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

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

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

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

Example: AMI Encoder (cont) Look-ahead by three, assuming input string 010 State Transition Matrix Current State 0 Current State 1 Concurrent architecture w/ block processing

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