iteration bound

ITERATION BOUND

• Feedback loops impose inherent fundamental

lower bound on the achievable iteration or

sample period

• IB is a characteristics of the representation of an

algorithm in the form of a DFG

• Different representation of the same algorithm –

different IB

• Not possible to achieve iteration period less than

the iteration bound

• Two techniques

– Longest path matrix

– Minimum cycle mean method

• Iteration of a node is the execution of the node

exactly once

• Iteration of the DFG is the execution of each node

in the DFG exactly once

• Precedence constraints• Intra-iteration

• Inter-iteration

• Critical path• The path with the longest computation time among all

paths that contains zero delays

� Critical path is the minimum computation time

for one iteration of the DFG

� DFG – recursive and nonrecursive

� Recursive DFG has a fundamental limit on how

fast the DSP program can be implemented in

hardware – the limit is called iteration bound

LOOP BOUND

• A loop is a directed path that begins and ends at

the same node

• loop/ cycle

• Loop bound – lower bound on the loop

computation time

• Loop bound of the j-thloop: defined as Tj/Wj,

where Tjis the loop computation time & Wj is the

number of delays in the loop

• Number of loops in a DFG can be exponential

with respect to the number of nodes