- 3.1.Capacitive Threshold Logic
- 3.2.Description of the Architecture
- 3.3.Realization of the Image Filter Chip
- 3.4.Design Problems Associated with the Taurus Architecture

In this section, we present the overall architecture of a dedicated chip, Taurus, which is a fully pipelined real-time programmable 3x3 image filter [3,7] based on Capacitive Threshold Logic (CTL) [8]. This chip has essentially been designed to demonstrate the capabilities and possible applications of a new circuit technique (CTL) in digital signal processing. This material is presented to serve as preliminary background for the Aries architecture which will be introduced in Chapter 4.

The extensive research on CTL has resulted in a wide range of building blocks like multipliers, parity generators and population counters. CTL blocks have the advantage of realizing high fan-in building blocks with a much lesser complexity than a CMOS counterparts. As most of these blocks have costly CMOS realizations, traditional designs often tend to avoid algorithms employing functions with high fan-in. Having developed these fast and compact blocks, research intensified on the realization of complex digital systems using CTL building blocks.

A number of applications and algorithms have been examined for their suitability to include CTL building blocks [8,9,10,11]. The time-domain two dimensional convolution (among others) proved to be suitable candidate for a CTL based application. The two dimensional convolution filter, depending on the window-or-kernel size of the filter, involves the multiplication of data values with their corresponding coefficients and the accumulation of the weighted sum of all the product terms. Thus an n x m filter needs n*m multiplications and n*m-1 additions with a total of 2*n*m-1 operations per result. These operations can be defined in mathematical notation as:

where x(p,q) is an element of the input set, y(p,q) is the filter result corresponding to the input and c(i,j) are the coefficients of the n x m window (kernel). The realization of an 3x3, (n=m=3) image filter was targeted as a demonstration of capabilities of the CTL blocks. Rewriting equation 3.1 for the given values of n and m we get

A real time implementation of this filter will need to have access to three subsequent lines (rows of pixels) of the image at any time during its operation. Three new values from each line needs to be taken at each clock cycle (Figure 3.1), thus at any given time the hardware would have access to any of these pixel values and the 2 dimensional convolution function can also be simplified into a 1-D FIR algorithm as follows:

where the indexes for the 2 dimensional position of the input pixel can be calculated from the 1 dimensional variable i using modulo and remainder operations:

and

Having this conversion form i to (p,q) in mind, equation 3.3 can be written in a more simplified way such as

A traditional high-speed implementation of this algorithm requires 9 parallel multiplier circuits to compute each product term, and an adder to calculate y(m) which increases the silicon area significantly [1].

A totally different approach to this problem can replace all multipliers with population counters. For image processing applications one may assume that x(m) is a 8 bit unsigned integer corresponding to the intensity of a pixel in the input image (Although any other value might also have been used within the algorithm). Any x(m) can be written as

where b(m,j) element of {0,1} is the j.th bit of the m.th image pixel. Breaking down image pixels
into bits leads to the definition of *bitplanes *which are 2
dimensional arrays that have the same dimensions as the image, but
only consist of the j.th bit of the image pixel values (see Figure 3.2).
Substituting this representation of a binary number in Equation 3.6
we get:

Using the associative property, we can further modify this equation into

This re-arrangement is very important in understanding the operation principle of the Taurus architecture. The inner parenthesis which involves a multiplication is a special multiplication operation as one of the operands has only two possible values (b(m,j) element of {0,1}). Therefore, the result of the multiplication can be expressed as:

The inner sum therefore, is only a conditional sum of the coefficients. Taurus uses a CTL based counter to generate this sum. An input switch matrix provides a programmable switch for each of the coefficients. If b(m(i),j)=1, c(i) number of inputs of a counter are made active. The counter simply counts the number of logic "1"s on its input which is the sum of all coefficients which have a non-zero corresponding bit on the bitplane. Once this sum is generated for each bitplane of the image, the result is obtained by weighting and adding these sums. The j.th sum has a weight of 2^j, but this weighting is relatively easy to implement with by the means of a simple j bit shift left operation. In fact, the shifting operation can easily be implemented within the adder with no extra cost at all.

Threshold Logic (TL) emerged in early 1960's as a unified theory of logic gates, which includes conventional switching logic as a subset. The formal TL gate can perform not only and/or primitives but any linearly separable boolean function [12]. But despite the theoretically obvious merits, until recently TL has never had a significant impact in practice, due to the limited success achieved in developing a suitable TL gate on silicon.

The similarities between the functionality of a TL gate and the hard limiting neuron structures used in artificial neural networks, has led to the development of Capacitive Threshold Logic (CTL) gates [8].

The CTL circuit technique offers a successfull implementation of threshold functions using conventional CMOS processes. A threshold gate is defined as an m input gate where the output Y is defined as follows:

where X(j) is the j.th binary input with a corresponding weight of W(j). A basic CTL gate of m inputs, as shown in Figure 3.3, comprises a row of weight-implementing capacitors C(i) and a chain of inverters which functions as a voltage comparator.

The CTL gate operates in a two phase non-overlapping clock consisting of a reset phase defined by the clock phi-R and an evaluation phase defined by phi-e. During the reset phase, the row voltage Vrow is reset to the threshold voltage of the first inverter Vth1 . The bottom plates of all input capacitors are forced to ground potential while all the threshold capacitors have their bottom plates connected to VDD. The total charge accumulated in the row during reset can be calculated as follows:

where Vth1 is the inversion (logic) threshold voltage of the first inverter within the comparator and Vth2 is the inversion (logic) threshold voltage of the inverter in the dummy column. In the evaluation phase all binary inputs are forced onto the m input columns while the threshold capacitors are connected to ground potential. The amount of charge in the row, for a given set of inputs, can be calculated as follows:

Since the row charge is retained (charge conservation) during both operational phases, the row voltage perturbation during the evaluation phase becomes:

The row perturbation is equal to the difference between row voltage in reset and evaluation phases.

Substituting this in Equation 3.17 yields

Notice that the first inverter of the comparator circuit is biased exactly at inversion threshold Vth1, which is also the operating point with the highest gain, at the beginning of the evaluation phase. If the voltage perturbation Delta Vrow is positive, the first inverter output will tend to drop to logic "0" and the second inverter will switch to logic "1". If the voltage perturbation Delta Vrow is negative, the opposite will happen.

It can be seen that Equations 3.20 and 3.21 correspond to the basic threshold gate Equations given in 3.13 and 3.14.

The CTL-based parallel counter (i.e. population counter) circuit constitutes the heart of the Taurus architecture [10]. A parallel counter is a multi-input, multi-output combinational logic circuits which determine the number of logic "1"s in their input vectors and generate a binary encoded output vector which corresponds to this number.

A traditional CMOS realization of a parallel counter involves a number of full adders (FA's) arranged in a tree like structure (See Figure 3.4). Swartzlander [13] reports the number of FA's for an m-input population counter as

Different threshold logic realizations of the population counter exists in the literature [14,15,16]. The CTL realization of the parallel counter used in this work is based on the two level Minnick counter (Figure 3.5).

The basic architecture of the Taurus comprises of the basic building blocks given in Figure 3.6:

**Input registers:**

At any given time the Taurus architecture needs access to a 3x3 snapshot of the image. Three rows of shift registers with a depth of three are used to store this snapshot.**Switch matrix:**

Each input bit within the input data has a corresponding weight. For a logic "1" bit, this weight is applied to the inputs of the counters. The switch matrix is used to store the filter weights. Each element within the switch matrix is trigerred by a different bit of the input image and can activate a programmable number of inputs of counters.**The CTL counters:**

For an 8-bit image, eight independent counters are used to accumulate the weights of corresponding bits. The switch matrix activates a number of inputs on each counter depending on the value of the corresponding bit. The total number of active inputs is accumulated by the CTL counter blocks.**Systolic adder tree:**

The output of the CTL counters corresponds to a partial sum of one bitplane of the image. All eight partial sums need to be added to get the result. Since each bitplane has a different weight, they can not be added directly. The systolic adder tree shifts (and thereby multiplies) the partial results according to their rank and accumulates the final result.

This basic architecture has been refined to achieve higher performance.

- The speed of the basic building blocks made it possible to use internal
time multiplexing, and to reduce the required hardware by 50\%. Instead
of operating on full 8-bits data, Taurus first operates on the lower
order 4-bits of the image data, this result is stored in an accumulator.
In the next clock cycle the higher order 4-bits are calculated using
the same blocks. This time the result is shifted four times and added
in the accumulator. The chip accepts three new input pixels in each
cycle, at a frequency of
**f**. The data is multiplexed at the output of the registers and the subsequent blocks operate at**2f**frequency. - The fan-in of the parallel counter circuits used in this design sets a hard limit for the sum of the coefficients. The basic counter block used was a 31-input counter, which was obviously insufficient for the sum of 9 4-bit coefficients. Therefore, two counters were used for each bitplane enabling a sum of coefficients of up to 62. This resulted in having two separate five bit results as the sum of the bitplanes. For increased efficiency two groups of four counters were developed. The four counter groups included one counter for each block and the corresponding systolic adder structure. The result of both systolic adders was later added using a second adder stage.
- The counting algorithm can not cope with negative coefficients directly. To allow negative coefficients, an exact copy of the first block is used. This block too has two separate outputs and the second adder mentioned above was enhanced to subtract these negative coefficient sum from the sum of the positive block. The second adder stage also included a switch to enable addition of all four numbers in case there were no negative coefficients needed, thereby increasing the coefficient dynamic range if all coefficients were positive (or negative).
- It was decided that all coefficients would be 4-bit integers and would
not exceed 15. The hardware also restricted the sum of all coefficients
to 60. For each bitplane this meant routing of sixty separate signals
from the switching matrix to the counters, taking up enormous amounts
of silicon area. As there would be only nine coefficients, each between
zero and fifteen and having a sum of at most sixty, it was evident
that there existed a grouping of input signals that did not impose
further limitations on the coefficients but minimized the number of
connections. Prof. Dr. I. Cem Göknar [17] provided
a group of numbers that made it possible to use only 25 connections
(the original solution was 25 numbers but 26 connections were used to
have the same groupings for both counters). These numbers were commonly
referred to as
*CG-magic*among the Taurus design group members.(CG-magic={6,5,4,3,3,2,2,1,1,1,1,1,1}).

Figure 3.7 shows the final detailed block diagram of the Taurus architecture with all these improvements and the pipeline registers.

To evaluate the performance of the proposed architecture a test chip has been designed and developed (See Figure 3.8) using conventional 1.2um double-poly double-metal CMOS technology. The chip contains a fixed weight version of the processing core which realizes a (3 x 3) smoothing function. The switch matrix array, which is used to facilitate coefficient programming, has been omitted to simplify testing. The realized test structure contains three eight-bit-wide and three-bit-deep input shift registers which facilitate simultaneous input of three eight-bit pixels during each cycle, the corresponding bitplane multiplexers, eight CTL-based parallel (30,5) counters, and two systolic adder arrays. edge triggered dynamic CMOS register cells were used for all pipeline registers. the parallel counters and the adder arrays each form separate pipeline stages in order to reduce the stage delays (These blocks can be seen in Figure 3.7 as shaded blocks).

Extensive post-layout simulations have shown that the signal propagation delay associated with the CTL based parallel counters is about 10 ns, whereas the overall delay of the CMOS adder array stage is well below 10 ns, using a supply voltage of 5 V. Thus, the maximum clock frequency can be as high as 100 MHz, allowing real-time processing of high-resolution (1024 x 1024) pixel images at a rate of 50 frames per second.

The core area of the implemented test chip 1.8 mm x 1.5 mm compares very favourably with other image filters using a similar fabrication technology. About 60% of the active area of the chip is occupied by the CTL counters and their input and output registers, while the systolic adder arrays occupy around 15% of the total area.

Although tests were hampered by different reasons, the calculation time for a single vector was measured to be around 7.9 ns [7] which is well under the designed 10 ns.

A number of problems both in the design and the implementation of the algorithm have been detected after carefull analysis of the Taurus design:

- The first problem that emerged was the difficulty of testing the chip. This was partly caused by the lack of built-in test hardware (scan registers for example). The complexity of pipeline operation and especially the very large internal data busses (up to 192-bits) made testing and problem detection an extremely difficult task.
- The coefficient dynamics are severely limited by the hardware. Increasing the coefficient dynamics would increase the internal routing and require more counters which would in turn further complicate the design of adders.
- The necessity to use a separate, identical block for negative coefficients introduced a high degree of redundancy and increased the silicon area.
- The switch matrix block turned out to have extreme routing requirements. The first few layouts of the switch matrix had unacceptably high routing area overhead.
- The most important shortcoming of the design of the Taurus is that the architecture is practically not scalable in terms of filter window size and filter order. It will require extremely complicated hardware to utilize a number of Taurus image filter chips to construct a higher order image filter.

A number of solutions to address the above mentioned problems have been evaluated and as a result of this research Aries was developed. In Aries the basic idea of computing a convolution without using conventional multiplier cells, in breaking up the input (image) data to bitplanes remained the same, but RAM blocks were used to calculate bitplane results instead of CTL blocks.

These pages by KGF

22.1.1998