Embodiments of the present invention relate to the field of data processing, in particular, to multiplexing a stream of data and combining two or more of the multiplexed substreams to facilitate compression of the stream of data.
Various encoding and decoding techniques have been developed and employed to facilitate efficient storage and/or transfer of data, e.g. media data, such as video and/or audio data.
Increasingly, the Extensible Markup Language (XML) has become the standard for sharing data over networks such as the Internet. With advances in networking, processor speed, memory, and client server/architecture enabling increased information sharing, the need for a language representing data in a platform independent manner became increasingly clear. Though capable of connecting to each other over the Internet and other networks, many computing devices struggled to share data due to their differing platforms. XML answered this need by separating data from programming and display language specific requirements, and facilitating the representation of the data itself and its structure, utilizing “elements” that described the data in a nested fashion (see
XML has become so prevalent that numerous other languages and standards based on XML have been developed. These languages and standards include XSL (the Extensible Stylesheet Language), which describes how an XML document is to be displayed; XSLT (Extensible Stylesheet Language Transformations), which transforms XML documents into other XML documents or into XHTML documents (Extensible Hypertext Markup Language); XPath, which is a language for finding information in an XML document; XQuery, which facilitates the querying of XML documents; DTD (Document Type Definition), which defines the legal building blocks (elements) of an XML document; and XML Schema Language, which serves as an XML-based alternative to DTDs, declaring elements that may occur in an XML document and the order of their occurrence. Numerous application interfaces, such as the XML DOM (Document Object Model), have also arisen, facilitating the accessing and manipulating of XML documents.
Given the increasing processor speeds of personal computers and workstations and the increasing use of fast, efficient broadband network connections, the large size of XML documents has not always been seen as a problem. However, from XML's inception, it has been recognized that its very large size (relative to its content) would be problematic for computer systems and enterprises that have high efficiency needs. With the revolution in small, mobile device technology, the problems of XML efficiency have become more acute. Mobile devices are limited by their size to smaller storage, memory, and bandwidth. An XML document that might not overwhelm a PC on a broadband connection might pose serious problems for a cell phone or PDA. For these devices, large XML files take too long to download, require too much memory and require lengthy processing times, draining the device's battery. In addition, providers of network connectivity for some of these devices bill for the amount of data transferred rather than the amount of time connected, leading to increasingly large bills for mobile devices. Thus, the large size and situational inefficiency of XML are becoming problematic.
In response, a number of application-specific and proprietary tools for reducing the size of XML have been developed. Such tools include ASN-1, WAP WB-XML, Millau, and compression tools such as Win-Zip. None of these tools, however, provides an efficient version of XML that works well for the full range of XML, including small documents, large documents, strongly typed data and loosely typed documents. In addition, none of them support the extensibility and flexibility required by XML applications and none of them scale well for a wide range of small, mobile devices and large, high-processing power devices.
Embodiments of the present invention will be described by way of exemplary embodiments, but not limitations, illustrated in the accompanying drawings in which like references denote similar elements, and in which:
a-4b illustrate exemplary substreams of data generated from the received stream of data, as well as recombined substreams generated by combining two or more of the substreams, in accordance with various embodiments; and
Illustrative embodiments of the present invention include but are not limited to methods and apparatuses for receiving a stream of data, splitting the stream of data into a plurality of substreams based on one or more criteria, and selectively recombining the substreams based on one or more additional criteria, to improve overall effectiveness in compressing the stream of data.
Various aspects of the illustrative embodiments will be described using terms commonly employed by those skilled in the art to convey the substance of their work to others skilled in the art. However, it will be apparent to those skilled in the art that alternate embodiments may be practiced with only some of the described aspects. For purposes of explanation, specific numbers, materials, and configurations are set forth in order to provide a thorough understanding of the illustrative embodiments. However, it will be apparent to one skilled in the art that alternate embodiments may be practiced without the specific details. In other instances, well-known features are omitted or simplified in order not to obscure the illustrative embodiments.
Further, various operations will be described as multiple discrete operations, in turn, in a manner that is most helpful in understanding the illustrative embodiments; however, the order of description should not be construed as to imply that these operations are necessarily order dependent. In particular, these operations need not be performed in the order of presentation.
The phrase “in one embodiment” is used repeatedly. The phrase generally does not refer to the same embodiment; however, it may. The terms “comprising,” “having,” and “including” are synonymous, unless the context dictates otherwise. The phrase “A/B” means “A or B”. The phrase “A and/or B” means “(A), (B), or (A and B)”. The phrase “at least one of A, B and C” means “(A), (B), (C), (A and B), (A and C), (B and C) or (A, B and C)”. The phrase “(A) B” means “(B) or (A B)”, that is, A is optional.
Further, the computer system or systems having one or more of the above processes may be of any type known in the art, including, but not limited to, PCs, workstations, servers, routers, mainframes, PDAs, set-top boxes, and mobile phones. Further, the network connecting any two or more of these systems may be any sort of network known in the art, including, but not limited to, a LAN, a WAN, or the Internet. Such a network may additionally utilize any sort of connection known in the art, such as a TCP/IP connection or an ATM virtual connection.
In various embodiments, stream of data 102 may be received via an application interface (API), the interface providing a stream of data from one or more processes, such as an encoder. The API (not shown) may represent any sort of API known in the art. The API may conform to one or more of the XML DOM, Simple API for XML (SAX), Streaming API for XML (StAX) and Java API for XML Binding (JAXB).
Stream of data 102, in some embodiments, may be generated by an encoder, although stream 102 may be generated by any sort of process or processes. Such an encoder may generate a plurality of smaller and/or lower entropy encoding values representing larger and/or higher entropy data, such as XML. Such an encoder is the subject of co-pending application Ser. No. 11/394,662, entitled “KNOWLEDGE BASED ENCODING OF DATA,” filed on Mar. 31, 2006.
The data comprising stream of data 102 may be any sequence of zero, one, or more bits, and may or may not have a structure. In various embodiments, stream of data 102 is structured as XML data, character data, data from a database, structures defined by a programming language, and/or structures defined by an interface definition language (IDL). Further, data items specified by the structure of stream of data 102 and contained within stream of data 102 may be one or more of the data types integer, long, short, byte, string, date, Boolean, float, double, qualified name, byte array, and/or typed list. Further, as mentioned above, the stream of data 102 having any one or more of the above structures and/or data types may be encoded by an encoder as a plurality of encoded values representing the data.
Additionally, in some embodiments, the API or process(es) providing the stream of data 102 may provide the stream as a one or more byte-aligned values. By providing the stream of data 102 as one or more byte-aligned values, the API or process(es) providing the stream of data 102 may facilitate compression algorithms that identify, analyze and operate on data items that occur on byte boundaries, such as the Deflate algorithm, that may compress the data to be compressed 112.
As is further illustrated, first one or more substreams 104, second one or more substreams 106, and third one or more substreams 108 may be determined in any of a number of ways. A computer system or systems determining a plurality of data substreams such as substreams 104, 106, and 108 may determine the streams randomly, placing portions of stream of data 102 at random into any number of substreams, the substreams acting as “buckets” for the portions of the stream 102 allocated into them.
In other embodiments, stream of data 102 may be split into a plurality of substreams 104, 106, and 106 based on one or more pre-determined criteria, to improve overall effectiveness in compressing the stream of data 102. The one or more criteria may comprise metadata describing the content and/or structure of stream of data 102, and the metadata may have any number of sources. The metadata may be derived from the data itself and/or one or more descriptions of the data. The metadata may be derived from one or more of names associated with data items, types associated with data items and/or the content of data items. Where the metadata is derived from an XML document, the metadata serving as the one or more criteria may include element names and/or attribute names. Where the metadata is derived from an XML schema, the one or more criteria may include data type names associated with XML elements, attributes and values, or base data types associated with XML elements, attributes or values, such as “String” and “Integer.” Where the metadata is derived from a database schema or database data, the one or more criteria may include names or types associated with database tables, rows, and/or columns. Further, the metadata may be derived from other sources of metadata known in the art, such as grammars and/or programming languages, and the one or more criteria may include names and/or types associated with grammar productions and/or structures defined by a programming language.
For example, if the one or more criteria comprise the base data types of portions of stream of data 102, the stream 102 may be split into a plurality of substreams, with characters in one substream, strings in another, integers in a third, and reserve yet another for other or unknown data types. Thus, a stream of data 102, “a 1 2 b cat c 3 a b rabbit 1 c 2 3 3.14 . . . ” might be placed into the following substreams: “a b c a b c . . . ” “1 2 3 1 2 3 . . . ” “cat rabbit . . . ” and “3.14 . . . ”, which each have lower entropy than the original stream and may compress better separately than together (assuming longer sequences than illustrated in the simple example above).
In yet other embodiments, the computer system or systems determining the plurality of substreams 104, 106, and 108 may derive and/or receive metadata describing one or more of the structure, names, types and content of data items in stream of data 102. Metadata may be derived from the data itself and/or any description of the data, such as the XML schemas, database schemas, grammars, and programming languages mentioned above. Such metadata may be provided separately, provided at the beginning of the stream 102 or may, in some embodiments, be derived while performing an initial pass through at least a portion of stream of data 102, extracting the metadata before or while determining the plurality of substreams to generate. In some embodiments, the computer system or systems determining the plurality of substreams, may specify a substream (e.g., the first substream) representing said metadata, such that a decoder may read the specified substream to retrieve said metadata and determine the criteria needed to decode the remaining substreams. In one embodiment, the specified substream containing a representation of said metadata is output and/or compressed concurrently with the first pass through of at least a portion of stream of data 102. For example,
The derivation and receipt of metadata is further discussed in “KNOWLEDGE BASED ENCODING OF DATA,” the co-pending application cited above.
Once a computer system or systems have determined the plurality of substreams 104, 106, and 108, that computer system or another system connected in the manner described above may split stream 102 into the plurality of substreams. The substreams may be created and implemented as any number of data structures, including buffers, streams, arrays, queues, and stacks, but may be implemented in any manner known in the art. Taking the example of a series of arrays, the substream splitting process may first call a function or functions initializing an array or arrays for each of the substreams. Thus, referring to the above example, the process might initialize arrays for portions of the stream 102 representing metadata and values of the <desc>, <color>, <size> and <quan> elements. Upon initializing the arrays or other data structures representing the substreams, the substream splitting process may read the received stream of data 102 from the beginning of the stream to its end. As the process encounters portions of data, the process will store the portion in, for example, the initialized array associated with the metadata or a particular element name associated with the portion of data. Referring to the example in
In some embodiments, each of the plurality of substreams 104, 106, and 108 may be assigned one or more identifiers based on metadata describing the stream 102. The one or more identifiers may then be used to facilitate selective recombining of the substreams of data, the selective recombining described in greater detail below.
Further, prior to recombining the substreams 104, 106, and 108, two or more of the substreams may be reordered based on one or more reordering criteria so that substreams that are likely to compress well together are adjacent. The one or more reordering criteria used for reordering two or more of the substreams may include one or more of identifiers associated with substreams, sizes associated with substreams (e.g., in bytes or number of data items), data types associated with data from substreams, names associated with data from the substream, and analysis results associated with the data of the substream, such as statistical averages of values in a substream, entropies of substreams, ranges of values in substreams, and frequency distributions of values in sub streams.
In various embodiments, one or more values of one or more of the plurality of substreams 104, 106, and 108 may also be modified based on one or more criteria to improve the relative entropy of one or more pairs of substreams. For example, a constant value may be added to values in one or more sub-streams, to reduce differences in their average values, entropies, value ranges, or frequency distributions. As another example, the criteria may also comprise a map that maps each original value to a different value.
As is shown, two or more of the plurality of substreams may be recombined to form one or more recombined substreams 110 based on one or more criteria, to improve overall effectiveness in compressing the stream of data 102. In various embodiments, the one or more criteria may include identifiers associated with the substreams, such as those mentioned above; sizes associated with the substreams, such as a substream's size in byte or length in values; data types associated with data from substreams; names associated with data from substream; and analysis results of the data of the substreams, such as statistical averages of values in a substream, entropies of substreams, ranges of values in substreams, and frequency distributions of values in substreams. Substreams may be successively recombined with other adjacent or non-adjacent substreams until the one or more criteria are met. Recombined substreams themselves may be recombined with other adjacent or non-adjacent substreams or with other recombined substreams until all substreams and recombined substreams meet the one or more criteria.
For example, if one of the one or more criteria is a substream length, the recombination process may begin by performing a function call to a method that returns a substream length. Upon determining substream lengths (methods for which are well known in the art), substreams having a length that is smaller than the criterion might be combined. If the criterion is that the length of each substream should be greater than one hundred items, for example, any substreams having a length that is less than one hundred items would be recombined into recombined substreams 110. The recombined substreams 110 themselves may be recombined, either further with other recombined substreams 110, or with substreams 104, 106, and/or 108, until all substreams and recombined substreams satisfy the substream length criteria or until only one substream remains. Referring now to the above example in
Further, the implementation of the combination process may involve the creation of a new buffer, stream, array, stack, or queue, or may involve the addition of items from one existing buffer, stream, array, stack, or queue to another existing array, stack, or queue.
Also, in various embodiments, after reordering the plurality of substreams, all of the substreams may be recombined into a single recombined stream, the recombined stream compressing better than stream 102 because it now includes repeating sequences of similar adjacent items.
As is further illustrated, upon recombining the substreams into the one or more recombined substreams 110, a computer system or systems may compress the substreams 108 that have not been recombined, and the recombined substreams 110. Thus, the data to be compressed 112 includes both substreams that have not been recombined and recombined substreams 110. The compression process may be facilitated by any compression algorithm known in the art, such as Huffman, Lempel-Ziv, or Deflate. These algorithms are well known to those skilled in the art, however, and the details of their implementations need not be described further. In one embodiment, a computer system or systems may determine that one or more substreams should not be compressed at all. The determination whether to compress a particular stream or substream may be made based on metadata. The metadata may be derived from a number of sources and may include identifiers associated with substreams, sizes associated with substreams (e.g., in bytes or number of data items), data types associated with data from substreams, names associated with data from the substream, and analysis results associated with the data of the substream, such as statistical averages of values in a substream, entropies of substreams, ranges of values in substreams, and frequency distributions of values in substreams.
In various embodiments, after compressing the data to be compressed 112, the computer system or systems may transmit the data 112 to another computer system or store data 112. Such transmission or storage may be facilitated by one or more networking fabrics, such as LANs, WANs, or the Internet, or by a storage medium capable of storing the data 112. In one embodiment substreams (compressed and/or uncompressed) may be concatenated as a single stream for transmission or storage. In other embodiments, substreams may be transmitted or stored separately.
The received stream of data 102, block 202, may be generated by an encoder (not shown), although stream 102 may be generated by any sort of process or processes. Such an encoder may generate a plurality of smaller and/or lower entropy encoding values representing larger and/or higher entropy data, such as XML. Such an encoder is the subject of “KNOWLEDGE BASED ENCODING OF DATA,” the co-pending application cited above.
Further, the data comprising stream of data 102 may be any sequence of zero, one, or more bits, and may or may not have a structure. In various embodiments, stream of data 102 is structured as XML data, character data, data from a database, structures defined by a programming language, and/or structures defined by an interface definition language (IDL). Additionally, data items contained within stream of data 102 may be one or more of the data types integer, long, short, byte, string, date, Boolean, float, double, qualified name, byte array, and/or typed list. And as mentioned above, the stream of data 102 having any one or more of the above structures and/or data types may be encoded by an encoder as a plurality of encoded values representing the data.
Additionally, in some embodiments, the stream of data 102 may be received as one or more byte aligned values, block 202, from the API or process(es) providing the stream 102. By providing the stream of data 102 as one or more byte-aligned values, the API or process(es) providing the stream of data 102 may facilitate compression algorithms that identify, analyze, and operate an data items that occur on byte boundaries, such as the Deflate algorithm, that may compress the data to be compressed 112.
As is further illustrated, first one or more substreams 104, second one or more substreams 106, and third one or more substreams 108 may be determined in any of a number of ways, block 204. A computer system or systems determining a plurality of data substreams such as substreams 104, 106, and 108 may determine the streams randomly, placing portions of stream of data 102 at random into any number of substreams, the substreams acting as “buckets” for the portions of the stream 102 allocated into them.
In other embodiments, stream of data 102 may be split into a plurality of substreams 104, 106, and 106 based on one or more pre-determined criteria, to improve overall effectiveness in compressing the stream of data 102, block 204. The one or more criteria may comprise metadata describing the content and/or structure of stream of data 102, and the metadata may have any number of sources. The metadata may be derived from the data itself and/or one or more descriptions of the data. The metadata may be derived from one or more of names associated with data items, types associated with data items, and/or the content of data items. Where the metadata is derived from an XML document, the metadata serving as the one or more criteria may include element names and/or attribute names. Where the metadata is derived from an XML schema, the one or more criteria may include data type names associated with XML elements, attributes and values, or base data types associated with XML elements, attributes, or values, such as “String” and “Integer.” Where the metadata is derived from a database schema or database data, the one or more criteria may include names or types associated with database tables, rows, and/or columns. Further, the metadata may be derived from other sources of metadata known in the art, such as grammars and/or programming languages, and the one or more criteria may include names and/or types associated with grammar productions and/or structures defined by a programming language.
For example, if the one or more criteria comprise the base data types of portions of stream of data 102, the stream 102 may be split into a plurality of substreams, with characters in one substream, strings in another, integers in a third, and reserve yet another for other or unknown data types. Thus, a stream of data 102, “a 1 2 b cat c 3 a b rabbit 1 c 2 3 3.14 . . . ” might be placed into the following substreams: “a b c a b c . . . ” “1 2 3 1 2 3 . . . ” “cat rabbit . . . ” and “3.14 . . . ”, which each have lower entropy than the original stream and may compress better separately than together (assuming longer sequences than illustrated in the simple example above).
In yet other embodiments, the computer system or systems determining the plurality of substreams 104, 106, and 108 may derive and/or receive metadata describing one or more of the structure, names, types, and content of data items in stream of data 102, the metadata serving as the one or more criteria for determining the plurality of substreams, block 204. Metadata may be derived from the data itself and/or any description of the data, such as the XML schemas, database schemas, grammars, and programming languages mentioned above. Such metadata may be provided separately, provided at the beginning of the stream 102 or may, in some embodiments, be derived while performing an initial pass through at least a portion of stream of data 102, extracting the metadata before or while determining the plurality of substreams to generate. In some embodiments, the computer system or systems determining the plurality of substreams, may specify a substream (e.g., the first substream) representing said metadata, such that a decoder may read the specified substream to retrieve said metadata and determine the criteria needed to decode the remaining substreams. In one embodiment, the specified substream containing a representation of said metadata is output and/or compressed concurrently with the first pass through of at least a portion of stream of data 102. For example,
Once a computer system or systems have determined the pluralities of data substreams 104, 106, and 108, that computer system or another system connected in the manner described above may split stream 102 into the plurality of substreams, block 206. The substreams may be created and implemented as any number of data structures, including buffers, streams, arrays, queues, and stacks, but may be implemented in any manner known in the art. Taking the example of a series of arrays, the substream splitting process may first call a function or functions initializing an array or arrays for each of the substreams. Thus, referring to the above example, the process might initialize arrays for portions of the stream 102 representing metadata and values of the <desc>, <color>, <size> and <quan> elements. Upon initializing the arrays or other data structures representing the substreams, the substream splitting process may read the received stream of data 102 from the beginning of the stream to its end. As the process encounters portions of data, the process will store the portion in, for example, the initialized array associated with the metadata or a particular element name associated with the portion of data. Referring to the example in
In some embodiments, each of the plurality of substreams 104, 106, and 108 may then be assigned one or more identifiers based on metadata describing the stream 102, block 208. The one or more identifiers may then be used to facilitate selective recombining of the substreams of data, the selective recombining described in greater detail below.
Upon receiving the plurality of substreams 104, 106, and 108, two or more of the substreams may be reordered based on one or more reordering criteria so that substreams that are likely to compress well together are adjacent, block 304. The one or more reordering criteria used for reordering two or more of the substreams may include one or more of identifiers associated with substreams, sizes associated with substreams (e.g., in bytes or number of data items), data types associated with data from substreams, names associated with data from the substream, and analysis results associated with the data of the substream, such as statistical averages of values in a substream, entropies of substreams, ranges of values in substreams, and frequency distributions of values in substreams.
In various embodiments, one or more values of one or more of the plurality of substreams 104, 106, and 108 may then be modified based on one or more criteria to improve the relative entropy of one or more pairs of substreams, block 306. For example, a constant value may be added to values in one or more sub-streams, to reduce differences in their average values, entropies, value ranges, or frequency distributions. As another example, the criteria may also comprise a map that maps each original value to a different value.
As is shown, the computer system or systems performing some or all of the operations of the present invention will then determine if any substreams 104, 106, and 108 match one or more criteria, block 308. Should any two or more of the substreams match the criterion, they may be combined to form a recombined substream 110, block 310. In various embodiments, the one or more criteria may include identifiers associated with the substreams, such as those mentioned above; sizes associated with the substreams, such as a substream's size in byte or length in values; data types associated with data from substreams; names associated with data from substreams; and analysis results of the data of the substreams, such as statistical averages of values in a substream, entropies of substreams, ranges of values in substreams, and frequency distributions of values in substreams. Substreams may be successively recombined with other adjacent or non-adjacent substreams until the one or more criteria are met. Recombined substreams themselves may be recombined with other adjacent or non-adjacent substreams or with other recombined substreams, block 310, until all substreams and recombined substreams meet the one or more criteria.
For example, if one of the one or more criteria is a substream length, the recombination process may begin by performing a function call to a method that returns a substream length. Upon determining substream lengths (methods for which are well known in the art), substreams having a length that is smaller than the criterion might be combined. If the criterion is that the length of each substream should be greater than one hundred items, for example, any substreams having a length that is less than one hundred items would be recombined into recombined substreams 110. The recombined substreams 110 themselves may be recombined, either further with other recombined substreams 110, or with substreams 104, 106, and/or 108, until all substreams and recombined substreams satisfy the substream length criteria or until only one substream remains. Referring now to the above example in
Also, in various embodiments, all of the substreams may be recombined into a single recombined stream, the recombined stream compressing better than stream 102 because it now includes repeating sequences of similar adjacent items.
As is further illustrated, upon combining two or more of the substreams into the one or more recombined substreams 110, a computer system or systems may compress the substreams 108 that have not been combined, and the recombined substreams 110, block 312. Thus, the data to be compressed 112 includes both substreams that have not been recombined, and recombined substreams 110. The compression process may be facilitated by any compression algorithm known in the art, such as Huffman, Lempel-Ziv, or Deflate. These algorithms are well known to those skilled in the art, however, and the details of their implementations need not be described further. In one embodiment, a computer system or systems may determine that one or more substreams should not be compressed at all. The determination whether to compress a particular stream or substream may be made based on metadata. The metadata may be derived from a number of sources and may include identifiers associated with substreams, sizes associated with substreams (e.g., in bytes or number of data items), data types associated with data from substreams, names associated with data from the substream, and analysis results associated with the data of the substream, such as statistical averages of values in a substream, entropies of substreams, ranges of values in substreams, and frequency distributions of values in substreams.
In various embodiments, after compressing the data to be compressed 112, the computer system or systems may transmit the data 112 to another computer system (not shown) or store data 112. Such transmission or storage may be facilitated by one or more networking fabrics, such as LANs, WANs, or the Internet, or by a storage medium capable of storing the data 112. In one embodiment substreams (compressed and/or uncompressed) may be concatenated as a single stream for transmission or storage. In other embodiments, substreams may be transmitted or stored separately.
a-4b illustrate exemplary substreams of data generated from the received stream of data, as well as recombined substreams generated by combining two or more of the substreams, in accordance with various embodiments.
a illustrates a received stream of data containing an XML document and five substreams generated from that received stream of data. Substream 1 contains a representation of metadata defining the sequence and structure of the data items in the stream of data. Each “/” symbol in substream represents a position where the associated data item might be found in another substream associated with the previous metadata item. Substreams 2 through 5 shown here have been determined based on the XML element names occurring in the stream of data, the XML element names serving as the one or more criteria. Here, substreams 2 through 5 correspond to four XML elements, “<desc>”, “<color>”, “<size>” and “<quan>”. The criterion might specify substreams for each of these four XML elements or may specify substreams for one or more of the XML elements occurring in the document and also specify another substream for all data items not matching the one or more specified XML elements. The XML elements used to determine substreams may be provided in advance, discovered during a first pass through the stream of data or discovered incrementally while processing the stream. In fact, analysis of a mere portion might be sufficient to determine each of the XML elements present in the stream of data. Further, such a sampling analysis might be complemented by the introductions of one or more additional substreams to hold data items associated with XML elements not encountered in the sampling. Also, though the substreams shown here are organized by XML element name, substreams generated from a stream need not be. Rather, the substreams can be generated and filled at random or in accordance with some other criterion.
b illustrates the generated substreams depicted in
Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a wide variety of alternate and/or equivalent implementations may be substituted for the specific embodiments shown and described, without departing from the scope of the present invention. This application is intended to cover any adaptations or variations of the embodiments discussed herein. Therefore, it is manifestly intended that this invention be limited only by the claims and the equivalents thereof.
This invention was made with government support under contract FA8750-06-C-0038 awarded by The Air Force Research Lab. The government has certain rights in the invention.
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