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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

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

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

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

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 i=2:length

if input(i) == input(i-1)

run_length = run_length + 1;

else

encoded = [encoded input(i-1) run_length];

run_length = 1;

end

end

if length > 1

% Add last value and run length to output

encoded = [encoded input(i) run_length];

else

% Special case if input is of length 1

encoded = [input(1) 1];

end

Encoder – Matlab Results

>> RLE_encode([1 0 0 0 0 2 2 2 1 1 3])

ans =

1 1 0 4 2 3 1 2 3 1

>> RLE_encode([0 0 0 0 0 0 0 0 0 0 0])

ans =

0 11

>> 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

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

Encoder

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

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

.data ;Data section begins

.copy "e_inputs.asm" ;Reads input values and initialize output

.text ;Executible code section begins.

count1 .set 1 ;Initialize a counter starting at the number 1

count2 .set 15 ;Initialize a counter starting at the number 15

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

;loop2 reads through the input data, and keeps

;track of the number of consecutive inputs

loop2 TC = (AR0 != AR5) ;Compares the number stored in AR5 with the

;number stored in AR0

A = *AR6+ ;Increment the pointer AR6

A = *AR3+ ;Increment the pointer AR3

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

if (*AR2- != 0) goto loop1 ;Stop encoder if count of AR2 reaches zero

stop nop

goto stop ;infinite loop

.end

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: 0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,1,10,1,11,1,12,1,13,1,14,1,15,1

Valid Output

Output Ends Here

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 <= length)

% get value which is followed by the run count

value = encoded(index);

run_length = encoded(index + 1);

for i=1:run_length

% loop adding \'value\' to output \'run_length\' times

decoded = [decoded value];

end

% put index at next value element (odd element)

index = index + 2;

end

Decoder – Matlab Results

>> RLE_decode([0 12])

ans =

0 0 0 0 0 0 0 0 0 0 0 0

>> RLE_decode([0 1 1 1 2 1 3 1 4 1 5 1])

ans =

0 1 2 3 4 5

>> RLE_decode(RLE_encode([0 0 3 1 4 4 5 6 10]))

ans =

0 0 3 1 4 4 5 6 10

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

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 keeps track of the number of repetitions

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

*AR4+ = A ;Add the repeated number to output

goto loop2

stop nop

goto stop ;infinite loop

.end

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

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

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