What if Dictionary size in LZW algorithm is full?
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I have been studying LZW compression and there is one thing that I can't satisfy myself with which is that while building up the dictionary in LZW mostly its maximum limit is set to 4096 entries. Why is that ?. Also if dictionary gets full then the dictionary is reset but what if the next few characters about to read were present in the dictionary before resetting the dictionary. Is this a limitation ? or my understanding is not correct?
algorithm lzw
edited Nov 11 at 7:52
Kromster
4,77364885
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
add a comment |
up vote
3
down vote
favorite
I have been studying LZW compression and there is one thing that I can't satisfy myself with which is that while building up the dictionary in LZW mostly its maximum limit is set to 4096 entries. Why is that ?. Also if dictionary gets full then the dictionary is reset but what if the next few characters about to read were present in the dictionary before resetting the dictionary. Is this a limitation ? or my understanding is not correct?
algorithm lzw
edited Nov 11 at 7:52
Kromster
4,77364885
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
2
One prominent early LZW implementation was BSD compress(1). It started with 9 bit codes (dictionary size 512 (2^9)) - Huffman coding the LZW code stream would have been slow, and arithmetic coding wasn't common, let alone speedy encoders unencumbered by patents. It grew codesize as needed up to a limit of 16, parametrisable down to 12. Compression ratio was monitored, a reset occurred when it got bad, only. Limiting dictionary size allowed computers with little memory to decompress the stream - think 1/3 century ago, 1200/75 modems, … Little input left is a valid concern not addressed AFAIR.
– greybeard
Oct 15 '16 at 5:55
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I have been studying LZW compression and there is one thing that I can't satisfy myself with which is that while building up the dictionary in LZW mostly its maximum limit is set to 4096 entries. Why is that ?. Also if dictionary gets full then the dictionary is reset but what if the next few characters about to read were present in the dictionary before resetting the dictionary. Is this a limitation ? or my understanding is not correct?
algorithm lzw
edited Nov 11 at 7:52
Kromster
4,77364885
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
I have been studying LZW compression and there is one thing that I can't satisfy myself with which is that while building up the dictionary in LZW mostly its maximum limit is set to 4096 entries. Why is that ?. Also if dictionary gets full then the dictionary is reset but what if the next few characters about to read were present in the dictionary before resetting the dictionary. Is this a limitation ? or my understanding is not correct?
algorithm lzw
algorithm lzw
edited Nov 11 at 7:52
Kromster
4,77364885
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
edited Nov 11 at 7:52
Kromster
4,77364885
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
edited Nov 11 at 7:52
Kromster
4,77364885
edited Nov 11 at 7:52
Kromster
4,77364885
edited Nov 11 at 7:52
Kromster
4,77364885
4,77364885
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
asked Oct 15 '16 at 2:03
Syed Ahmed Jamil
187215
187215
2
One prominent early LZW implementation was BSD compress(1). It started with 9 bit codes (dictionary size 512 (2^9)) - Huffman coding the LZW code stream would have been slow, and arithmetic coding wasn't common, let alone speedy encoders unencumbered by patents. It grew codesize as needed up to a limit of 16, parametrisable down to 12. Compression ratio was monitored, a reset occurred when it got bad, only. Limiting dictionary size allowed computers with little memory to decompress the stream - think 1/3 century ago, 1200/75 modems, … Little input left is a valid concern not addressed AFAIR.
– greybeard
Oct 15 '16 at 5:55
add a comment |
2
One prominent early LZW implementation was BSD compress(1). It started with 9 bit codes (dictionary size 512 (2^9)) - Huffman coding the LZW code stream would have been slow, and arithmetic coding wasn't common, let alone speedy encoders unencumbered by patents. It grew codesize as needed up to a limit of 16, parametrisable down to 12. Compression ratio was monitored, a reset occurred when it got bad, only. Limiting dictionary size allowed computers with little memory to decompress the stream - think 1/3 century ago, 1200/75 modems, … Little input left is a valid concern not addressed AFAIR.
– greybeard
Oct 15 '16 at 5:55
2
2
One prominent early LZW implementation was BSD compress(1). It started with 9 bit codes (dictionary size 512 (2^9)) - Huffman coding the LZW code stream would have been slow, and arithmetic coding wasn't common, let alone speedy encoders unencumbered by patents. It grew codesize as needed up to a limit of 16, parametrisable down to 12. Compression ratio was monitored, a reset occurred when it got bad, only. Limiting dictionary size allowed computers with little memory to decompress the stream - think 1/3 century ago, 1200/75 modems, … Little input left is a valid concern not addressed AFAIR.
– greybeard
Oct 15 '16 at 5:55
One prominent early LZW implementation was BSD compress(1). It started with 9 bit codes (dictionary size 512 (2^9)) - Huffman coding the LZW code stream would have been slow, and arithmetic coding wasn't common, let alone speedy encoders unencumbered by patents. It grew codesize as needed up to a limit of 16, parametrisable down to 12. Compression ratio was monitored, a reset occurred when it got bad, only. Limiting dictionary size allowed computers with little memory to decompress the stream - think 1/3 century ago, 1200/75 modems, … Little input left is a valid concern not addressed AFAIR.
– greybeard
Oct 15 '16 at 5:55
add a comment |
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
The dictionary size is limited to the output symbol size. 12 bits can encode 4096 distinct values. It is a common choice for lecture notes and simple/assignment implementations.
However, ANY symbol bits more than the source bits can be used: a 16 bit symbol would allow 65k dictionary entries. The more bits, the more entries in the current dictionary can exist which can increase the “maximum” compression. Conversely, as each output symbol is larger it may decrease compression rates, especially for smaller inputs (insufficient time to generate a dictionary) and data that is more random (reduced ability to re-use the symbols in the dictionary). In practice, 19-20 bits seems to be about the useful limit2, while 16 bit symbols naturally align to bytes.
It is also possible to have an adaptive symbol size based on log2 of the CURRENT number of mapped symbols1- but this benefit disappears as data size increases, as the dictionary quickly fills. It is also largely superseded by Huffman coding.
When the dictionary is "reset", it is effectively the same as compressing multiple chunks of data and appending the compressed output: the dictionaries are separate. However, the data can be “split” dynamically based on when it fills the dictionary as opposed to, say, every X bytes of input. Since the symbol size is fixed, it is more efficient to ensure the dictionary is filled up before making the decision.
The primary purpose to reset a dictionary is to avoid “fixating” the symbols to data characteristics in one part of the input that might not be true for later data. A compressor can use a single non-resetting dictionary, reset the dictionary as soon as it is full, reset the dictionary when it’s full and a drop in compression is encountered, etc.: the goal is to achieve the highest compression within the domain/parameters.
Many LZ77/LZ78/LZW variations (and optimizations they utilize) are briefly discussed in "On parsing optimality for dictionary-based text compression—the Zip case" by AlessioLangiu; these excerpts contain lots of juicy details to further additional research.
1"Improving LZW' by R. Nigel Horspool goes into some details on adaptive symbol sizes. Nigel's "The Effect of Non-Greedy Parsing
in Ziv-Lempel Compression Methods" paper also includes a summary on compress's handling of dictionary resets.
2"The Relative Efficiency of Data Compression by LZW and LZSS" by Yair Wiseman includes a sample graph of symbols sizes vs. compression efficiency. The graph is highly dependent on the data.
answered Nov 11 at 7:24
user2864740
43.3k669142
Your link is broken.
– Michael Foukarakis
Nov 11 at 7:47
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
The dictionary size is limited to the output symbol size. 12 bits can encode 4096 distinct values. It is a common choice for lecture notes and simple/assignment implementations.
However, ANY symbol bits more than the source bits can be used: a 16 bit symbol would allow 65k dictionary entries. The more bits, the more entries in the current dictionary can exist which can increase the “maximum” compression. Conversely, as each output symbol is larger it may decrease compression rates, especially for smaller inputs (insufficient time to generate a dictionary) and data that is more random (reduced ability to re-use the symbols in the dictionary). In practice, 19-20 bits seems to be about the useful limit2, while 16 bit symbols naturally align to bytes.
It is also possible to have an adaptive symbol size based on log2 of the CURRENT number of mapped symbols1- but this benefit disappears as data size increases, as the dictionary quickly fills. It is also largely superseded by Huffman coding.
When the dictionary is "reset", it is effectively the same as compressing multiple chunks of data and appending the compressed output: the dictionaries are separate. However, the data can be “split” dynamically based on when it fills the dictionary as opposed to, say, every X bytes of input. Since the symbol size is fixed, it is more efficient to ensure the dictionary is filled up before making the decision.
The primary purpose to reset a dictionary is to avoid “fixating” the symbols to data characteristics in one part of the input that might not be true for later data. A compressor can use a single non-resetting dictionary, reset the dictionary as soon as it is full, reset the dictionary when it’s full and a drop in compression is encountered, etc.: the goal is to achieve the highest compression within the domain/parameters.
Many LZ77/LZ78/LZW variations (and optimizations they utilize) are briefly discussed in "On parsing optimality for dictionary-based text compression—the Zip case" by AlessioLangiu; these excerpts contain lots of juicy details to further additional research.
1"Improving LZW' by R. Nigel Horspool goes into some details on adaptive symbol sizes. Nigel's "The Effect of Non-Greedy Parsing
in Ziv-Lempel Compression Methods" paper also includes a summary on compress's handling of dictionary resets.
2"The Relative Efficiency of Data Compression by LZW and LZSS" by Yair Wiseman includes a sample graph of symbols sizes vs. compression efficiency. The graph is highly dependent on the data.
answered Nov 11 at 7:24
user2864740
43.3k669142
Your link is broken.
– Michael Foukarakis
Nov 11 at 7:47
add a comment |
up vote
2
down vote
accepted
The dictionary size is limited to the output symbol size. 12 bits can encode 4096 distinct values. It is a common choice for lecture notes and simple/assignment implementations.
However, ANY symbol bits more than the source bits can be used: a 16 bit symbol would allow 65k dictionary entries. The more bits, the more entries in the current dictionary can exist which can increase the “maximum” compression. Conversely, as each output symbol is larger it may decrease compression rates, especially for smaller inputs (insufficient time to generate a dictionary) and data that is more random (reduced ability to re-use the symbols in the dictionary). In practice, 19-20 bits seems to be about the useful limit2, while 16 bit symbols naturally align to bytes.
It is also possible to have an adaptive symbol size based on log2 of the CURRENT number of mapped symbols1- but this benefit disappears as data size increases, as the dictionary quickly fills. It is also largely superseded by Huffman coding.
When the dictionary is "reset", it is effectively the same as compressing multiple chunks of data and appending the compressed output: the dictionaries are separate. However, the data can be “split” dynamically based on when it fills the dictionary as opposed to, say, every X bytes of input. Since the symbol size is fixed, it is more efficient to ensure the dictionary is filled up before making the decision.
The primary purpose to reset a dictionary is to avoid “fixating” the symbols to data characteristics in one part of the input that might not be true for later data. A compressor can use a single non-resetting dictionary, reset the dictionary as soon as it is full, reset the dictionary when it’s full and a drop in compression is encountered, etc.: the goal is to achieve the highest compression within the domain/parameters.
Many LZ77/LZ78/LZW variations (and optimizations they utilize) are briefly discussed in "On parsing optimality for dictionary-based text compression—the Zip case" by AlessioLangiu; these excerpts contain lots of juicy details to further additional research.
1"Improving LZW' by R. Nigel Horspool goes into some details on adaptive symbol sizes. Nigel's "The Effect of Non-Greedy Parsing
in Ziv-Lempel Compression Methods" paper also includes a summary on compress's handling of dictionary resets.
2"The Relative Efficiency of Data Compression by LZW and LZSS" by Yair Wiseman includes a sample graph of symbols sizes vs. compression efficiency. The graph is highly dependent on the data.
answered Nov 11 at 7:24
user2864740
43.3k669142
Your link is broken.
– Michael Foukarakis
Nov 11 at 7:47
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
The dictionary size is limited to the output symbol size. 12 bits can encode 4096 distinct values. It is a common choice for lecture notes and simple/assignment implementations.
However, ANY symbol bits more than the source bits can be used: a 16 bit symbol would allow 65k dictionary entries. The more bits, the more entries in the current dictionary can exist which can increase the “maximum” compression. Conversely, as each output symbol is larger it may decrease compression rates, especially for smaller inputs (insufficient time to generate a dictionary) and data that is more random (reduced ability to re-use the symbols in the dictionary). In practice, 19-20 bits seems to be about the useful limit2, while 16 bit symbols naturally align to bytes.
It is also possible to have an adaptive symbol size based on log2 of the CURRENT number of mapped symbols1- but this benefit disappears as data size increases, as the dictionary quickly fills. It is also largely superseded by Huffman coding.
When the dictionary is "reset", it is effectively the same as compressing multiple chunks of data and appending the compressed output: the dictionaries are separate. However, the data can be “split” dynamically based on when it fills the dictionary as opposed to, say, every X bytes of input. Since the symbol size is fixed, it is more efficient to ensure the dictionary is filled up before making the decision.
The primary purpose to reset a dictionary is to avoid “fixating” the symbols to data characteristics in one part of the input that might not be true for later data. A compressor can use a single non-resetting dictionary, reset the dictionary as soon as it is full, reset the dictionary when it’s full and a drop in compression is encountered, etc.: the goal is to achieve the highest compression within the domain/parameters.
Many LZ77/LZ78/LZW variations (and optimizations they utilize) are briefly discussed in "On parsing optimality for dictionary-based text compression—the Zip case" by AlessioLangiu; these excerpts contain lots of juicy details to further additional research.
1"Improving LZW' by R. Nigel Horspool goes into some details on adaptive symbol sizes. Nigel's "The Effect of Non-Greedy Parsing
in Ziv-Lempel Compression Methods" paper also includes a summary on compress's handling of dictionary resets.
2"The Relative Efficiency of Data Compression by LZW and LZSS" by Yair Wiseman includes a sample graph of symbols sizes vs. compression efficiency. The graph is highly dependent on the data.
answered Nov 11 at 7:24
user2864740
43.3k669142
The dictionary size is limited to the output symbol size. 12 bits can encode 4096 distinct values. It is a common choice for lecture notes and simple/assignment implementations.
However, ANY symbol bits more than the source bits can be used: a 16 bit symbol would allow 65k dictionary entries. The more bits, the more entries in the current dictionary can exist which can increase the “maximum” compression. Conversely, as each output symbol is larger it may decrease compression rates, especially for smaller inputs (insufficient time to generate a dictionary) and data that is more random (reduced ability to re-use the symbols in the dictionary). In practice, 19-20 bits seems to be about the useful limit2, while 16 bit symbols naturally align to bytes.
It is also possible to have an adaptive symbol size based on log2 of the CURRENT number of mapped symbols1- but this benefit disappears as data size increases, as the dictionary quickly fills. It is also largely superseded by Huffman coding.
When the dictionary is "reset", it is effectively the same as compressing multiple chunks of data and appending the compressed output: the dictionaries are separate. However, the data can be “split” dynamically based on when it fills the dictionary as opposed to, say, every X bytes of input. Since the symbol size is fixed, it is more efficient to ensure the dictionary is filled up before making the decision.
The primary purpose to reset a dictionary is to avoid “fixating” the symbols to data characteristics in one part of the input that might not be true for later data. A compressor can use a single non-resetting dictionary, reset the dictionary as soon as it is full, reset the dictionary when it’s full and a drop in compression is encountered, etc.: the goal is to achieve the highest compression within the domain/parameters.
Many LZ77/LZ78/LZW variations (and optimizations they utilize) are briefly discussed in "On parsing optimality for dictionary-based text compression—the Zip case" by AlessioLangiu; these excerpts contain lots of juicy details to further additional research.
1"Improving LZW' by R. Nigel Horspool goes into some details on adaptive symbol sizes. Nigel's "The Effect of Non-Greedy Parsing
in Ziv-Lempel Compression Methods" paper also includes a summary on compress's handling of dictionary resets.
2"The Relative Efficiency of Data Compression by LZW and LZSS" by Yair Wiseman includes a sample graph of symbols sizes vs. compression efficiency. The graph is highly dependent on the data.
answered Nov 11 at 7:24
user2864740
43.3k669142
edited Nov 12 at 5:23
answered Nov 11 at 7:24
user2864740
43.3k669142
answered Nov 11 at 7:24
user2864740
43.3k669142
answered Nov 11 at 7:24
user2864740
43.3k669142
43.3k669142
Your link is broken.
– Michael Foukarakis
Nov 11 at 7:47
add a comment |
Your link is broken.
– Michael Foukarakis
Nov 11 at 7:47
Your link is broken.
– Michael Foukarakis
Nov 11 at 7:47
Your link is broken.
– Michael Foukarakis
Nov 11 at 7:47
add a comment |
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2
One prominent early LZW implementation was BSD compress(1). It started with 9 bit codes (dictionary size 512 (2^9)) - Huffman coding the LZW code stream would have been slow, and arithmetic coding wasn't common, let alone speedy encoders unencumbered by patents. It grew codesize as needed up to a limit of 16, parametrisable down to 12. Compression ratio was monitored, a reset occurred when it got bad, only. Limiting dictionary size allowed computers with little memory to decompress the stream - think 1/3 century ago, 1200/75 modems, … Little input left is a valid concern not addressed AFAIR.
– greybeard
Oct 15 '16 at 5:55