1. Fei Li Jinjun Xiong University of Wisconsin-Madison
Speed up an FSM Via Nonlinear Look-ahead Transformation & Its Application to Huffman Decoding
Fei Li
Jinjun Xiong
University of Wisconsin-Madison

2. Motivation Finite state machine (FSM)
Most commonly used in sequential circuits
Perform non-linear recursive algorithms
Processing rate limited by iteration bound
Applications require high-throughput
Real-time processing
Huffman decoding
Nonlinear algorithm transformation techniques and concurrent architectures may be of help
time to compute the next state

3. Our Approach Nonlinear look-ahead transformation
More state transitions in one computational step
A formal transformation method using state transition matrix
Concurrent block processing
High-order look-ahead transformation
High hardware complexity
Long critical path
Block processing
Explore more concurrency
Easy to pipeline

4. Example: AMI Encoder Alternate Mask Inversion (AMI) Encoder
map a binary sequence into a bipolar pulse sequence
Maintain zero DC bias
Formal representation of state transition
S(n+1) = T(n) * S(n)
S(n+m) = T(n+m-1)… T(n) S(n)
State indicator vector
State transformation matrix T(n)
Independent of current state
Easy to perform look-ahead

5. Example: AMI Encoder (cont)
Look-ahead by three, assuming input string 010
State Transition Matrix
Current State Current State 1
Concurrent architecture w/ block processing

6. Achieved and Expected Results
Achieved Results
Derived formal representation of nonlinear look-ahead using state transition matrix
Designed concurrent block processing architecture
Method applied and verified on the AMI encoder design in Verilog
Expected Results
Apply the method to Huffman decoder
Handle the issue of variable length code
Implement it in Verilog
Achieve high-throughput