L7: Pipelining and Parallel Processing VADA Lab.

Introduction (1) qPipelining transformation leads to a reduction in the critical path, which can be exploited to increase the clock speed (sample speed), or to reduce power consumption at same speed. qIn the parallel processing, multiple outputs are computed in parallel in a clock period. Therefore, the effective sampling speed is increased by the level of parallelism.

Introduction (2) q3-tap FIR digital filter y(n) = ax(n)+bx(n-1)+cx(n-2) q Sample Period q Sampling frequency

Pipelining of FIR digital filter qPipelined implementation of the 3-tap FIR filter is obtained by placing 2 additional latches. qThe critical path is reduced from T M +2T A to T M +T A. qThe two main drawbacks of the pipelining are increase in the number of latches and in system latency.

Pipelining of FIR digital filter (2) qThe critical path (longest path) can be reduced by suitably placing the pipelining latches in the architecture. qThe pipelining latches can only be placed across any feed-forward cutset of the graph qIntroduce 2 definitions of graph for pipelining. q Cutset A cutset is a set of edges of a graph such that if these edges are removed from the graph, the graph becomes disjoint. q Feed-forward Cutset A cutset is called a feed-forward cutset if the data move in the forward direction on all the edges of the cutset. qTo obtain an appropriate pipelining circuit, pipelining latches should be inserted on all the edges in the feed-forward cutset !!

Pipelining of FIR digital filter (3) qSignal-flow graph example

Pipelining of FIR digital filter (4) qData-Broadcast Structures q The critical path of the original 3-tap FIR filter can be reduced without introducing any pipelining latches by transposing the structure. q Transposition theorem “ Reversing the direction of all the edges in a given SFG (signal- flow graph) and interchanging the input and output ports preserves the functionality of the system.”

Pipelining of FIR digital filter (5) < SFG representation of the FIR filter> < Transposed SFG representation of the FIR filter>

Pipelining of FIR digital filter (6) qTransposed SFG representation leads to the data-broadcast structure where data are not stored but are broadcast to all the multipliers simultaneously.

Pipelining of FIR digital filter (7) qFine-Grain Pipelining q Let T M =10 units and T A units, and the desired clock period be (T M +T A )/2=6 units. q In this case the multiplier is broken into 2 smaller units with processing times of 6 units and 4 units, respectively. q By placing the latches on the horizontal cutset across the multiplier, the desired clock speed can be achieved.

Parallel Processing (1) qDesigning a Parallel FIR System q To obtain a parallel processing structure, the SISO(single-input single-output) system must be converted into a MIMO(multiple- input multiple-output) system. y(3k) = ax(3k)+bx(3k-1)+cx(3k-2) y(3k+1) = ax(3k+1)+bx(3k)+cx(3k-1) y(3k+2) = ax(3k+2)+bx(3k+1)+cx(3k) o Parallel Processing systems are also referred to as block processing systems.

Parallel Processing (2) qParallel processing architecture for a 3-tap FIR filter (with block size 3)

Parallel Processing (3) qThe critical path of the parallel processing system has remained unchanged and the clock period (T clk ) must satisfy : qBut since 3 samples are processed in 1 clock cycle instead of 3, the iteration period is given by qIn a Pipelined system : T clk = T sample

Parallel Processing (4) qComplete parallel processing system with block size 4

Parallel Processing (5) qWhy do we use parallel processing when we can use pipelining ? q Due to a fundamental limit to pipelining imposed by the I/O bottlenecks. q Pipelining can be combined with parallel processing to further increase the speed of the architecture. q By combining parallel processing and pipelining, the sample period has been reduced to q Parallel processing is also used for reduction of power consumption while using slow clocks.

Parallel Processing (6)

Parallel Processing (7) <Combined fine-grain pipelining and parallel processing for 3-tap FIR filter>

Pipelining and Parallel processing for Low power qThere are two main advantages of using pipelining and parallel processing : q Higher speed q Lower power qFor CMOS circuit, the propagation delay can be written as : qPower consumption of a CMOS circuit can be estimated as :

Pipelining for Low power (1) q represent the power consumed in the original filter. (where T seq is the clock period of the original sequential filter) qIn the M-level pipelined system, the critical path is reduced to 1/M of its original length and the capacitance to be charged/discharged in a single clock cycle is reduced to C charge / M. q supply voltage can be reduced to

Pipelining for Low power (2) qThe power consumption factor,, can be determined by examining the relationship between the propagation delay of the original filter and the pipelined filter.

Parallel processing for Low power (1) qParallel processing, like pipelining, can reduce the power consumption of a system by allowing the supply voltage to be reduced. qIn an L-parallel system, the charging capacitance does not change while the total capacitance is increased by L times. qIn order to maintain the same sample rate, the clock period of the L- parallel circuit must be increased to LT seq, where T seq is the propagation delay of the sequential circuit. qThere is more time to charge the same capacitance => supply voltage can be reduced to supply voltage can be reduced to

Parallel processing for Low power (2) qThe propagation delay of the L-parallel system is given by :

Conclusions §The pipelining l Pipelining latches are placed across the feed-forward cutsets in the SFG and computation time of the critical path is reduced l The clock frequency can be increased and hence the sampling rate is increased. §Parallel processing l The hardware for the original serial system is duplicated and the resulting system is MIMO parallel system. l The clock freq. Stays the same, and the sampling freq. is increased. §Two scheme is used for higher speed and lower power design (using lower supply voltage).