1 ECE734 VLSI Arrays for Digital Signal Processing Chapter 3 Parallel and Pipelined Processing

2 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Basic Ideas Parallel processingPipelined processing a1a2a3a4 b1b2b3b4 c1c2c3c4 d1d2d3d4 a1b1c1d1 a2b2c2d2 a3b3c3d3 a4b4c4d4 P1 P2 P3 P4 P1 P2 P3 P4 time Colors: different types of operations performed a, b, c, d: different data streams processed Less inter-processor communication Complicated processor hardware time More inter-processor communication Simpler processor hardware

3 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Data Dependence Parallel processing requires NO data dependence between processors Pipelined processing will involve inter-processor communication P1 P2 P3 P4 P1 P2 P3 P4 time

4 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Usage of Pipelined Processing By inserting latches or registers between combinational logic circuits, the critical path can be shortened. Consequence: –reduce clock cycle time, –increase clock frequency. Suitable for DSP applications that have (infinity) long data stream. Method to incorporate pipelining: Cut-set retiming Cut set: –A cut set is a set of edges of a graph. If these edges are removed from the original graph, the remaining graph will become two separate graphs. Retiming: –The timing of an algorithm is re-adjusted while keeping the partial ordering of execution unchanged so that the results correct

5 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Graphic Transpose Theorem The transfer function of a signal flow graph remain unchanged if –The directions of each arc is reversed –The input and output labels are switched. z1z1 z1z1 x[n] y[n] h[2] h[1] h[0] z1z1 z1z1 y[n] x[n] h[2] h[1] h[0] u[n] = ?

6 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Data broadcast structure Algorithm transform may lead to pipelined structure without adding additional delays. Given a FIR filter SFG Critical path T M +2T A Use graph transposition theorem: –Reverse all arcs –Reverse input/output We obtain Critical path T M + T A No additional delay added!

7 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Fine-grain pipelining To further reduce T M. Critical Path = Max {T M1, T M2, T A }

8 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Block Processing One form of vectorized parallel processing of DSP algorithms. (Not the parallel processing in most general sense) Block vector: [x(3k) x(3k+1) x(3k+2)] Clock cycle: can be 3 times longer Original (FIR filter): Rewrite 3 equations at a time: Define block vector Block formulation:

9 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Block Processing

10 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu General approach for block processing

11 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Original formulation: Rewrite Define block vectors Then Block Processing for IIR Digital Filter Time indices –n: sampling period –k: clock period (processor) –k = 2n Note: –Pipelining: clock period = sampling period. Block (parallel): clock period not equal to sampling period.

12 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Block IIR Filter D D S/PP/S + +   x(2k) x(2k+1) y(2k+1) y(2k) x(n)y(n) y(2(k  1)) y(2(k  1)+1)

13 ECE734 VLSI Arrays for Digital Signal Processing (C) by Yu Hen Hu Timing Comparison Pipelining Block processing 1234 x(1)x(2)x(3)x(4) y(1)y(2)y(3)y(4) x(1)x(2)x(3)x(4)x(5)x(6)x(7) MAC y(1)y(2)y(3)y(4)y(5)y(6)y(7) Add a y(1) Mul x(2)x(4)x(6)x(8) x(1)x(3)x(5)x(7)