Abstract: The transmission of broadcast data, such as financial data and news feeds, is accelerated over a communication channel using data compression and decompression to provide secure transmission and transparent multiplication of communication bandwidth, as well as reduce the latency. Broadcast data may include packets having fields. Encoders associated with particular fields may be selected to compress those particular fields.

Abstract: A method for encoding an input sequence of symbols to produce a bitstream and a method of decoding the bitstream to generate a reconstructed binary sequence. Encoding employs an encoding tree having primary codewords associated with leaf nodes and secondary codewords associated with internal nodes. A flush event may cause output of secondary codewords. A context model is used to select an encoding tree corresponding to an estimated probability at the encoder. The same context model is used by the decoder to select a decoding tree. The decoder interleaves bits from decoded bit sequences associated with different estimated probabilities based on the context model.

Abstract: Methods and apparatus for compressing data for network transport in support of continuous availability of applications are described. One computer-implemented method of compressing data includes receiving a current instance of data in an input buffer. A candidate chunk of data is selected from the input buffer. A signature hash is computed from a signature length range of data within the candidate chunk. A matching dictionary entry having a matching signature hash from a multi-tiered dictionary is identified. The matching dictionary entry prospectively identifies a location of a prior occurrence of a selected range of consecutive symbols including the signature length range of data within at least one of the current instance of data and a prior instance of data in the input buffer. A dedupe processed representation of the instance of data is formed wherein a dedupe item is substituted for the selected range of consecutive symbols if the selected range is verified as recurring.

Abstract: A size comparison unit reports, to an access control unit, the size of a piece of compressed data having the smallest size from among pieces of compressed data generated via compression processing units compressing blocks, an algorithm name representing a compression processing unit that has generated the piece of compressed data having the smallest size; the access control unit selects a piece of compressed data to be written in a tape medium and reports, to a statistical information processing unit, an algorithm name representing a compression processing unit that has generated this selected piece of compressed data; the statistical information processing unit extracts, from the reported algorithm name, a regularity present in a result of the selection of compressed data and, in accordance with this extracted regularity, specifies and stops a compression processing unit to be stopped.

Abstract: In response to receiving an input string to be compressed, a plurality of diverse lossless compression techniques are applied to the input string to obtain a plurality of compressed strings. The plurality of diverse lossless compression techniques include a template-based compression technique and a non-template-based compression technique. A most compressed string among the plurality of compressed strings is selected. A determination is made regarding whether or not the most compressed string was obtained by application of the template-based compression technique. In response to determining that the most compressed string was obtained by application of the template-based compression technique, the most compressed string is compressed utilizing the non-template-based compression technique to obtain an output string and outputting the output string.

Abstract: The present disclosure includes apparatuses and methods for data compression and management. A number of methods include receiving a number of data segments corresponding to a managed unit amount of data, determining a respective compressibility of each of the number of data segments, compressing each of the number of data segments in accordance with its respective determined compressibility, forming a compressed managed unit that includes compressed and/or uncompressed data segments corresponding to the number of data segments corresponding to the managed unit amount of data, and forming a page of data that comprises at least the compressed managed unit.

Abstract: The present invention relates to data compression and decompression, and particularly relates to a method and an apparatus for compressing and decompressing signal data. In an embodiment of the present invention, there is disclosed a method for compressing signal data, comprising: obtaining signal data; determining block lengths of a plurality of data blocks into which the signal data are divided, and determining exponents of the data blocks; forming a mantissa sequence of the data block by using the exponent of the data block to compress signal data contained in the data block; and forming a compressed data block by using the block length, the exponent and the mantissa sequence of the data block. By constructing a variable-length data block adapted to dynamic characteristics of signal data, the method for compressing signal data of the present invention increases the compression ratio of signal data.

Abstract: The present invention relates to data compression and decompression, and particularly relates to a method and an apparatus for compressing and decompressing signal data. In an embodiment of the present invention, there is disclosed a method for compressing signal data, comprising: obtaining signal data; determining block lengths of a plurality of data blocks into which the signal data are divided, and determining exponents of the data blocks; forming a mantissa sequence of the data block by using the exponent of the data block to compress signal data contained in the data block; and forming a compressed data block by using the block length, the exponent and the mantissa sequence of the data block. By constructing a variable-length data block adapted to dynamic characteristics of signal data, the method for compressing signal data of the present invention increases the compression ratio of signal data.

Abstract: A method for reducing ultrasound data from an ultrasound signal includes rectifying the ultrasound signal and generating an envelope curve about maximum values of the rectified ultrasound signal. Each ultrasound pulse is represented as a curve portion with a single maximum value. A first negative envelope curve signal, which is reduced by a first factor f, and a delayed envelope curve signal which is not modified but is delayed by a time period td, are produced. The first negative envelope curve signal and the delayed envelope curve signal are added to form a first sum signal with a first zero crossing, wherein the first zero crossing represents a first time value. An amplitude is associated with the first time value, the amplitude corresponding to a signal height consistent with a maximum peak height from the envelope curve within a time interval about the first time value.

Abstract: An apparatus for compressing and decompressing data is disclosed. The apparatus for compressing data includes a block setting unit that divides data of at least one original file into two or more blocks, a compression unit that generates block compression data by applying a compression algorithm to data corresponding to at least one block among blocks divided by the block setting unit, and a compression file generation unit that generates a block header and the block body of the block for each block divided by the block setting unit, in which the block body includes the block compression data if the block is compressed by the compression unit or includes the original data of the block if the block is not compressed the by compression unit.

Abstract: Systems and methods for performing compression of data. A data buffer is separated into equal-sized segments of data. A frequency count is performed to determine how often each segment of data appears in the data buffer. Frequently occurring segments are encoded with unique compression codes, while all other infrequently occurring segments are encoded with a common compression code. The compressed data buffer includes the compression codes, which are all of the same bit-length, and the uncompressed segments. The compression codes and the uncompressed segments are stored in the compressed data buffer in the order in which the corresponding segments appear in the original data buffer.

Abstract: The invention relates to a method for the vector quantization of a feature vector, in particular with respect to a data compression of a signal to be transmitted or to be stored, particularly a voice signal or a video signal, wherein at least one codebook from a plurality of codebook vectors is searched for a code vector representing the feature vector. During the search, a sequence of codebook vectors is examined for the suitability thereof to represent the feature vector. In the course of the search for the code vector, a set of neighboring vectors is dedicated to at least one of the codebook vectors potentially to be examined, preferably prior to the search. The search for the code vector includes at least part of the neighboring vectors.

Abstract: A compression system configured to compress logical data objects into one or more accommodation blocks with a predefined size, and a method of operating thereof are provided. The compression system includes a compression engine capable of compressing input data with the help of sequential encoding one or more input strings and a counter operatively coupled to the compression engine. The counter is configured to keep its ongoing value indicative of a number of input bytes in one or more strings successfully encoded into a given accommodation block; and, responsive to unsuccessful compression of a string into the given accommodation block, to provide the compression engine with information indicative of starting point in the input stream for encoding into the next accommodation block, thus giving rise to a “start indication.

Abstract: A method for differential compression of a sequence of digital values adapted to avoid error propagation during restoration of the values.

Abstract: A device for compressing a feature descriptor includes a non-uniform quantizer and a run-length encoder. The non-uniform quantizer accesses a source feature descriptor from a storage device, and non-uniformly quantizes the source feature descriptor having source vectors into an intermediate feature descriptor having intermediate vectors according to a vector default value. The run-length encoder executes run-length coding for the intermediate feature descriptor to generate a compressed feature descriptor.

Abstract: A forward compatibility guaranteed data compression and decompression method and apparatus are provided. The compressed data decompression apparatus includes a compressed file parsing unit which parses a compressed file comprising compressed data, a header including information on the compressed data and an extension field to extract the compressed data, and an original file generating unit which decompresses the compressed data to generate an original file. The extension field includes one or more extension field units and an extension field terminating code indicating an end of a region capable of including the extension field units, each of the header and the extension field units starts with a data identification code having the same number of bytes, and the extension field unit further includes its own length data separated by a predetermined number of bytes from its own data identification code.

Abstract: A system and method of selecting a predefined Huffman dictionary from a bank of dictionaries. The dictionary selection mechanism of the present invention effectively breaks the built-in tradeoff between compression ratio and compression rate for both hardware and software compression implementations. A mechanism is provided for automatically creating a predefined Huffman dictionary for a set of input files. The dictionary selection mechanism achieves high compression rate and ratio leveraging predefined Huffman dictionaries and provides a mechanism for dynamically speculating which predefined dictionary to select per input data block, thereby achieving close to a dynamic Huffman ratio at a static Huffman rate. In addition, a feedback loop is used to monitor the ongoing performance of the preset currently selected for use by the hardware accelerator. If the current preset is not optimal it is replaced with an optimal preset.

Abstract: There is determined an amount of available memory that is allocated for automatic repeat-request data. Then for each of a plurality of received data transmissions, an nth compression level is selected, in dependence at least in part on the amount of available memory, from among N possible compression levels for storing the respective received data transmission. In one specific embodiment each of the received data transmissions represents one HARQ process, and the nth compression level is selected from comparing an amount of memory needed to store the respective received data transmission and all other received data transmissions representing parallel HARQ processes as compressed according to the nth compression level against the determined amount of available memory. An algorithm iteratively checks the amount of memory needed for each of the N possible compression levels, from least compressed to most compressed in this specific embodiment.

Abstract: Various embodiments of the present invention provide systems and methods for data processing. For example, a data processing system is disclosed that includes a data decoder circuit. The data decoder circuit is operable to: apply a decoding algorithm to a decoder input on a first decoder iteration to yield a first decoder output; compress an output derived from the first decoder output to yield a compressed decoder output; de-compress the compressed decoder output to yield a second decoder output; and apply the decoding algorithm to the second decoder output to yield a third decoder output.

Abstract: Provided are methods and computer program products for providing a circular buffer of values representing performance data that corresponds to a network application on a network device. Methods may include compressing a binary representation of a value using bit-oriented compression that is biased based on a frequency of occurrence of values and/or value ranges, and appending the compressed binary representation to a circular buffer. The bit-oriented compressed may be biased such that values and/or value ranges that occur with a higher degree of frequency are compressed to a higher degree, while values and/or value ranges that occur with a lower degree of frequency are compressed to a lower degree.

Abstract: Provided is a method for quickly obtaining an intensity value at a desired m/z value in a compressed data obtained by run-length encoding of a mass analysis data. An index is created by pairing either the start position of a section where zero-intensity consecutively occurs two or more times in an array of an original spectrum data, or the start position of a sequence of data having significant intensity values in an array of the original spectrum data, with the corresponding position in an array of a compressed data. This index is stored separate from the compressed data. The creation of the index does not affect the array of the compressed data. Therefore, the data can be decompressed even by a data processing system that does not use the index. The index helps to quickly locate a compressed data corresponding to the desired m/z and obtain the necessary intensity value.

Abstract: Systems and methods for performing compression of data. A data buffer is separated into equal-sized segments of data. A frequency count is performed to determine how often each segment of data appears in the data buffer. Frequently occurring segments are encoded with unique compression codes, while all other infrequently occurring segments are encoded with a common compression code. The compressed data buffer includes the compression codes, which are all of the same bit-length, and the uncompressed segments. The compression codes and the uncompressed segments are stored in the compressed data buffer in the order in which the corresponding segments appear in the original data buffer.

Abstract: An electronic device configured for high throughput binarization mode is described. The electronic device includes a processor and instructions stored in memory that is in electronic communication with the processor. The electronic device obtains a block of transformed and quantized coefficients (TCQs). The electronic device determines whether a high throughput binarization mode condition is met. If the condition is met, the electronic device uses the high throughput binarization mode to process the block. If the condition is not met, the electronic device does not use the high throughput binarization mode to process the block. The electronic device transmits the generated first or second bitstream to a decoder.

Abstract: In embodiments of compression match enumeration, a suffix array can be generated that is representative of data sequences stored in a memory buffer. The suffix array can then be converted into a trie structure that overwrites the suffix array in the memory buffer as the trie structure is generated in-place of the suffix array. The trie structure includes nodes that each represent one or more suffixes of the suffix array, where each consecutive suffix is either grouped with an existing node in the trie structure or added as a new node of the trie structure. Data sequence matches can then be enumerated as determined from the trie structure.

Abstract: The present invention provides a method and apparatus for compressing or decompressing data in Fiber Channel (FC) services. In the solution of the present invention, when compressing FC data, a K code indicator bit and an ERR code indicator bit are compressed into a K/ERR code indicator bit, and 8b codes and the K/ERR code indicator bit are compressed into 9b codes; when decompressing FC data, the 9b code is decompressed into 8b codes and a K/ERR code indicator bit, and the K/ERR code indicator bit is decompressed into a K code indicator bit and an ERR code indicator bit. The solution provided by the present invention overcomes the disadvantages that in conventional art, when processing FC service, the K code indicator bit and the ERR code indicator bit must be retained, and the K code and the ERR code are processed separately, which lead to a high bandwidth utilization ratio and a complex processing procedure.

Abstract: A method and apparatus are described for determining whether to convey a communication signal in a compressed form along a communication path. The method comprises the steps of: (i) providing the communication signal that should be conveyed along said communication path; (ii) determining whether at least part of the communication signal comprises data having a non-random distribution; (iii) if the at least part of the communication signal is determined to comprise data having at least partially a non-random distribution, applying a compression algorithm onto that at least part of the communication signal to form a compressed form of the communication signal provided; and (iv) conveying the communication signal in its compressed form along the communication path.

Abstract: A first and a second data value are co-compressed by generating a sequence of symbols having a most significant symbol that is the most significant symbol of a compressed representation of the first data value and a least significant symbol that is the most significant symbol of a compressed representation of the second data value. The compressed representation of the first data value corresponds to at least a portion of the symbols of the sequence of symbols starting from the most significant symbol and extending towards the least significant symbol in a first reading direction. The compressed representation of the second data value also corresponds to at least a portion of the symbols of the sequence of symbols, however, starting from the least significant symbol and extending in an opposite reading direction towards the most significant symbol.

Abstract: A method for recovering a signal by measuring the signal to produce a plurality of compressive sensing measurements, discarding saturated measurements from the plurality of compressive sensing measurements and reconstructing the signal from remaining measurements from the plurality of compressive sensing measurements. Alternatively, a method for recovering a signal comprising the steps of measuring a signal to produce a plurality of compressive sensing measurements, identifying saturated measurements in the plurality of compressive sensing measurements and reconstructing the signal from the plurality of compressive sensing measurements, wherein the recovered signal is constrained such that magnitudes of values corresponding to the identified saturated measurements are greater than a predetermined value.

Abstract: Various embodiments of the present invention provide systems and methods for data processing. For example, a data processing system is disclosed that includes a data decoder circuit. The data decoder circuit is operable to: apply a decoding algorithm to a decoder input on a first decoder iteration to yield a first decoder output; compress an output derived from the first decoder output to yield a compressed decoder output; de-compress the compressed decoder output to yield a second decoder output; and apply the decoding algorithm to the second decoder output to yield a third decoder output.

Abstract: A method for compressing a data stream includes transforming a data stream into a transformed data stream of referencing symbols and other data elements, the referencing symbols representing a data sequence identical to a data sequence in a reference data block; and encoding the referencing symbols by replacing them with codewords according to an encoding scheme, the transformed stream includes at least one control symbol indicating a change between a portion of the transformed data stream containing a sequence of the other data elements and a portion of the transformed data stream containing a sequence of the codewords for the referencing symbols, the location of the control symbol within the transformed data stream defines the end of the respective portion of the transformed data stream, the encoding scheme providing at least one codeword associated to one of the referencing symbols is longer than a codeword representing the control symbol.

Abstract: A size comparison unit reports, to an access control unit, the size of a piece of compressed data having the smallest size from among pieces of compressed data generated via compression processing units compressing blocks, an algorithm name representing a compression processing unit that has generated the piece of compressed data having the smallest size; the access control unit selects a piece of compressed data to be written in a tape medium and reports, to a statistical information processing unit, an algorithm name representing a compression processing unit that has generated this selected piece of compressed data; the statistical information processing unit extracts, from the reported algorithm name, a regularity present in a result of the selection of compressed data and, in accordance with this extracted regularity, specifies and stops a compression processing unit to be stopped.

Abstract: Some embodiments concern a method of detecting usage of one or more electrical devices coupled to an electrical power line. An electrical power signal with a predetermined period is on the electrical power line. The one or more electrical devices place one or more noise signals on the electrical power line. The electrical power signal comprises the one or more noise signals. The method can include: using a data acquisition device to acquire first data about the electrical power signal on the electrical power line such that the acquiring of the first data is synchronized with the predetermined period of the electrical power signal; processing the first data to create frequency domain data; and applying a feature extraction algorithm to the frequency domain data to determine a transition of an electrical state of at least a first one of the one or more electrical devices. Other embodiments are disclosed.

Abstract: In an embodiment, an indicator is set to indicate that all of a plurality of most significant bytes of characters in a character array are zero. A first index and an input character are received. The input character comprises a first most significant byte and a first least significant byte. The first most significant byte is stored at a first storage location and the first least significant byte is stored at a second storage location, wherein the first storage location and the second storage location have non-contiguous addresses. If the first most significant byte does not equal zero, the indicator is set to indicate that at least one of a plurality of most significant bytes of the characters in the character array is non-zero. The character array comprises the first most significant byte and the first least significant byte.

Abstract: A method for parallel context modeling through reordering the bits of an input sequence to form groups of bits in accordance with a context model-specific reordering schedule. The reordering schedule is developed such that the groups of bits are formed to satisfy two conditions: first, that the context for each of the bits in a group of bits is different from the context of each of the other bits in that group, and the context of each of the bits in that group is determined independently from each of the other bits in that group. The parallel context modeling may be used in encoding or decoding operations.

Abstract: Provided are a computer program product, system, method, and data structure for using variable length code tables to compress an input data stream to a compressed output data stream. A determination is made as to whether a number of at least two consecutive data units in the input data stream match the number of consecutive data units in a history buffer of previously received data units in the input data stream. If so, a copy pointer symbol is generated including data indicating a copy pointer symbol referencing previously received data units in the history buffer and indicating the determined number of consecutive data units. A determination is made of a relative displacement count in the history buffer at which the number of matching consecutive data units start. A determination is made from a variable length code table an encoding of the relative displacement count in the history buffer.

Abstract: Provided are methods and computer program products for providing a circular buffer of values representing performance data that corresponds to a network application on a network device. Methods may include compressing a binary representation of a value using bit-oriented compression that is biased based on a frequency of occurrence of values and/or value ranges, and appending the compressed binary representation to a circular buffer. The bit-oriented compressed may be biased such that values and/or value ranges that occur with a higher degree of frequency are compressed to a higher degree, while values and/or value ranges that occur with a lower degree of frequency are compressed to a lower degree.

Abstract: A method and apparatus for data compression, particularly applicable to spectral signals such as Fast Fourier Transforms of vibration data. The data is merged to remove redundant frequencies when recorded at multiple sample rates, thresholded with respect to a noise floor to remove even more redundant data, and then the positions of non-zero signal values, with respect to the noise floor, are recorded in a first dataword and the non-zero signal values themselves are all recorded concatenated to form a second dataword. The compressed data set consists of the first and second datawords, together with the value of the noise floor, maximum original amplitude and the broadband power. In the event of successive data sets having the same or similar locations for non-zero signal values a re-use flag may be set and the locations dataword discarded. Preferably the signal values are non-linearly quantized to further reduce the amount of data.

Abstract: A method for encoding data to be placed into a weight constrained memory array includes designating a set of crosspoints within a crossbar memory array as indicator crosspoints and a set of crosspoints within the memory array as data crosspoints, the set of indicator crosspoints selected so that a net number of times that each data crosspoint has been flipped can be determined from a subset of the set of indicator crosspoints, placing an input stream of data into a matrix corresponding to crosspoints within the memory array, bits of the input stream being placed into matrix elements that correspond to data crosspoints of the memory array, setting each matrix element corresponding to indicator crosspoints to a value corresponding to a fixed resistive state, and flipping each bit corresponding to a conductor of the memory array until no conductors within the memory array violate a weight constraint.

Abstract: A technique includes compressing or decompressing data using a relative displacement of a location of a data pattern.

Abstract: The disclosure provides a system and method to vary bandwidth/speed of a compression engine to tradeoff with compression quality. The system comprises an input port receiving a data stream having a current byte and a stream of preceding and subsequent bytes thereof; a history memory storing the stream of preceding bytes in blocks of history data an index engine having a table of keys associated to memory addresses of the blocks, the index engine accessing the table to output a plurality of potential string matches upon entry of the current byte; a search engine processing the potential string matches by fetching the blocks of history data associated with each of the plurality of potential string matches and comparing a portion of each of the blocks to the current byte to output a string upon matching consecutive bytes in the block to the current byte and subsequent bytes thereof; and a control input limiting the number of potential string matches processed by the search engine.

Abstract: Simplifying transmission in a distributed parallel computing system. The method includes: identifying at least one item in a data input to the parallel computing unit; creating a correspondence relation between the at least one item and indices thereof according to a simplification coding algorithm, where the average size of the indices is less than the average size of the at least one item; replacing the at least one item with the corresponding indices according to the correspondence relation; generating simplified intermediate results by the parallel computing unit based on the indices; and transmitting the simplified intermediate results. The invention also provides a system corresponding to the above method.

Abstract: In one aspect, methods and systems for variable-block length encoding of data, such as an inverted index for a file are disclosed. These methods and systems provide for relatively fast encoding and decoding, while also providing for compact storage. Other aspects include a nearly 1:1 inverted index comprising a position vector and a data store, wherein values that have a unique location mapping are represented directly in the position vector, while for 1:n values (n>1), the position vector can include a pointer, and potentially some portion of information that would typically be stored in the data area, in order to fully use fixed width portions of the position vector (where a maximum pointer size is smaller than a maximum location identifier size).

Abstract: Systems, methods, and apparatus for a scalable processor architecture for variety of string processing application are described. In one such apparatus, n input first in, first out (FIFO) buffer stores an input stream. A plurality of memory banks store data from the input stream. A re-configurable controller processes the input stream. And an output FIFO buffer stores the processed input stream.

Abstract: A technique includes compressing or decompressing data using a relative displacement of a location of a data pattern.

Abstract: An apparatus for compressing and decompressing data is disclosed. The apparatus for compressing data includes a block setting unit that divides data of at least one original file into two or more blocks, a compression unit that generates block compression data by applying a compression algorithm to data corresponding to at least one block among blocks divided by the block setting unit, and a compression file generation unit that generates a block header and the block body of the block for each block divided by the block setting unit, in which the block body includes the block compression data if the block is compressed by the compression unit or includes the original data of the block if the block is not compressed the by compression unit.

Abstract: The disclosure relates to a system and a method for hardware encoding and decoding according to the Limpel Ziv STAC (LZS) and Deflate protocols based upon a configuration bit.

Abstract: Methods and devices are described for entropy coding data using an entropy coder to encode quantized transform domain coefficient data. Last significant coefficient information is signaled in the bitstream using two-dimensional coordinates for the last significant coefficient. The context for bins of one of the coordinates is based, in part, upon the value of the other of the coordinates. In one case, instead of signaling last significant coefficient information, the number of non-zero coefficients is binarized and entropy encoded.

Abstract: An embodiment may include first circuitry and second circuitry. The first circuitry may compress, at least in part, based at least in part upon a first set of statistics, input to produce first output exhibiting a first compression ratio. If the first compression ratio is less than a desired compression ratio, the second circuitry may compress, at least in part, based at least in part upon a second set of statistics, the first output to produce second output. The first set of statistics may be based, at least in part, after an initial compression, upon other data that has been previously compressed and is associated, at least in part, with the input. The second set of statistics may be based at least in part upon the input. Many alternatives, variations, and modifications are possible.

Abstract: Systems, methods, and other embodiments associated with compression and real-time decompression of executable code are described. According to one embodiment, an apparatus includes a memory that stores compressed blocks of data. The data is executable code for a processing element. The apparatus also includes a decompression logic. The decompression logic receives a request from the processing element for data and determines a compressed block that stores the data. The compressed block is decompressed to produce an uncompressed block. The decompression logic then provides the requested data to the processing element. In one embodiment an uncompressed block has a predetermined fixed block size. The predetermined fixed block size is selected based on at least one of an amount of uncompressed data, a desired compression ratio, and a desired access time.

Abstract: A method of data compression is provided. The method comprises, dividing a stream of sequentially received-generated data coefficients into multiple sets of data coefficients, each set of data coefficients representing a time period and, for each set of data coefficients, selecting N data coefficients having the greatest magnitude, and ordering the N data coefficients according to their magnitude; selecting, for each N ordered data coefficients, a subset of data coefficients having a magnitude greater than a threshold value; comparing the data coefficient with the greatest magnitude from each subset to one another and selecting the Q largest data coefficients; and repeating the previous comparison step excluding the previously selected Q data coefficients until a total of P data coefficients have been selected, where N>P>Q.