

22. In a paper I published in 1966 (some three years after I joined USC full-time) titled “run-length encoding”, I described a simple type of lossless data compression, easy to implement and well-suited to situations where you don’t know in advance the statistics of what you will encounter. I was very pleased, a few years ago, to learn that these “Golomb codes” were being used to send back pictures from Mars on the two Mars Rovers.

23. One final note, about my study on nonlinear sequences. Some 30 years after my work at JPL on boolean functions, a paper was published by James L. Massey (an American then living in Zurich) and Guo-Zhen Xiao (of Xidi’an University in Xi’an, China) in the IEEE Trans. on Information Theory, in which they “rediscovered” my cryptanalysis by correlation of nonlinear sequences.

24. I know both Xiao and Massey quite well. Both have copies of my Shift Register Sequences book. I am sure they did not consciously plagiarize, but the similarities are striking. When I enquired about getting my old JPL reports declassified (so I could prove that my original application was the same as theirs), I ran into a catch-22. Those reports could only be declassified by the agency that classified them originally, and that agency no longer exists!