Run%20Length%20Encoder/Decoder

1
Run Length Encoder/Decoder

• EE113D Project
• Authors Imran Hoque
• Yipeng Li
• Diwei Zhang

2
Introduction What is RLE?

• Compression technique
• Represents data using value and run length
• Run length defined as number of consecutive equal
  values
• e.g
• 1110011111 1 3 0 2 1 5

RLE
Values
Run Lengths
3
Introduction - Applications

• Useful for compressing data that contains
  repeated values
• e.g. output from a filter, many consecutive
  values are 0.
• Very simple compared with other compression
  techniques
• Reversible (Lossless) compression
• decompression is just as easy

4
Introduction - Applications

• Image Compression JPEG

Run Length Encoder!
5
Introduction

• Compression effectiveness depends on input
• Must have consecutive runs of values in order to
  maximize compression
• Best case all values same
• Can represent any length using two values
• Worst case no repeating values
• Compressed data twice the length of original!!
• Should only be used in situations where we know
  for sure have repeating values

6
Encoder - Algorithm

• Start on the first element of input
• Examine next value
• If same as previous value
• Keep a counter of consecutive values
• Keep examining the next value until a different
  value or end of input then output the value
  followed by the counter. Repeat
• If not same as previous value
• Output the previous value followed by 1 (run
  length. Repeat

7
Encoder Matlab Code

• Run Length Encoder
• EE113D Project
• function encoded RLE_encode(input)
• my_size size(input)
• length my_size(2)
• run_length 1
• encoded
• for i2length
• if input(i) input(i-1)
• run_length run_length 1
• else
• encoded encoded input(i-1)
  run_length
• run_length 1
• end
• end

8
Encoder Matlab Results

• gtgt RLE_encode(1 0 0 0 0 2 2 2 1 1 3)
• ans
• 1 1 0 4 2 3 1 2
  3 1
• gtgt RLE_encode(0 0 0 0 0 0 0 0 0 0 0)
• ans
• 0 11
• gtgt RLE_encode(0 1 2 3 4 5 6 7 8 9)
• ans
• 0 1 1 1 2 1 3 1
  4 1 5 1 6 1 7 1
  8 1 9 1

9
Encoder

• Input from separate .asm file
• In the form of a vector
• e.g. array .word 4,5,5,2,7,3,6,9,9,10,10,10,10,
  10,10,0,0
• Output is declared as data memory space
• Examine memory to get output
• Originally declared to be all -1.
• Immediate Problem
• Output size not known until run-time (depends on
  input size as well as input pattern)
• Cannot initialize variable size array

10
Encoder

• Solution
• Limit user input to preset length (16)
• Initialize output to worst case (double input
  length 32)
• Initialize output to all -1s (were only
  handling positive numbers and 0 as inputs)
• Output ends when -1 first appears or if length of
  output equals to worst case

11
Encoder DSP Code

• 
  
• EE113D Final Project (encoder)
• Run Length Encoder Shortens a series of input
  data by representing
• consecutive repeated numbers as the repeated
  number, followed by
• the number of repetitions.
• (Written by Yi-peng Li, Diwei Zhang, Imran
  Hoque)
• .setsect ".text", 0x500,0
  Executible code in ".text"
• 
  section will begin at 0x500
• in
  program memory
• .setsect ".data", 0x800,1 Numbers
  to be sorted will
• begin
  at 0x800 in data memory

12
Encoder DSP Code

• AR6 array AR6 points to the
  input data location
• AR3 array AR3 points to
  the next input data location
• A AR3
• A AR3
• AR5 A AR5 represents the actual number
  stored
• in the memory address AR3 points to
• (the actual number represented in the
  input)
• A AR6
• AR0 A AR0 represents the actual number
  stored
• in the memory address AR6 points to
• AR4 output AR4 points to the output data
  location
• AR2 count2 AR2 keeps track of how much of
  the input
• data has been read
• loop1 initializes the count of AR1 to '1'
• loop1 AR1 count1 Register AR1
  is used to keep track of the
• number of repeated inputs in succession

13
Encoder DSP Code

• A AR3
• AR5 A Re-initialize AR5
• A AR6
• AR0 A Re-initialize AR0
• if (TC) goto loop3 Break loop if next number
  different
• A AR1 else continue counting
• if (AR2- ! 0) goto loop2 Stop encoder
  if count of AR2 reaches zero
• A AR2 Leave count of AR2 at zero
• loop3 stores the encoded input, followed by
• its repeated count into the output array
• loop3 A AR6- Point back to the last
  repeated number
• A AR6
• AR4 A Add the repeated number to output
• A AR1
• AR4 A Add the count of repeated number to
  output
• A AR6 Move pointer back to where it left
  off

14
Encoder DSP Results

• Input 4,5,5,2,7,3,6,9,9,10,10,10,10,10,10,0,0
• Output 4,1,5,2,2,1,7,1,3,1,6,1,9,2,10,6,0,2,-1,-
  1,-1,-1,-1,-1,-1,-1,-1,-1
• Best Case
• Input 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
• Output 0,16,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
  -1,-1,-1,-1,-1,-1
• Worst Case
• Input 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
• Output 0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,1,1
  0,1,11,1,12,1,13,1,14,1,15,1

Valid Output
Output Ends Here
15
Decoder Matlab Code

• Run Length Decoder
• EE113D Project
• The input to this function should be the output
  from Run Length Encoder,
• which means it assumes even number of elements
  in the input. The first
• element is a value followed by the run count.
  Thus all odd elements in
• the input are assumed the values and even
  elements the run counts.
• function decoded RLE_decode(encoded)
• my_size size(encoded)
• length my_size(2)
• index 1
• decoded
• iterate through the input
• while (index lt length)
• get value which is followed by the run
  count
• value encoded(index)
• run_length encoded(index 1)

16
Decoder Matlab Results

• gtgt RLE_decode(0 12)
• ans
• 0 0 0 0 0 0 0 0
  0 0 0 0
• gtgt RLE_decode(0 1 1 1 2 1 3 1 4 1 5 1)
• ans
• 0 1 2 3 4 5
• gtgt RLE_decode(RLE_encode(0 0 3 1 4 4 5 6 10))
• ans
• 0 0 3 1 4 4 5 6
  10

17
Decoder DSP Code

• 
  
• EE113D Final Project (decoder)
• Run Length Encoder Takes as its input, a string
  of data encoded
• according the the run length encoder algorithm,
  and outputs it
• as the decoded string of data originally input
  to the encoder.
• (Written by Yi-peng Li, Diwei Zhang, Imran
  Hoque)
• .setsect ".text", 0x500,0
  Executible code in ".text section will begin
  at 0x500
• in
  program memory
• .setsect ".data", 0x800,1 Numbers
  to be sorted will begin at 0x800 in data memory
• .data Data section
  begins
• .copy "d_inputs.asm" Get input values and
  initialze outputs
• .text
  Executible code section begins.
• count2 .set 14 Initialize a counter starting at
  the number 14

18
Decoder DSP Code

• AR4 output AR4 points to the output data
  location
• AR2 count2 AR0 keeps track of how much of
  the input
• data has been read
• loop2 reads through the input data to the
  decoder
• loop2 if (AR5- ! 0) goto loop3 Keep outputting
  the current input number until
• the following count of that number reaches
  zero
• A AR6 Else continue reading thru input
• A AR6 Increment twice to get next number
  in output
• A AR3
• A AR3 Increment twice to get the count of
  that number
• A AR3
• AR5 A Re-initialize AR5
• if (AR2- ! 0) goto loop2 Stop encoder if
  count of AR2 reaches zero
• goto stop
• loop3 stores the decoded output, by expanding
  the number of repeated inputs
• loop3 A AR6

19
Decoder DSP Results

• Input 0,16
• Output 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
• Input 1,5,0,11
• Output 1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0

20
Conclusion

• Results obtained from DSP match theoretical
  results as well as Matlab results
• Limitations
• Does not handle negative numbers
• Input to encoder limited to 16 numbers in this
  implementation
• Future Improvements
• Variable input lengths
• Allocate memory for output real-time