Noise-based information processing: Noise-based logic and computing: what do we have so far?

We briefly introduce noise-based logic. After describing the main motivations we outline classical, instantaneous (squeezed and non-squeezed), continuum, spike and random-telegraph-signal based schemes with applications such as circuits that emulate the brain functioning and string verification via a slow communication channel. Deterministic logic; multivalued logic; brain mimetics; noise as information carrier. I. ERRORS, SPEED AND POWER DISSIPATION We present a short summary of our ongoing efforts in the concept creation, development, and design of several noisebased deterministic multivalued logic schemes and elements. The numerous problems with current microprocessors and the struggle to continue to follow Moore's law [1-6] intensify the academic search for non-conventional computing alternatives. Among them, quantum computers have been proven to be disadvantageous for general-purpose computing [7,8] due to their error and energy dissipation problems; they are, at most, applicable for special-purpose-computing with a few specific applications. In general, quantum informatics is not the way to go for everyday use [8]. Today's computer logic circuitry is a system of coupled DC amplifier stages, and this situation represents enhanced vulnerability against variability [1] of fabrication parameters such as threshold voltage inaccuracies in CMOS. Thin oxides imply great power dissipation due to leakage currents [1]. Thermal noise and its error generation, see Figure 1, and the related power dissipation limits are problems of fundamental nature [2-4]. If we want to increase the logic values in a CMOS gate while the error rate and clock frequency is kept constant, idealistically, with zero MOS threshold voltage, the necessary supply voltage scales with the number of logic values and the power dissipation scales with the square of the number of logic values, see Figure 1. Such a high price is unacceptable. Figure 1. Upper: model for the MOSFET gate and its driving. Left: Gaussian noise (thermal, 1/f, shot) and its amplitude distribution and its levelcrossing events. Right: critical levels in binary logic: when the signal is beyond UH it is interpreted as H and when it is below UL , it is interpreted as L. Because the speed (bandwidth), energy dissipation and error probability are interrelated issues, it is important to emphasize that: • Claims about high performance without error rate and energy efficiency aspects are interesting but meaningless for practical developments. • Claims about good energy efficiency without error rate and performance drop aspects are interesting but meaningless for practical developments. • Claims about efficient error correction without energy requirement and performance drop aspects are interesting but meaningless for practical developments. • Finally, all these performance-error-energy implications must be addressed at the system level otherwise they are meaningless for practical developments. For example, improvements at the single gate level are interesting but unimportant if they are lost at the system level. II. INSPIRATION OF NOISE-BASED LOGIC: THE BRAIN Exploring unconventional computing, we can ask: How does biology do it??? Let us take a look at a comparison between a digital computer and the brain in Table 1. We conjecture that the brain utilizes noise as information carrier. The result is a logic engine with a relatively low number of neurons (100 billions), extraordinary performance, acceptable error probability and extremely low power dissipation [9]. TABLE I. THE COMPUTER AND THE BRAIN, A QUICK COMPARISON. Laptop computer Human Brain Processor dissipation: 40 W Brain dissipation: 12-20 W Deterministic digital signal Stochastic signal: analog/digital? Very high bandwidth (GHz range) Low bandwidth (<100 Hz) Sensitive for errors (freezing) Error robust Deterministic binary logic Unknown logic Potential-well based memory Unknown memory mechanism Addressed memory access Associative memory access (?) Motivated by these observations and the fact that stochastic logic is very slow and produces too much errors, our goal has been to study the possibility of constructing deterministic highperformance logic schemes utilizing noise as information carrier [10-14]. III. NOISE-BASED LOGIC WITH CONTINUUM NOISES The first open question is what form of signal to utilize: a continuum-noise-based logic [11,12] with continuum amplitude distribution function or, rather, with discrete density functions like random spike trains [13], like in the brain, or random telegraph waves? Some of the other concerns are listed here: • Deterministic logic from noise: How to handle statistical averaging and the associated speed reduction? • Speed in general: what is the potential speed gain due to the multivalued logic operations? • Number of logic values: what is the most appropriate number of logic values in a single wire? • Energy need: power dissipation versus performance? • Error probability: how much errors can be tolerated and at what cost? • Devices and logic gates: advantages and disadvantages of various realizations? In Figure 2, the schematic of a continuum-noise-based logic gate is shown. The reference noises should be small to reduce power dissipation originating from their distribution. The scheme is very robust against the accumulation and propagation of fast switching errors. Thus the DC switches can be of extremely poor quality with enormously high error probability, such as 10%. This situation helps to reduce switching power dissipation [11].