Abstract: A method and a system for exchanging electronic information data, using a color code recognition device are provided. An electronic information data from the first computer is recognized in either in the ASCII code or in the binary digit format. The electronic information data is encoded by substituting each character of the ASCII codes or the binary digit recognized with a color value. The encoded data is transmitted to the second computer, and the transmitted data is decoded into the original electronic information data. The system for exchanging an electronic information data includes a storage device for storing the user identification database and the legend database, an encoding device for encoding the electronic information data, a decoding device for decoding the encoded data to restore the encoded data into its original format, and a network device for transmitting the data between a plurality of computers over the network.

Abstract: A method and a device for compressing a feature descriptor are disclosed. The device 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 method, controller and system in accordance with various aspects of the present disclosure facilitate reduced energy consumption in a motion sensing device having an inertial measurement unit (IMU), with a strap down integration unit, and an application processing unit (AP). The system and method include rounding velocity increments and orientation increments at the inertial measurement unit, thereby producing a remainder values. The remainder values are added to subsequent velocity increments and orientation increments prior to rounding of those values, and so on. In this way, while motion granularity is slightly decreased, there is no drift of integration errors over time.

Abstract: A method to at least one of compress and decompress data includes providing a string (T) consisting of multiple given substrings. Identification symbols ($,$1,$2,$3) are assigned to the substrings of the string (T). The substrings of the string (T) are transferred by permutation into a permuted string (O(T),O*(T)). The permuted string (O(T),O*(T)) is sorted into a sorted permuted string (oSort(T), oSort*(T)) according to a given sorting criterion. The identification symbols ($,$1,$2,$3) are permuted and sorted together with the substrings of the sting (T) so that, in a partial inverse transformation step, characters of an Nth substring are sequentially determined within the permuted string (O(T),O*(T)) after determining a position (P) of an Nth identification symbol ($,$1,$2,$3) assigned to an Nth substring within the sorted permuted string (oSort(T),oSort*(T)) without reading characters of other substrings of the permuted string (O(T),O*(T)).

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for encoding and decoding information. In one aspect, methods of encoding information in an encoder include the actions of receiving a signal representing information using a collection of discrete digits, converting, by an encoder, the received signal into a time-based code, and outputting the time-based code. The time-based code is divided into time intervals. Each of the time intervals of the time-based code corresponds to a digit in the received signal. Each digit of a first state of the received signal is expressed as a event occurring at a first time within the corresponding time interval of the time-based code. Each digit of a second state of the received signal is expressed as a event occurring at a second time within the corresponding time intervals of the time-based code, the first time is distinguishable from the second time.

Abstract: Data decompression apparatus is disclosed which is arranged to act on compressed data comprising: an ordered stream of references to groups of previously decoded data items; an ordered stream of direct representations of data items to be decoded; and an ordered stream of flags indicating whether each successive decompression operation should act on a reference or a direct representation. The apparatus comprises an output memory area; a detector to detect the number n of consecutive flags indicating that a decompression operation should act on a direct representation; and a data copier for copying to the output memory area either a next referenced group of previously decoded data or a group of n consecutive direct representations from the ordered stream of direct representations.

Abstract: A history buffer for use in adaptive lossless data compression comprises a plurality of memory locations. The memory locations are partitioned into two or more segments, each segment configured to detect a match sequence independently of the other segments. Control logic is provided for controlling the detection of match sequences between the two or more segments.

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: Devices and methods for entropy decoding a bitstream of encoded data by extracting a plurality of encoded subsequences from a payload field of the bitstream for parallel decoding on a set of parallel entropy decoders. The method includes dividing the payload of concatenated encoded subsequences into segments using a distribution function and distributing the segments amongst the set of parallel entropy decoders to balance the computational load among the parallel entropy decoders. The received bitstream includes auxiliary information inserted by the encoder to enable the decoder to entropy decode segments that begin with a portion of an encoded subsequence.

Abstract: A method for encoding an input file into an output file that is compressed so that the number of bits required to represent the output file is less than the number of bits of the input file. The encoding method includes the parsing of the input file into a series of data items, the data items having an order and collectively corresponding to the input file. The encoding method compares the series of data items against a static dictionary having at least mappings between terminal sequence pointers and representations of data items.

Abstract: In one embodiment, an initial series of bytes are scanned to determine a frequency of occurrence within the initial series of bytes for a plurality of byte strings. A data structure is generated containing the plurality of byte strings and count values representing a frequency of occurrence for the plurality of byte strings in the initial series of bytes. A most common byte string of the plurality of byte strings in the initial series of bytes is determined from the count values. Each instance of the most common byte string in the initial series of bytes is replaced with a first substitute byte string to form a revised series of bytes. A most common byte string in the revised series of bytes is determined from the data structure without resetting the count values associated with at least some of the plurality of byte strings.

Abstract: A method of operating a data compression device includes analyzing data using an analyzer and generating a result of the analysis, while the data is buffered by an input buffer, and selectively compressing the buffered data according to the result of the analysis. A data compression device includes a data pattern analyzer configured to analyze data transmitted to an input buffer, and generate an analysis code based on the analysis of the data; and a data compression manager configured to selectively compress the data in the input buffer based on the analysis code.

Abstract: The invention provides a data compression method, comprising: (a) obtaining a first reading sequence and a second reading sequence from an identical source by a receiving unit; (b) comparing the first reading sequence with the second reading sequence according to a comparison condition to generate a sequence comparison result by the processor; (c) outputting a final template sequence according to the sequence comparison result by the processor; (d) comparing the final template sequence to each of the first and second reading sequences, to generate a respective difference between the final template sequence and each of the first and second reading sequences by the processor; and (e) compressing the first and second reading sequences according to the final template sequences and all generated differences between the final template sequence and the first and second reading sequences, to generate a compression file by the processor.

Abstract: A compression technique includes storing respective fixed-size symbols for each of a plurality of words in a data block, e.g., a cache line, into a symbol portion of a compressed data block, e.g., a compressed cache line, where each of the symbols provides information about a corresponding one of the words in the data block. Up to a first plurality of data segments are stored in a data portion of the compressed data block, each data segment corresponds to a unique one of the symbols in the compressed data block and a unique one of the words in the cache line. Up to a second plurality of dictionary entries are stored in the data portion of the compressed cache line. The dictionary entries can correspond to multiple ones of the symbols.

Abstract: Techniques for resource management of a PPM context model are described herein. According to one embodiment, in response to a sequence of symbols to be coded, contexts are allocated, each having multiple entries and each entry representing a symbol that the current context is able to encode, including a counter value representing a frequency of each entry being used. For each symbol coded by a context, a local counter value and a global counter value are maintained. The global counter value represents a total number of symbols that have been coded by the context model and the local counter value represents a number symbols that have been coded by the respective context. Thereafter, a resource management operation is performed for system resources associated with the plurality of contexts based on a global counter value and a local counter value associated with each of the plurality of contexts.

Abstract: An encoder employs a trellis coded quantization (TCQ) unit and a compression unit. The TCQ uses a set of polynomials that have been selected to maximize granular gain. The TCQ unit operates on a block of samples from a source. The compression unit compresses bit planes of the TCQ output, using parity check matrices of corresponding LDPC codes, to obtain corresponding syndromes. The parity check matrices are selected so their compression performance approaches close to the limit for Slepian-Wolf coding. A decoder employs a decoding unit and an estimation unit. The decoding unit decodes the syndromes using side information to produce an estimate for the TCQ output. The side information is correlated with the source. The estimation unit estimates the block of source samples using the estimated TCQ output and the side information. Trellis coded vector quantization may be used as an alternative to TCQ.

Abstract: It provides a method for encoding a set of elements by using components defining the structure of each of the set of elements, wherein each element comprises data structure information and at least one data value. The method comprises the steps of: selecting a current element for encoding; determining whether the current element has the same data structure information as a previously encoded element; in the negative, encoding the data structure information of the current element and the at least one data value of the current element; and in the affirmative, encoding the at least one data value of the current element and providing an indication value associated with the current element indicating the current element has the same data structure information as said previously encoded element. The method is used to reduce the encoding redundancy of the structure information.

Abstract: Functionality is described for compressing and decompressing mass spectrometry data, therefore making it easier to store, retrieve, transfer, and process the mass spectrometry data. The functionality operates by mapping data values (e.g., mass-to-charge data values or intensity data values) into index values, and then mapping the index values into delta values. The functionality then uses an encoding algorithm (such as a coding tree) to represent the delta values in compressed form. In a decoding stage, the functionality can interpret each encoded delta value with reference to a chain of preceding delta values, which ultimately link to an initial data value that is expressed in non-relative form. In one implementation, the functionality can define multiple such initial data values which correspond to multiple access points in a stream of compressed mass spectrometry data.

Abstract: A coding method according to the present invention comprises: transforming an input signal; quantizing a transformed output signal; and entropy coding quantized coefficients, wherein the transforming includes: generating a first transformed output signal by performing a first transform on the input signal using a first transform coefficient; generating a second transformed output signal by performing, using a second transform coefficient, a second transform on a first partial signal which is a part of the first transformed output signal, and outputting the transformed output signal including the generated second transformed output signal and a second partial signal which is the remaining part of the first transformed output signal other than the first partial signal; and modifying the first transformed output signal.

Abstract: A coding method according to an implementation of the present invention includes: transforming an input signal to generate a transformed output signal (S110); quantizing the transformed output signal to generate a quantized coefficient (S120); and entropy coding the quantized coefficient to generate a coded signal (S130), and the transforming (S110) includes: generating a first transformed output signal by performing a first transform on the input signal using a first transform coefficient (S112); and generating a second transformed output signal by performing, using a second transform coefficient, a second transform on a first partial signal that is a part of the first transformed output signal (S116), and in the entropy coding (S130), the second transform coefficient or a second inverse transform coefficient is compression coded by calculating a difference between a predetermined value and an element included in the second transform coefficient or a second inverse transform coefficient, and compression codi

Abstract: Some embodiments of a method to automatically compress content in a digital device have been presented. In some embodiments, available data storage space in the digital device is monitored. When the available data storage space falls below a predetermined threshold, a user of the digital device is automatically asked whether the user allows compression of one or more types of content stored on the digital device in order to increase data storage space available.

Abstract: There is provided 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. 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: Embodiments of the present invention may provide a signal processing circuit that may comprises an analog-to-digital converter (ADC), and an output restriction circuit. The output restriction circuit may reduce the accuracy of the digital output of the ADC when signal content exceeds a pre-determined spectrum mask in an undesirable band. In one embodiment, the input signal spectrum may be actively monitored and when the input spectrum is inconsistent with an intended application, the output resolution may be restricted, for example, by truncating least significant bits (LSBs) of the digital output or adding digital noise.

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: 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 history buffer for use in adaptive lossless data compression comprises a plurality of memory locations. The memory locations are partitioned into two or more segments, each segment configured to detect a match sequence independently of the other segments. Control logic is provided for controlling the detection of match sequences between the two or more segments.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for encoding and decoding information. In one aspect, methods of encoding information in an encoder include the actions of receiving a signal representing information using a collection of discrete digits, converting, by an encoder, the received signal into a time-based code, and outputting the time-based code. The time-based code is divided into time intervals. Each of the time intervals of the time-based code corresponds to a digit in the received signal. Each digit of a first state of the received signal is expressed as a event occurring at a first time within the corresponding time interval of the time-based code. Each digit of a second state of the received signal is expressed as a event occurring at a second time within the corresponding time intervals of the time-based code, the first time is distinguishable from the second time.

Abstract: The present invention discloses a method and a device for pulse encoding, and a method and a device for pulse decoding. The method for pulse encoding includes: calculating an index value of an input pulse; selecting an adjustment threshold value according to the number of pulses, and comparing the index value of the pulse with the adjustment threshold value; if the index value is smaller than the adjustment threshold value, adopting the first number of encoding bits to encode the index value, if the index value is not smaller than the adjustment threshold value, adopting the second number of encoding bits to encode the index value plus an offset value, where the first number is smaller than the second number, the first number and the second number are both positive integers, and the offset value is greater than or equal to the adjustment threshold value.

Abstract: Targeted compression of strings is provided for XML and other documents using local tables whose scope need not align with syntactically well-formed document regions. The local table's scope is fixed (not sliding), and may be nested within other local table scopes. A string is nominated for inclusion, and record(s) are inserted in a document encoding to effect the nomination. The nominated string is placed in the local table in correspondence with a token identifier. During compression, reference(s) to the string's token identifier are included in the document encoding; during decompression the references are replaced by the string. The local table is deleted at the end of its scope. Tables may have multiple channels, with nominated strings placed in a channel based on frequency of references to the strings. The document encoding may include the local table(s), static table(s), and dynamic table(s) in a flat token value space.

Abstract: Embodiments described herein may include example embodiments of a method, article and apparatus for compressing data utilizing combinatorial coding which may be used for communicating between two or more components connected to an interconnection medium (e.g., a bus) within a single computer or digital data processing system, and/or for communication between computing platforms via a network or other interconnection medium.

Abstract: The invention provides a method and system for reducing redundant data blocks. The method includes reducing redundant data blocks by decoding a first data block from a first plurality of data blocks and a bitstream.

Abstract: An apparatus includes: a storage storing data input and sliding stored data per input; first and second comparators comparing in parallel the input data with each stored data and obtaining a position of data matching the input data; first and second determiners each determining whether a stored data matches the input data; a holder holding the result by the first or second comparator; a generator generating a value representing the position; a generator obtaining a longest length of a matching data list of the stored data that match the input data compared by the second comparator and that is at positions consecutive over each input, and generating a value representing the length; a generator generating a value using the input data as is; and a generator generating a code including these values. The comparison by the second comparator is controlled based on the result by the first or second comparator.

Abstract: In one embodiment, an initial series of bytes are scanned to determine a frequency of occurrence within the initial series of bytes for a plurality of byte strings. A data structure is generated containing the plurality of byte strings and count values representing a frequency of occurrence for the plurality of byte strings in the initial series of bytes. A most common byte string of the plurality of byte strings in the initial series of bytes is determined from the count values. Each instance of the most common byte string in the initial series of bytes is replaced with a first substitute byte string to form a revised series of bytes. A most common byte string in the revised series of bytes is determined from the data structure without resetting the count values associated with at least some of the plurality of byte strings.

Abstract: The invention relates to compressing of sparse data sets contains sequences of data values and position information therefor. The position information may be in the form of position indices defining active positions of the data values in a sparse vector of length N. The position information is encoded into the data values by adjusting one or more of the data values within a pre-defined tolerance range, so that a pre-defined mapping function of the data values and their positions is close to a target value. In one embodiment, the mapping function is defined using a sub-set of N filler values which elements are used to fill empty positions in the input sparse data vector. At the decoder, the correct data positions are identified by searching though possible sub-sets of filler values.

Abstract: For context based compression techniques, for example Context Based YK compression, a method and system for grouping contexts from a given context model together to create a new context model that has fewer contexts, but retains acceptable compression gains compared to the original context model. According to an exemplary embodiment of the method empirical statistics are determined for a file type of a file to be compressed; and the context model is generated by iteratively grouping contexts of an initial context model in accordance with the empirical statistics, the context model having fewer contexts than an initial context model.

Abstract: A method for encoding an input file into an output file that is compressed so that the number of bits required to represent the output file is less than the number of bits of the input file. The encoding method includes the parsing of the input file into a series of data items, the data items having an order and collectively corresponding to the input file. The encoding method compares the series of data items against a static dictionary having at least mappings between terminal sequence pointers and representations of data items.

Abstract: The present invention, in particular embodiments, is directed to methods, apparatuses and systems that provide an efficient compression technique for data streams transmitted to storage devices or over networks to remote hosts. Local storage as well as network transmission of streams is made more efficient by awareness and utilization of repeated sequences of data blocks. Such data blocks can be placed in a dictionary on persistent storage and shared across all streams. The dictionary is hierarchically indexed (two or more levels of indexing) to combine high efficiency search with efficient access to the stored data blocks. Additionally, data blocks, in particular implementations, are stored sequentially in order to improve overall performance.

Abstract: Methods and apparatus for gathering information from processors by using compressive sampling are presented. The invention can monitor multicore processor performance and schedule processor tasks to optimize processor performance. Using compressive sampling minimizes processor-memory bus usage by the performance monitoring function. An embodiment of the invention is a method of gathering information from a processor, the method comprising compressive sampling of information from at least one processor core. The compressive sampling produces compressed information. The processor comprises the at least one processor core, and the at least one processor core is operative to process data.

Abstract: The invention is made in the technical field of encoding and decoding of bit sequences. The invention proposes a device for compression-encoding an input bit sequence in which Zeroes and Ones occur equally frequent, comprising an XOR gate adapted for receiving pairs of immediately succeeding bits of the input bit sequence as inputs and for outputting further bits of another bit sequence, means for adding a bit to said other bit sequence wherein the added bit is a primary bit which is equal to a primary bit of the input bit sequence or a last bit which is equal to a last bit of the input bit sequence, and means for encoding the other sequence. The XOR gate transforms the input bit sequence into the other bit sequence which comprises more uneven frequencies of occurrence of Zeroes and Ones than the input bit sequence.

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 D/A conversion circuit in accordance with the present invention, which is provided with a switch swD, allows a writing operation of a voltage (a true gradation voltage) to be performed at a higher speed by first applying a first voltage (a voltage close to the true gradation voltage), which is supplied without passing through a resistor element, to an output line and then applying a second voltage (the true gradation voltage), which is supplied via the resistor element, to the output line. Thus, the present invention can provide a D/A conversion circuit capable of writing display data to liquid crystal cells with higher precision at higher speed, and a semiconductor device utilizing such a D/A conversion circuit.

Abstract: A code transforming apparatus inputs therein a first codestream of a target file, and outputs a second codestream transformed from the first codestream. In the code transforming apparatus, a BOX decomposing unit extracts BOX information from the first codestream. A sharing/referencing determining unit determines whether sharing process or referencing process is to be performed on the BOX information. A sharing/referencing processing unit performs the sharing process or the referencing process on the BOX information based on a determination result from the sharing/referencing determining unit. The sharing/referencing processing unit can specify a logical set of codes on a referenced side as a unit of reference for referencing an incremental codestream.

Abstract: Systems and methods for providing fast and efficient data compression using a combination of content independent data compression and content dependent data compression. In one aspect, a method for compressing data comprises the steps of: analyzing a data block of an input data stream to identify a data type of the data block, the input data stream comprising a plurality of disparate data types; performing content dependent data compression on the data block, if the data type of the data block is identified; performing content independent data compression on the data block, if the data type of the data block is not identified.

Abstract: A transient signal encoding method and device, decoding method and device, and processing system, where the transient signal encoding method includes: obtaining a reference sub-frame where a maximal time envelope having a maximal amplitude value is located from time envelopes of all sub-frames of an input transient signal; adjusting an amplitude value of the time envelope of each sub-frame before the reference sub-frame in such a way that a first difference is greater than a preset first threshold, in which the first difference is a difference between the amplitude value of the time envelope of each sub-frame before the reference sub-frame and the amplitude value of the maximal time envelope; and writing the adjusted time envelope into bitstream.

Abstract: Systems and methods of storing previously transmitted data and using it to reduce bandwidth usage and accelerate future communications are described. By using algorithms to identify long compression history matches, a network device may improve compression efficiently and speed. A network device may also use application specific parsing to improve the length and number of compression history matches. Further, by sharing compression histories and compression history indexes across multiple devices, devices can utilize data previously transmitted to other devices to compress network traffic. Any combination of the systems and methods may be used to efficiently find long matches to stored data, synchronize the storage of previously sent data, and share previously sent data among one or more other devices.

Abstract: Systems and methods decode sequentially-dependent data by using a plurality of processing units substantially in parallel. A splitting procedure determines at least one splitting point dividing a data-stream into at least two portions and each processing unit is assigned one portion of the data-stream for decoding. A skimming procedure is performed by at least one processing unit to decode relevant data for at least one portion of the data-stream, where the relevant data is sufficient to enable a processing unit to fully decode another portion of the data-stream. Each processing unit then performs a scanning procedure to fully decode its assigned portion of data-stream substantially in parallel.

Abstract: The invention relates to a computer-implemented method for compressing numerical data comprising a structured set of floating point actual values. A floating point value is defined by a sign, an exponent and a mantissa. The method comprises computing a floating point predicted value related to a target actual value of the set. The computing includes performing operations on integers corresponding to the sign, to the exponent and/or to the mantissa of actual values of a subset of the set. The method also comprises storing a bit sequence representative of a difference between integers derived from the target actual value and the predicted value. Such a method is particularly efficient for reducing the storage size of a CAD file.

Abstract: The present disclosure includes apparatus, systems and techniques relating to lossless data compression. In some implementations, an apparatus includes a memory module to store data. The memory module includes a first buffer portion to store encoded symbols of the data, and a second buffer portion to store symbols of the data to be encoded. The apparatus includes an encoder to compare the symbols stored in the second buffer portion with the encoded symbols stored in the first buffer portion and to compress the data. The encoder can operate in a first encoding mode to encode the symbols in the second buffer portion with corresponding codewords until detecting a repeated pattern of symbols in the second buffer portion that matches the encoded symbols in the first buffer portion. The encoder can operate in a second encoding mode responsive to detecting the repeated pattern.

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: Information that includes first information identifying integer quotients obtained by divisions using prediction residuals or integers not smaller than 0 that increase monotonically with increases in the amplitude of the prediction residuals, as dividends, and a separation parameter decided for a time segment corresponding to the prediction residuals or a mapped integer value of the separation parameter, as a modulus, and second information identifying the remainders obtained when the dividends are divided by the modulus is generated as a code corresponding to the prediction residuals, and each piece of side information that includes the separation parameter is subjected to variable length coding.