Tunstall V2F Coding Algorithm
• Assumption:
– a binary instruction stream has i.i.d.
– the probability of a bit to be 1 is Prob(1) and
the probability of a bit to be 0 is Prob(0).
• N-bit Tunstall codewords : number of
codewords is 2N
Tunstall V2F Coding Algorithm
• Algorithm:
– Step1: initiate the root and attach 2 nodes.
– Step2: leaf node with higher probability is
attached with 2 more nodes.
– Step3: Repeat step2 until number of leaf nodes is
2N.
– Step4: assign codewords to leaf nodes (length = N)
An example: 2-bit Tunstall V2F coding
000 01 001
COMPRESSION
11 01 10
Improvement of Tunstall V2F
Coding Algorithm
• Using a Markov model to represent the
dependence in data.
• Procedure
– Step1: statistics-gathering
– Step2: codebook construction
– Step3: compression
Another example: 2-bit Tunstall V2F
coding using Markov model
2 issues during compression
• End of block
– Pad extra bits when compression.
– Truncate padded bits when decompression.
• Byte alignment
– To facilitate compression/decompression.
– Pad extra bits if the compressing block is not a
multiple of 8(in bits).
Arithmetic V2F Coding Algorithm
• Assumption:
– a binary instruction stream has i.i.d.
– the probability of a bit to be 1 is Prob(1) and
the probability of a bit to be 0 is Prob(0).
• N-bit arithmetic codewords : number of
codewords is 2N
Arithmetic V2F Coding Algorithm
• Algorithm:
– Step1: Initiate integer interval with range [0,2N)
– Step2: If current interval is not a unit interval:
• Divide the interval to be two subintervals.
• Left subinterval is for input 0 and the right subinterval is
for input 1.
• The size of the subintervals is approximately proportional
to the probability of the input bit.
– Step3: Repeat step2 until all subintervals become
unit intervals.
– Step4: Assign codewords (length = N) to unit
intervals.
Arithmetic V2F Coding Algorithm
• Each unit interval is disjointed from all other
unit intervals.
• Each unit interval uniquely represents a
particular input binary sequence.
An example: 2-bit Arithmetic V2F Coding
000 01 001
COMPRESSION
00 10 01
Another example: 2-bit Arithmetic V2F
Coding using Markov model