1. Run Length Encoder/Decoder EE113D Project Authors: Imran Hoque Yipeng Li Yipeng Li Diwei Zhang Diwei Zhang

2. Introduction – What is RLE? Compression technique Compression technique Represents data using value and run lengthRepresents data using value and run length Run length defined as number of consecutive equal valuesRun length defined as number of consecutive equal valuese.g 1110011111 1 3 0 2 1 5 RLE ValuesRun Lengths

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

4. Introduction - Applications Image Compression – JPEG Image Compression – JPEG Run Length Encoder!

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

6. Encoder - Algorithm Start on the first element of input Start on the first element of input Examine next value Examine next value If same as previous valueIf same as previous value Keep a counter of consecutive values 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 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 valueIf not same as previous value Output the previous value followed by ‘1’ (run length. Repeat 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 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 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

8. 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 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 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 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 Input from separate.asm file In the form of a vectorIn 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’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 Output is declared as data memory space Examine memory to get outputExamine memory to get output Originally declared to be all -1.Originally declared to be all -1. Immediate Problem Immediate Problem Output size not known until run-time (depends on input size as well as input pattern)Output size not known until run-time (depends on input size as well as input pattern) Cannot initialize variable size array Cannot initialize variable size array

10. Encoder Solution Solution Limit user input to preset length (16)Limit user input to preset length (16) Initialize output to worst case (double input length – 32)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)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 caseOutput 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".setsect ".text", 0x500,0 ;Executible code in ".text" ;section will begin at 0x500 ;section will begin at 0x500 ;in program memory ;in program memory.setsect ".data", 0x800,1 ;Numbers to be sorted will.setsect ".data", 0x800,1 ;Numbers to be sorted will ;begin at 0x800 in data memory ;begin at 0x800 in data memory.data ;Data section begins.data ;Data section begins.copy "e_inputs.asm";Reads input values and initialize output.text ;Executible code section begins..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

12. Encoder – DSP Code AR6 = #array ;AR6 points to the input data location AR3 = #array ;AR3 points to the next 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

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 loop3A = *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 goto stop ;infinite loop.end.end

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

16. Decoder – Matlab Results >> RLE_decode([0 12]) ans = 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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.setsect ".text", 0x500,0 ;Executible code in ".text“ section will begin at 0x500 ;in program memory ;in program memory.setsect ".data", 0x800,1 ;Numbers to be sorted will begin at 0x800 in data 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..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

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 loop2if (*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 loop3A = *AR6 *AR4+ = A;Add the repeated number to output goto loop2 stop nop goto stop ;infinite loop goto stop ;infinite loop.end.end

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