Signal Transition Activity Research Articles

Estimation of signal transition activity in FIR filters implemented by a MAC architecture

A novel method for the accurate calculation of the transition activity at the nodes of a multiplier-accumulator (MAC) architecture implementing finite impulse response filters is proposed in this paper. The method is developed for input signals, which can be described by a stationary Gaussian process. The transition activity per bit of a signal word is modeled according to the dual-bit-type (DBT) model and it is described as a function of the signal statistics. An efficient analytical method has been developed for the determination of the signal statistics at each node of the MAC architecture. It is based on the mathematical formulation of the multiplexing in time of signal sequences with known statistics. The effect of the multiplexing mechanism on the breakpoints of the DBT model, which influences significantly the accuracy of the method, is also determined. Several experiments both with synthetic and real data have been conducted. The numerical results produced by the proposed models are in very good agreement with the measured values of the transition activity.

Information-theoretic bounds on average signal transition activity [VLSI systems

Transitions on high-capacitance buses in very large scale integration systems result in considerable system power dissipation. Therefore, various coding schemes have been proposed in the literature to encode the input signal in order to reduce the number of transitions. In this paper, we derive lower and upper bounds on the average signal transition activity via an information-theoretic approach, in which symbols generated by a process (possibly correlated) with entropy rate H are coded with an average of R bits per symbol. The bounds are asymptotically achievable if the process is stationary and ergodic. We also present a coding algorithm based on the Lempel-Ziv data-compression algorithm to achieve the bounds. Bounds are also obtained on the expected number of ones (or zeros). These results are applied to determine the activity-reducing efficiency of different coding algorithms such as, entropy coding, transition signaling, and bus-invert coding, and determine the lower bound on the power-delay product given H and R. Two examples are provided where transition activity within 4% and 9% of the lower bound is achieved when blocks of eight symbols and 13 symbols, respectively, are coded at a time.

Analytical estimation of signal transition activity from word-level statistics

Presented in this paper is a novel methodology to determine the average number of transitions in a signal from its word-level statistical description. The proposed methodology employs: (1) high-level signal statistics, (2) a statistical signal generation model, and (3) the signal encoding (or number representation) to estimate the transition activity for that signal. In particular, the signal statistics employed are mean (/spl mu/), variance (/spl sigma//sup 2/), and autocorrelation (/spl rho/). The signal generation models considered are autoregressive moving-average (ARMA) models. The signal encoding includes unsigned, one's complement, two's complement, and sign-magnitude representations. First, the foilowing exact relation between the transition activity (t/sub i/), bit-level probability (p/sub i/), and the bit-level autocorrelation (/spl rho//sub i/) for a single bit signal b/sub i/ is derived: t/sub i/=2p/sub i/(1-p/sub i/)(1-/spl rho//sub i/) (1). Next, two techniques are presented which employ the word-level signal statistics, the signal generation model, and the signal encoding to determine /spl rho//sub i/ (i=0, /spl middot//spl middot//spl middot/, B-1) in (1) for a B-bit signal. The word-level transition activity T is obtained as a summation over t/sub i/ (i=0,/spl middot//spl middot//spl middot/, B-1); where t/sub i/ is obtained from (1). Simulation results for 16-bit signals generated via ARMA models indicate that an error in T of less than 2% can be achieved. Employing AR(1) and MA(10) models for audio and video signals, the proposed method results in errors of less than 10%. Both analysis and simulations indicate the sign-magnitude representation to have lower transition activity than unsigned, ones' complement, or two's complement. Finally, the proposed method is employed in estimation of transition activity in digital signal processing (DSP) hardware. Signal statistics are propagated through various DSP operators such as adders, multipliers, multiplexers, and delays, and then the transition activity T is calculated. Simulation results with ARMA inputs show that errors less than 4% are achievable in the estimation of the total transition activity in the filters. Furthermore, the transpose form structure is shown to have fewer signal transitions as compared to the direct form structure for the same input.