Patent Publication Number: US-2023162742-A1

Title: Audio encoder, audio decoder, method for encoding an audio information, method for decoding an audio information and computer program using a detection of a group of previously-decoded spectral values

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of copending U.S. patent application Ser. No. 15/845,616, filed Dec. 18, 2017, which is a continuation of copending U.S. patent application Ser. No. 14/083,412, filed Nov. 18, 2013, now U.S. Pat. No. 9,978,380, issued May 22, 2018, which is a continuation of copending U.S. patent application Ser. No. 13/450,014, Apr. 18, 2012, now U.S. Pat. No. 8,706,510, issued Apr. 22, 2014, which is a continuation of copending International Application No. PCT/EP2010/065725, filed Oct. 19, 2010, which are incorporated herein by reference in their entirety, and additionally claims priority from U.S. Application No. 61/253,459, filed Oct. 20, 2009, which is also incorporated herein by reference in its entirety. 
     Embodiments according to the invention are related to an audio decoder for providing a decoded audio information on the basis of an encoded audio information, an audio encoder for providing an encoded audio information on the basis of an input audio information, a method for providing a decoded audio information on the basis of an encoded audio information, a method for providing an encoded audio information on the basis of an input audio information and a computer program. 
     Embodiments according to the invention are related an improved spectral noiseless coding, which can be used in an audio encoder or decoder, like, for example, a so-called unified speech-and-audio coder (USAC). 
    
    
     BACKGROUND OF THE INVENTION 
     In the following, the background of the invention will be briefly explained in order to facilitate the understanding of the invention and the advantages thereof. During the past decade, big efforts have been put on creating the possibility to digitally store and distribute audio contents with good bitrate efficiency. One important achievement on this way is the definition of the International Standard ISO/IEC 14496-3. Part 3 of this Standard is related to an encoding and decoding of audio contents, and subpart 4 of part 3 is related to general audio coding. ISO/IEC 14496 part 3, subpart 4 defines a concept for encoding and decoding of general audio content. In addition, further improvements have been proposed in order to improve the quality and/or to reduce the bit rate that may be used. 
     According to the concept described in said Standard, a time-domain audio signal is converted into a time-frequency representation. The transform from the time-domain to the time-frequency-domain is typically performed using transform blocks, which are also designated as “frames”, of time-domain samples. It has been found that it is advantageous to use overlapping frames, which are shifted, for example, by half a frame, because the overlap allows to efficiently avoid (or at least reduce) artifacts. In addition, it has been found that a windowing should be performed in order to avoid the artifacts originating from this processing of temporally limited frames. 
     By transforming a windowed portion of the input audio signal from the time-domain to the time-frequency domain, an energy compaction is obtained in many cases, such that some of the spectral values comprise a significantly larger magnitude than a plurality of other spectral values. Accordingly, there are, in many cases, a comparatively small number of spectral values having a magnitude, which is significantly above an average magnitude of the spectral values. A typical example of a time-domain to time-frequency domain transform resulting in an energy compaction is the so-called modified-discrete-cosine-transform (MDCT). 
     The spectral values are often scaled and quantized in accordance with a psychoacoustic model, such that quantization errors are comparatively smaller for psychoacoustically more important spectral values, and are comparatively larger for psychoacoustically less-important spectral values. The scaled and quantized spectral values are encoded in order to provide a bitrate-efficient representation thereof. 
     For example, the usage of a so-called Huffman coding of quantized spectral coefficients is described in the International Standard ISO/IEC 14496-3:2005(E), part 3, subpart 4. 
     However, it has been found that the quality of the coding of the spectral values has a significant impact on the bitrate that may be used. Also, it has been found that the complexity of an audio decoder, which is often implemented in a portable consumer device, and which should therefore be cheap and of low power consumption, is dependent on the coding used for encoding the spectral values. 
     In view of this situation, there is a need for a concept for an encoding and decoding of an audio content, which provides for an improved trade-off between bitrate-efficiency and resource efficiency. 
     SUMMARY 
     According to an embodiment, an audio decoder for providing a decoded audio information on the basis of an encoded audio information may have: an arithmetic decoder for providing a plurality of decoded spectral values on the basis of an arithmetically-encoded representation of the spectral values; and a frequency-domain-to-time-domain converter for providing a time-domain audio representation using the decoded spectral values, in order to acquire the decoded audio information; wherein the arithmetic decoder is configured to select a mapping rule describing a mapping of a code value onto a symbol code in dependence on a context state; and wherein the arithmetic decoder is configured to determine the current context state in dependence on a plurality of previously-decoded spectral values, wherein the arithmetic decoder is configured to detect a group of a plurality of previously-decoded spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes, and to determine or modify the current context state in dependence on a result of the detection. 
     According to another embodiment, an audio encoder for providing an encoded audio information on the basis of an input audio information may have: an energy-compacting time-domain-to-frequency-domain converter for providing a frequency-domain audio representation on the basis of a time-domain representation of the input audio information, such that the frequency-domain audio representation has a set of spectral values; and an arithmetic encoder configured to encode a spectral value or a preprocessed version thereof, using a variable length codeword, wherein the arithmetic encoder is configured to map a spectral value, or a value of a most significant bitplane of a spectral value onto a code value, wherein the arithmetic encoder is configured to select a mapping rule describing a mapping of a spectral value, or of a most significant bitplane of a spectral value, onto a code value, in dependence on a context state; and wherein the arithmetic encoder is configured to determine the current context state in dependence on a plurality of previously-encoded spectral values, wherein the arithmetic encoder is configured to detect a group of a plurality of previously-encoded spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes, and to determine or modify the current context state in dependence on a result of the detection. 
     According to another embodiment, a method for providing a decoded audio information on the basis of an encoded audio information may have the steps of: providing a plurality of decoded spectral values on the basis of an arithmetically-encoded representation of the spectral values; and providing a time-domain audio representation using the decoded spectral values, in order to acquire the decoded audio information; wherein providing the plurality of decoded spectral values includes selecting a mapping rule describing a mapping of a code value representing a spectral value, or a most-significant bit-plane of a spectral value, in an encoded form onto a symbol code representing a spectral value, or a most-significant bit-plane of a spectral value, in a decoded form, in dependence on a context state; and wherein the current context state is determined in dependence on a plurality of previously decoded spectral values, wherein a group of a plurality of previously-decoded spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes is detected, and wherein the current context state is determined or modified in dependence on a result of the detection. 
     According to another embodiment, a method for providing an encoded audio information on the basis of an input audio information may have the steps of: providing a frequency-domain audio representation on the basis of a time-domain representation of the input audio information using an energy-compacting time-domain-to-frequency-domain conversion, such that the frequency-domain audio representation has a set of spectral values; and arithmetically encoding a spectral value, or a preprocessed version thereof, using a variable-length codeword, wherein a spectral value or a value of a most significant bitplane of a spectral value is mapped onto a code value; wherein a mapping rule describing a mapping of a spectral value, or of a most significant bitplane of a spectral value, onto a code value is selected in dependence on a context state; and wherein a current context state is determined in dependence on a plurality of previously-encoded adjacent spectral values; and wherein a group of a plurality of previously-decoded spectral values, which fulfill, individually or together, a predetermined condition regarding their magnitudes, is detected and the current context state is determined or modified in dependence on a result of the detection. 
     Another embodiment may have a computer program for performing the method for providing a decoded audio information on the basis of an encoded audio information, which method may have the steps of: providing a plurality of decoded spectral values on the basis of an arithmetically-encoded representation of the spectral values; and providing a time-domain audio representation using the decoded spectral values, in order to acquire the decoded audio information; wherein providing the plurality of decoded spectral values includes selecting a mapping rule describing a mapping of a code value representing a spectral value, or a most-significant bit-plane of a spectral value, in an encoded form onto a symbol code representing a spectral value, or a most-significant bit-plane of a spectral value, in a decoded form, in dependence on a context state; and wherein the current context state is determined in dependence on a plurality of previously decoded spectral values, wherein a group of a plurality of previously-decoded spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes is detected, and wherein the current context state is determined or modified in dependence on a result of the detection, when the program runs on a computer. 
     Another embodiment may have a computer program for performing the method for providing an encoded audio information on the basis of an input audio information, which method may have the steps of: providing a frequency-domain audio representation on the basis of a time-domain representation of the input audio information using an energy-compacting time-domain-to-frequency-domain conversion, such that the frequency-domain audio representation has a set of spectral values; and arithmetically encoding a spectral value, or a preprocessed version thereof, using a variable-length codeword, wherein a spectral value or a value of a most significant bitplane of a spectral value is mapped onto a code value; wherein a mapping rule describing a mapping of a spectral value, or of a most significant bitplane of a spectral value, onto a code value is selected in dependence on a context state; and wherein a current context state is determined in dependence on a plurality of previously-encoded adjacent spectral values; and wherein a group of a plurality of previously-decoded spectral values, which fulfill, individually or together, a predetermined condition regarding their magnitudes, is detected and the current context state is determined or modified in dependence on a result of the detection, when the program runs on a computer. 
     An embodiment according to the invention creates an audio decoder for providing a decoded audio information (or decoded audio representation) on the basis of an encoded audio information (or encoded audio representation). The audio decoder comprises an arithmetic decoder for providing a plurality of decoded spectral values on the basis of an arithmetically-encoded representation of the spectral values. The audio decoder also comprises a frequency-domain to time-domain converter for providing a time-domain audio representation using the decoded spectral values, in order to obtain the decoded audio information. The arithmetic decoder is configured to select a mapping rule describing a mapping of a code-value onto a symbol code in dependence on a context state. The arithmetic decoder is configured to determine the current context state in dependence on a plurality of previously-decoded spectral values. The arithmetic decoder is configured to detect a group of a plurality of previously-decoded spectral values, which fulfil, individually or taken together, a predetermined condition regarding their magnitudes, and to determine or modify the current context state in dependence on a result of the detection. 
     This embodiment according to the invention is based on the finding that the presence of a group of a plurality of previously-decoded (advantageously, but not necessarily, adjacent) spectral values, which fulfill the predetermined condition regarding their magnitudes, allows for a particularly efficient determination of the current context state since such a group of previously-decoded (advantageously adjacent) spectral values is a characteristic feature within the spectral representation, and can therefore be used to facilitate the determination of the current context state. By detecting a group of a plurality of previously-decoded (advantageously adjacent) spectral values which comprise, for example, a particularly small magnitude, it is possible to recognize portions of comparatively low amplitude within the spectrum, and to adjust (determine or modify) the current context state accordingly, such that further spectral values can be encoded and decoded with good coding efficiency (in terms of bitrate). Alternatively, groups of a plurality of previously-decoded adjacent spectral values which comprise a comparatively large amplitude can be detected, and the context can be appropriately adjusted (determined or modified) to increase the efficiency of the encoding and decoding. Furthermore, the detection of groups of a plurality of previously-decoded (advantageously adjacent) spectral values which fulfill, individually or taken together, the predetermined condition, is often executable with lower computational effort than a context computation in which many previously-decoded spectral values are combined. To summarize, the above discussed embodiment according to the invention, allows for a simplified context computation and allows for an adjustment of the context to specific signal constellations in which, there are groups of adjacent comparatively small spectral values or groups of adjacent comparatively large spectral values. 
     In an advantageous embodiment, the arithmetic decoder is configured to determine or modify the current context state independent from the previously decoded spectral values in response to the detection that the predetermined condition is fulfilled. Accordingly, a computationally particularly efficient mechanism is obtained for the derivation of a value describing the context. It has been found that a meaningful adaptation of the context can be achieved if the detection of a group of a plurality of previously decoded spectral values, which fulfill the predetermined condition, results in a simple mechanism, which does not require a computationally demanding numeric combination of previously decoded spectral values. Thus, the computational effort is reduced when compared to other approaches. Also, an acceleration of the context derivation can be achieved by omitting complex calculation steps which are dependent on the detection, because such a concept is typically inefficient in a software implementation executed on a processor. 
     In an advantageous embodiment, the arithmetic decoder is configured to detect a group of a plurality of previously-decoded adjacent spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes. 
     In an advantageous embodiment, the arithmetic decoder is configured to detect a group of a plurality of previously-decoded adjacent spectral values which, individually or taken together, comprise a magnitude which is smaller than a predetermined threshold magnitude, and to determine the current context state in dependence on the result of the detection. It has been found that a group of a plurality of adjacent comparatively low spectral values may be used for selecting a context which is well-adapted to this situation. If there is a group of adjacent comparatively small spectral values, there is a significant probability that the spectral value to be decoded next also comprises a comparatively small value. Accordingly, an adjustment of the context provides a good encoding efficiency and may assist in the avoidance of time consuming context computations. 
     In an advantageous embodiment, the arithmetic decoder is configured to detect a group of a plurality of previously-decoded adjacent spectral values, wherein each of the previously-decoded spectral values is a zero value, and to determine the context state in dependence on the result of the detection. It has been found that due to spectral or temporal masking effects, there are often groups of adjacent spectral values which take a zero value. The described embodiment provides an efficient handling for this situation. In addition, the presence of a group of adjacent spectral values, which are quantized to zero, makes it very probable that the spectral value to be decoded next is either, a zero value or a comparatively large spectral value, which results in the masking effect. 
     In an advantageous embodiment, the arithmetic decoder is configured to detect a group of a plurality of previously-decoded adjacent spectral values, which comprise a sum value which is smaller than a predetermined threshold value, and to determine the context state in dependence on a result of the detection. It has been found that in addition to groups of adjacent spectral values which are zero, also groups of adjacent spectral values which are almost zero in an average (i.e. a sum value of which is smaller than a predetermined threshold value), constitute a characteristic feature of a spectral representation (e.g. a time-frequency representation of the audio content) which can be used for the adaptation of the context. 
     In an advantageous embodiment, the arithmetic decoder is configured to set the current context state to a predetermined value in response to the detection of the predetermined condition. It has been found that this reaction is very simple to implement and still results in an adaptation of the context which provides for a good coding efficiency. 
     In an advantageous embodiment, the arithmetic decoder is configured to selectively omit a calculation of the current context state in dependence on the numeric values of a plurality of previously-decoded spectral values in response to the detection of the predetermined condition. Accordingly, the context computation is significantly simplified in response to the detection of a group of a plurality of previously-decoded adjacent spectral values which fulfill the predetermined condition. By saving computational effort, a power consumption of the audio signal decoder is also reduced, which provides for significant advantages in mobile devices. 
     In an advantageous embodiment, the arithmetic decoder is configured to set the current context state to a value which signals the detection of the predetermined condition. By setting the context state to such a value, which may be within a predetermined range of values, the later evaluation of the context state may be controlled. However, it should be noted that the value to which the current context state is set, may be dependent on other criteria as well, even though the value may be in a characteristic range of values which signals the detection of the predetermined condition. 
     In an advantageous embodiment, the arithmetic decoder is configured to map a symbol code onto a decoded spectral value. 
     In an advantageous embodiment, the arithmetic decoder is configured to evaluate spectral values of a first time-frequency region, to detect a group of a plurality of spectral values which fulfill, individually or taken together, the predetermined condition regarding their magnitudes. The arithmetic decoder is configured to obtain a numeric value which represents the context state, in dependence on spectral values of a second time frequency region, which is different from the first time frequency region, if the predetermined condition is not fulfilled. It has been found that it is recommendable to detect a group of a plurality of spectral values that fulfill the predetermined condition regarding the magnitude within a region which differs from the region normally used for the context computation. This is due to the fact that an extension, for example, a frequency extension, of regions comprising comparatively small spectral values, or comparatively large spectral values, is typically larger than a dimension of a region of spectral values that are to be considered for a numeric calculation of a numeric value representing the context state. Accordingly, it is recommendable to analyze different regions for the detection of a group of a plurality of spectral values fulfilling the predetermined condition, and for the numeric computation of a numeric value representing the context state (wherein the numeric calculation may only be expected in a second step if the detection does not provide a bit. 
     In an advantageous embodiment, the arithmetic decoder is configured to evaluate one or more hash tables to select a mapping rule in dependence on the context state. It has been found that the selection of the mapping rule can be controlled by the mechanism of detecting a plurality of adjacent spectral values which fulfill the predetermined condition. 
     An embodiment according to the invention creates an audio encoder for providing an encoded audio information, on the basis of an input audio information. The audio encoder comprises an energy-compacting time-domain-to-frequency-domain converter for providing a frequency-domain audio representation, on the basis of a time-domain representation of the input audio information, such that the frequency-domain audio representation comprises a set of spectral values. The audio encoder also comprises an arithmetic encoder configured to encode a spectral value, or a pre-processed version thereof, using a variable-length codeword. The arithmetic encoder is configured to map a spectral value or a value of a most-significant bit-plane of a spectral value onto a code value. The arithmetic encoder is configured to select a mapping rule describing a mapping of a spectral value or of a most-significant bit-plane of a spectral value onto a code value in dependence on the context state. The arithmetic encoder is configured to determine the current context state in dependence on a plurality of previously-encoded adjacent spectral values. The arithmetic encoder is configured to detect a group of a plurality of previously-encoded adjacent spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes, and to determine the current context state in dependence on a result of the detection. 
     This audio signal encoder is based on the same findings as the audio signal decoder discussed above. It has been found that the mechanism for the adaptation of the context, which has been shown to be efficient for the decoding of an audio content, should also be applied at the encoder side, in order to allow for a consistent system. 
     An embodiment according to the invention creates a method for providing decoded audio information on the basis of encoded audio information. 
     Yet another embodiment according to the invention creates a method for providing encoded audio information on the basis of an input audio information. 
     Another embodiment according to the invention creates a computer program for performing one of said methods. 
     The methods and the computer program are based on the same findings as the above described audio decoder and the above described audio encoder. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments according to the present invention will subsequently be described taking reference to the enclosed figures, in which: 
         FIGS.  1   a - 1   b    show a block schematic diagram of an audio encoder, according to an embodiment of the invention; 
         FIGS.  2   a - 2   b    show a block schematic diagram of an audio decoder, according to an embodiment of the invention; 
         FIG.  3    shows a pseudo-program-code representation of an algorithm “value_decode( )” for decoding a spectral value; 
         FIG.  4    shows a schematic representation of a context for a state calculation; 
         FIG.  5   a    shows a pseudo-program-code representation of an algorithm “arith_map_context( )” for mapping a context; 
         FIGS.  5   b  and  5   c    show a pseudo-program-code representation of an algorithm “arith_get_context( )” for obtaining a context state value; 
         FIGS.  5   d     1  and  5   d   2  show a pseudo-program-code representation of an algorithm “get_pk(s)” for deriving a cumulative-frequencies-table index value “pki” from a state variable; 
         FIG.  5   e    shows a pseudo-program-code representation of an algorithm “arith_get_pk(s)” for deriving a cumulative-frequencies-table index value “pki” from a state value; 
         FIG.  5   f    shows a pseudo-program-code representation of an algorithm “get_pk(unsigned long s)” for deriving a cumulative-frequencies-table index value “pki” from a state value; 
         FIGS.  5   g     1  and  5   g   2  show a pseudo-program-code representation of an algorithm “arith_decode( )” for arithmetically decoding a symbol from a variable-length codeword; 
         FIG.  5   h    shows a pseudo-program-code representation of an algorithm “arith_update_context( )” for updating the context; 
         FIG.  5   i    shows a legend of definitions and variables; 
         FIG.  6   a    shows as syntax representation of a unified-speech-and-audio-coding (USAC) raw data block; 
         FIG.  6   b    shows a syntax representation of a single channel element; 
         FIG.  6   c    shows syntax representation of a channel pair element; 
         FIG.  6   d    shows a syntax representation of an “ics” control information; 
         FIG.  6   e    shows a syntax representation of a frequency-domain channel stream; 
         FIG.  6   f    shows a syntax representation of arithmetically-coded spectral data; 
         FIG.  6   g    shows a syntax representation for decoding a set of spectral values; 
         FIG.  6   h    shows a legend of data elements and variables; 
         FIG.  7    shows a block schematic diagram of an audio encoder, according to another embodiment of the invention: 
         FIG.  8    shows a block schematic diagram of an audio decoder, according to another embodiment of the invention; 
         FIG.  9    shows an arrangement for a comparison of a noiseless coding according to a working draft 3 of the USAC draft standard with a coding scheme according to the present invention: 
         FIG.  10   a    shows a schematic representation of a context for a state calculation, as it is used in accordance with the working draft 4 of the USAC draft standard; 
         FIG.  10   b    shows a schematic representation of a context for a state calculation, as it is used in embodiments according to the invention; 
         FIG.  11   a    shows an overview of the table as used in the arithmetic coding scheme according to the working draft 4 of the USAC draft standard; 
         FIG.  11   b    shows an overview of the table as used in the arithmetic coding scheme according to the present invention; 
         FIG.  12   a    shows a graphical representation of a read-only memory demand for the noiseless coding schemes according to the present invention and according to the working draft 4 of the USAC draft standard; 
         FIG.  12   b    shows a graphical representation of a total USAC decoder data read-only memory demand in accordance with the present invention and in accordance with the concept according to the working draft 4 of the USAC draft standard; 
         FIG.  13   a    shows a table representation of average bitrates which are used by a unified-speech-and-audio-coding coder, using an arithmetic coder according to the working draft 3 of the USAC draft standard and an arithmetic decoder according to an embodiment of the present invention; 
         FIG.  13   b    shows a table representation of a bit reservoir control for a unified-speech-and-audio-coding coder, using the arithmetic coder according to the working draft 3 of the USAC draft standard and the arithmetic coder according to an embodiment of the present invention; 
         FIG.  14    shows a table representation of average bitrates for a USAC coder according to the working draft 3 of the USAC draft standard, and according to an embodiment of the present invention; 
         FIG.  15    shows a table representation of minimum, maximum and average bitrates of USAC on a frame basis; 
         FIG.  16    shows a table representation of the best and worst cases on a frame basis; 
         FIGS.  17   ( 1 ) and  17 ( 2 ) show a table representation of a content of a table “ari_s_hash[387]”; 
         FIG.  18    shows a table representation of a content of a table “ari_gs_hash[225]”; 
         FIGS.  19   ( 1 ) and  19 ( 2 ) show a table representation of a content of a table “ari_cf_m[64][9]”; and 
         FIGS.  20   ( 1 ) and  20 ( 2 ) show a table representation of a content of a table “ari_s_hash[387]. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     1. Audio Encoder According to  FIG.  7     
       FIG.  7    shows a block schematic diagram of an audio encoder, according to an embodiment of the invention. The audio encoder  700  is configured to receive an input audio information  710  and to provide, on the basis thereof, an encoded audio information  712 . The audio encoder comprises an energy-compacting time-domain-to-frequency-domain converter  720  which is configured to provide a frequency-domain audio representation  722  on the basis of a time-domain representation of the input audio information  710 , such that the frequency-domain audio representation  722  comprises a set of spectral values. The audio encoder  700  also comprises an arithmetic encoder  730  configured to encode a spectral value (out of the set of spectral values forming the frequency-domain audio representation  722 ), or a pre-processed version thereof, using a variable-length codeword, to obtain the encoded audio information  712  (which may comprise, for example, a plurality of variable-length codewords). 
     The arithmetic encoder  730  is configured to map a spectral value or a value of a most-significant bit-plane of a spectral value onto a code value (i.e. onto a variable-length codeword), in dependence on a context state. The arithmetic encoder  730  is configured to select a mapping rule describing a mapping of a spectral value, or of a most-significant bit-plane of a spectral value, onto a code value, in dependence on a context state. The arithmetic encoder is configured to determine the current context state in dependence on a plurality of previously-encoded (advantageously, but not necessarily, adjacent) spectral values. For this purpose, the arithmetic encoder is configured to detect a group of a plurality of previously-encoded adjacent spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes, and determine the current context state in dependence on a result of the detection. 
     As can be seen, the mapping of a spectral value or of a most-significant bit-plane of a spectral value onto a code value may be performed by a spectral value encoding  740  using a mapping rule  742 . A state tracker  750  may be configured to track the context state and may comprise a group detector  752  to detect a group of a plurality of previously-encoded adjacent spectral values which fulfill, individually or taken together, the predetermined condition regarding their magnitudes. The state tracker  750  is also advantageously configured to determine the current context state in dependence on the result of said detection performed by the group detector  752 . Accordingly, the state tracker  750  provides an information  754  describing the current context state. A mapping rule selector  760  may select a mapping rule, for example, a cumulative-frequencies-table, describing a mapping of a spectral value, or of a most-significant bit-plane of a spectral value, onto a code value. Accordingly, the mapping rule selector  760  provides the mapping rule information  742  to the spectral encoding  740 . 
     To summarize the above, the audio encoder  700  performs an arithmetic encoding of a frequency-domain audio representation provided by the time-domain-to-frequency-domain converter. The arithmetic encoding is context-dependent, such that a mapping rule (e.g., a cumulative-frequencies-table) is selected in dependence on previously-encoded spectral values. Accordingly, spectral values adjacent in time and/or frequency (or at least, within a predetermined environment) to each other and/or to the currently-encoded spectral value (i.e. spectral values within a predetermined environment of the currently encoded spectral value) are considered in the arithmetic encoding to adjust the probability distribution evaluated by the arithmetic encoding. When selecting an appropriate mapping rule, a detection is performed in order to detect whether there is a group of a plurality of previously-encoded adjacent spectral values which fulfill, individually or taken together, a predetermined condition regarding their magnitudes. The result of this detection is applied in the selection of the current context state, i.e. in the selection of a mapping rule. By detecting whether there is a group of a plurality of spectral values which are particularly small or particularly large, it is possible to recognize special features within the frequency-domain audio representation, which may be a time-frequency representation. Special features such as, for example, a group of a plurality of particularly small or particularly large spectral values, indicate that a specific context state should be used as this specific context state may provide a particularly good coding efficiency. Thus, the detection of the group of adjacent spectral values which fulfill the predetermined condition, which is typically used in combination with an alternative context evaluation based on a combination of a plurality of previously-coded spectral values, provides a mechanism which allows for an efficient selection of an appropriate context if the input audio information takes some special states (e.g., comprises a large masked frequency range). 
     Accordingly, an efficient encoding can be achieved while keeping the context calculation sufficiently simple. 
     2. Audio Decoder According to  FIG.  8     
       FIG.  8    shows a block schematic diagram of an audio decoder  800 . The audio decoder  800  is configured to receive an encoded audio information  810  and to provide, on the basis thereof, a decoded audio information  812 . The audio decoder  800  comprises an arithmetic decoder  820  that is configured to provide a plurality of decoded spectral values  822  on the basis of an arithmetically-encoded representation  821  of the spectral values. The audio decoder  800  also comprises a frequency-domain-to-time-domain converter  830  which is configured to receive the decoded spectral values  822  and to provide the time-domain audio representation  812 , which may constitute the decoded audio information, using the decoded spectral values  822 , in order to obtain a decoded audio information  812 . 
     The arithmetic decoder  820  comprises a spectral value determinator  824  which is configured to map a code value of the arithmetically-encoded representation  821  of spectral values onto a symbol code representing one or more of the decoded spectral values, or at least a portion (for example, a most-significant bit-plane) of one or more of the decoded spectral values. The spectral value determinator  824  may be configured to perform the mapping in dependence on a mapping rule, which may be described by a mapping rule information  828   a.    
     The arithmetic decoder  820  is configured to select a mapping rule (e.g. a cumulative-frequencies-table) describing a mapping of a code-value (described by the arithmetically-encoded representation  821  of spectral values) onto a symbol code (describing one or more spectral values) in dependence on a context state (which may be described by the context state information  826   a ). The arithmetic decoder  820  is configured to determine the current context state in dependence on a plurality of previously-decoded spectral values  822 . For this purpose, a state tracker  826  may be used, which receives an information describing the previously-decoded spectral values. The arithmetic decoder is also configured to detect a group of a plurality of previously-decoded (advantageously, but not necessarily, adjacent) spectral values, which fulfill, individually or taken together, a predetermined condition regarding their magnitudes, and to determine the current context state (described, for example, by the context state information  826   a ) in dependence on a result of the detection. 
     The detection of the group of a plurality of previously-decoded adjacent spectral values which fulfill the predetermined condition regarding their magnitudes may, for example, be performed by a group detector, which is part of the state tracker  826 . Accordingly, a current context state information  826   a  is obtained. The selection of the mapping rule may be performed by a mapping rule selector  828 , which derives a mapping rule information  828   a  from the current context state information  826   a , and which provides the mapping rule information  828   a  to the spectral value determinator  824 . 
     Regarding the functionality of the audio signal decoder  800 , it should be noted that the arithmetic decoder  820  is configured to select a mapping rule (e.g. a cumulative-frequencies-table) which is, on an average, well-adapted to the spectral value to be decoded, as the mapping rule is selected in dependence on the current context state, which in turn is determined in dependence on a plurality of previously-decoded spectral values. Accordingly, statistical dependencies between adjacent spectral values to be decoded can be exploited. Moreover, by detecting a group of a plurality of previously-decoded adjacent spectral values which fulfill, individually or taken together, a predetermined condition regarding their magnitudes, it is possible to adapt the mapping rule to special conditions (or patterns) of previously-decoded spectral values. For example, a specific mapping rule may be selected if a group of a plurality of comparatively small previously-decoded adjacent spectral values is identified, or if a group of a plurality of comparatively large previously-decoded adjacent spectral values is identified. It has been found that the presence of a group of comparatively large spectral values or of a group of comparatively small spectral values may be considered as a significant indication that a dedicated mapping rule, specifically adapted to such a condition, should be used. Accordingly, a context computation can be facilitated (or accelerated) by exploiting the detection of such a group of a plurality of spectral values. Also, characteristics of an audio content can be considered that could not be considered as easily without applying the above-mentioned concept. For example, the detection of a group of a plurality of spectral values which fulfill, individually or taken together, a predetermined condition regarding their magnitudes, can be performed on the basis of a different set of spectral values, when compared to the set of spectral values used for a normal context computation. 
     Further details will be described below. 
     3. Audio Encoder According to  FIG.  1     
     In the following, an audio encoder according to an embodiment of the present invention will be described.  FIG.  1    shows a block schematic diagram of such an audio encoder  100 . 
     The audio encoder  100  is configured to receive an input audio information  110  and to provide, on the basis thereof, a bitstream  112 , which constitutes an encoded audio information. The audio encoder  100  optionally comprises a preprocessor  120 , which is configured to receive the input audio information  110  and to provide, on the basis thereof, a pre-processed input audio information  110   a . The audio encoder  100  also comprises an energy-compacting time-domain to frequency-domain signal transformer  130 , which is also designated as signal converter. The signal converter  130  is configured to receive the input audio information  110 ,  110   a  and to provide, on the basis thereof, a frequency-domain audio information  132 , which advantageously takes the form of a set of spectral values. For example, the signal transformer  130  may be configured to receive a frame of the input audio information  110 ,  110   a  (e.g. a block of time-domain samples) and to provide a set of spectral values representing the audio content of the respective audio frame. In addition, the signal transformer  130  may be configured to receive a plurality of subsequent, overlapping or non-overlapping, audio frames of the input audio information  110 ,  110   a  and to provide, on the basis thereof, a time-frequency-domain audio representation, which comprises a sequence of subsequent sets of spectral values, one set of spectral values associated with each frame. 
     The energy-compacting time-domain to frequency-domain signal transformer  130  may comprise an energy-compacting filterbank, which provides spectral values associated with different, overlapping or non-overlapping, frequency ranges. For example, the signal transformer  130  may comprise a windowing MDCT transformer  130   a , which is configured to window the input audio information  110 ,  110   a  (or a frame thereof) using a transform window and to perform a modified-discrete-cosine-transform of the windowed input audio information  110 ,  110   a  (or of the windowed frame thereof). Accordingly, the frequency-domain audio representation  132  may comprise a set of, for example, 1024 spectral values in the form of MDCT coefficients associated with a frame of the input audio information. 
     The audio encoder  100  may further, optionally, comprise a spectral post-processor  140 , which is configured to receive the frequency-domain audio representation  132  and to provide, on the basis thereof, a post-processed frequency-domain audio representation  142 . The spectral post-processor  140  may, for example, be configured to perform a temporal noise shaping and/or a long term prediction and/or any other spectral post-processing known in the art. The audio encoder further comprises, optionally, a scaler/quantizer  150 , which is configured to receive the frequency-domain audio representation  132  or the post-processed version  142  thereof and to provide a scaled and quantized frequency-domain audio representation  152 . 
     The audio encoder  100  further comprises, optionally, a psycho-acoustic model processor  160 , which is configured to receive the input audio information  110  (or the post-processed version  110   a  thereof) and to provide, on the basis thereof, an optional control information, which may be used for the control of the energy-compacting time-domain to frequency-domain signal transformer  130 , for the control of the optional spectral post-processor  140  and/or for the control of the optional scaler/quantizer  150 . For example, the psycho-acoustic model processor  160  may be configured to analyze the input audio information, to determine which components of the input audio information  110 ,  110   a  are particularly important for the human perception of the audio content and which components of the input audio information  110 ,  110   a  are less important for the perception of the audio content. Accordingly, the psycho-acoustic model processor  160  may provide control information, which is used by the audio encoder  100  in order to adjust the scaling of the frequency-domain audio representation  132 ,  142  by the scaler/quantizer  150  and/or the quantization resolution applied by the scaler/quantizer  150 . Consequently, perceptually important scale factor bands (i.e. groups of adjacent spectral values which are particularly important for the human perception of the audio content) are scaled with a large scaling factor and quantized with comparatively high resolution, while perceptually less-important scale factor bands (i.e. groups of adjacent spectral values) are scaled with a comparatively smaller scaling factor and quantized with a comparatively lower quantization resolution. Accordingly, scaled spectral values of perceptually more important frequencies are typically significantly larger than spectral values of perceptually less important frequencies. 
     The audio encoder also comprises an arithmetic encoder  170 , which is configured to receive the scaled and quantized version  152  of the frequency-domain audio representation  132  (or, alternatively, the post-processed version  142  of the frequency-domain audio representation  132 , or even the frequency-domain audio representation  132  itself) and to provide arithmetic codeword information  172   a  on the basis thereof, such that the arithmetic codeword information represents the frequency-domain audio representation  152 . 
     The audio encoder  100  also comprises a bitstream payload formatter  190 , which is configured to receive the arithmetic codeword information  172   a . The bitstream payload formatter  190  is also typically configured to receive additional information, like, for example, scale factor information describing which scale factors have been applied by the scaler/quantizer  150 . In addition, the bitstream payload formatter  190  may be configured to receive other control information. The bitstream payload formatter  190  is configured to provide the bitstream  112  on the basis of the received information by assembling the bitstream in accordance with a desired bitstream syntax, which will be discussed below. 
     In the following, details regarding the arithmetic encoder  170  will be described. The arithmetic encoder  170  is configured to receive a plurality of post-processed and scaled and quantized spectral values of the frequency-domain audio representation  132 . The arithmetic encoder comprises a most-significant-bit-plane-extractor  174 , which is configured to extract a most-significant bit-plane m from a spectral value. It should be noted here that the most-significant bit-plane may comprise one or even more bits (e.g. two or three bits), which are the most-significant bits of the spectral value. Thus, the most-significant bit-plane extractor  174  provides a most-significant bit-plane value  176  of a spectral value. 
     The arithmetic encoder  170  also comprises a first codeword determinator  180 , which is configured to determine an arithmetic codeword acod_m [pki][m] representing the most-significant bit-plane value m. Optionally, the codeword determinator  180  may also provide one or more escape codewords (also designated herein with “ARITH_ESCAPE”) indicating, for example, how many less-significant bit-planes are available (and, consequently, indicating the numeric weight of the most-significant bit-plane). The first codeword determinator  180  may be configured to provide the codeword associated with a most-significant bit-plane value m using a selected cumulative-frequencies-table having (or being referenced by) a cumulative-frequencies-table index ph. 
     In order to determine as to which cumulative-frequencies-table should be selected, the arithmetic encoder advantageously comprises a state tracker  182 , which is configured to track the state of the arithmetic encoder, for example, by observing which spectral values have been encoded previously. The state tracker  182  consequently provides a state information  184 , for example, a state value designated with “s” or “t”. The arithmetic encoder  170  also comprises a cumulative-frequencies-table selector  186 , which is configured to receive the state information  184  and to provide an information  188  describing the selected cumulative-frequencies-table to the codeword determinator  180 . For example, the cumulative-frequencies-table selector  186  may provide a cumulative-frequencies-table index “pki” describing which cumulative-frequencies-table, out of a set of 64 cumulative-frequencies-tables, is selected for usage by the codeword determinator. Alternatively, the cumulative-frequencies-table selector  186  may provide the entire selected cumulative-frequencies-table to the codeword determinator. Thus, the codeword determinator  180  may use the selected cumulative-frequencies-table for the provision of the codeword acod_m[pki][m] of the most-significant bit-plane value m, such that the actual codeword acod_m[pki][m] encoding the most-significant bit-plane value m is dependent on the value of m and the cumulative-frequencies-table index pki, and consequently on the current state information  184 . Further details regarding the coding process and the obtained codeword format will be described below. 
     The arithmetic encoder  170  further comprises a less-significant bit-plane extractor  189   a , which is configured to extract one or more less-significant bit-planes from the scaled and quantized frequency-domain audio representation  152 , if one or more of the spectral values to be encoded exceed the range of values encodable using the most-significant bit-plane only. The less-significant bit-planes may comprise one or more bits, as desired. Accordingly, the less-significant bit-plane extractor  189   a  provides a less-significant bit-plane information  189   b . The arithmetic encoder  170  also comprises a second codeword determinator  189   c , which is configured to receive the less-significant bit-plane information  189   d  and to provide, on the basis thereof, 0, 1 or more codewords “acod_r” representing the content of 0, 1 or more less-significant bit-planes. The second codeword determinator  189   c  may be configured to apply an arithmetic encoding algorithm or any other encoding algorithm in order to derive the less-significant bit-plane codewords “acod_r” from the less-significant bit-plane information  189   b.    
     It should be noted here that the number of less-significant bit-planes may vary in dependence on the value of the scaled and quantized spectral values  152 , such that there may be no less-significant bit-plane at all, if the scaled and quantized spectral value to be encoded is comparatively small, such that there may be one less-significant bit-plane if the current scaled and quantized spectral value to be encoded is of a medium range and such that there may be more than one less-significant bit-plane if the scaled and quantized spectral value to be encoded takes a comparatively large value. 
     To summarize the above, the arithmetic encoder  170  is configured to encode scaled and quantized spectral values, which are described by the information  152 , using a hierarchical encoding process. The most-significant bit-plane (comprising, for example, one, two or three bits per spectral value) is encoded to obtain an arithmetic codeword “acod_m[pki][m]” of a most-significant bit-plane value. One or more less-significant bit-planes (each of the less-significant bit-planes comprising, for example, one, two or three bits) are encoded to obtain one or more codewords “acod_r”. When encoding the most-significant bit-plane, the value m of the most-significant bit-plane is mapped to a codeword acod_m[pki][m]. For this purpose, 64 different cumulative-frequencies-tables are available for the encoding of the value m in dependence on a state of the arithmetic encoder  170 , i.e. in dependence on previously-encoded spectral values. Accordingly, the codeword “acod_m[pki][m]” is obtained. In addition, one or more codewords “acod_r” are provided and included into the bitstream if one or more less-significant bit-planes are present. 
     Reset Description 
     The audio encoder  100  may optionally be configured to decide whether an improvement in bitrate can be obtained by resetting the context, for example by setting the state index to a default value. Accordingly, the audio encoder  100  may be configured to provide a reset information (e.g. named “arith_reset_flag”) indicating whether the context for the arithmetic encoding is reset, and also indicating whether the context for the arithmetic decoding in a corresponding decoder should be reset. 
     Details regarding the bitstream format and the applied cumulative-frequency tables will be discussed below. 
     4. Audio Decoder 
     In the following, an audio decoder according to an embodiment of the invention will be described.  FIG.  2    shows a block schematic diagram of such an audio decoder  200 . 
     The audio decoder  200  is configured to receive a bitstream  210 , which represents an encoded audio information and which may be identical to the bitstream  112  provided by the audio encoder  100 . The audio decoder  200  provides a decoded audio information  212  on the basis of the bitstream  210 . 
     The audio decoder  200  comprises an optional bitstream payload de-formatter  220 , which is configured to receive the bitstream  210  and to extract from the bitstream  210  an encoded frequency-domain audio representation  222 . For example, the bitstream payload de-formatter  220  may be configured to extract from the bitstream  210  arithmetically-coded spectral data like, for example, an arithmetic codeword “acod_m [pki][m]” representing the most-significant bit-plane value m of a spectral value a, and a codeword “acod_r” representing a content of a less-significant bit-plane of the spectral value a of the frequency-domain audio representation. Thus, the encoded frequency-domain audio representation  222  constitutes (or comprises) an arithmetically-encoded representation of spectral values. The bitstream payload deformatter  220  is further configured to extract from the bitstream additional control information, which is not shown in  FIG.  2   . In addition, the bitstream payload deformatter is optionally configured to extract from the bitstream  210  a state reset information  224 , which is also designated as arithmetic reset flag or “arith_reset_flag”. 
     The audio decoder  200  comprises an arithmetic decoder  230 , which is also designated as “spectral noiseless decoder”. The arithmetic decoder  230  is configured to receive the encoded frequency-domain audio representation  220  and, optionally, the state reset information  224 . The arithmetic decoder  230  is also configured to provide a decoded frequency-domain audio representation  232 , which may comprise a decoded representation of spectral values. For example, the decoded frequency-domain audio representation  232  may comprise a decoded representation of spectral values, which are described by the encoded frequency-domain audio representation  220 . 
     The audio decoder  200  also comprises an optional inverse quantizer/rescaler  240 , which is configured to receive the decoded frequency-domain audio representation  232  and to provide, on the basis thereof, an inversely-quantized and rescaled frequency-domain audio representation  242 . 
     The audio decoder  200  further comprises an optional spectral pre-processor  250 , which is configured to receive the inversely-quantized and rescaled frequency-domain audio representation  242  and to provide, on the basis thereof, a pre-processed version  252  of the inversely-quantized and rescaled frequency-domain audio representation  242 . The audio decoder  200  also comprises a frequency-domain to time-domain signal transformer  260 , which is also designated as a “signal converter”. The signal transformer  260  is configured to receive the pre-processed version  252  of the inversely-quantized and rescaled frequency-domain audio representation  242  (or, alternatively, the inversely-quantized and rescaled frequency-domain audio representation  242  or the decoded frequency-domain audio representation  232 ) and to provide, on the basis thereof, a time-domain representation  262  of the audio information. The frequency-domain to time-domain signal transformer  260  may, for example, comprise a transformer for performing an inverse-modified-discrete-cosine transform (IMDCT) and an appropriate windowing (as well as other auxiliary functionalities, like, for example, an overlap-and-add). 
     The audio decoder  200  may further comprise an optional time-domain post-processor  270 , which is configured to receive the time-domain representation  262  of the audio information and to obtain the decoded audio information  212  using a time-domain post-processing. However, if the post-processing is omitted, the time-domain representation  262  may be identical to the decoded audio information  212 . 
     It should be noted here that the inverse quantizer/rescaler  240 , the spectral pre-processor  250 , the frequency-domain to time-domain signal transformer  260  and the time-domain post-processor  270  may be controlled in dependence on control information, which is extracted from the bitstream  210  by the bitstream payload deformatter  220 . 
     To summarize the overall functionality of the audio decoder  200 , a decoded frequency-domain audio representation  232 , for example, a set of spectral values associated with an audio frame of the encoded audio information, may be obtained on the basis of the encoded frequency-domain representation  222  using the arithmetic decoder  230 . Subsequently, the set of, for example, 1024 spectral values, which may be MDCT coefficients, are inversely quantized, rescaled and pre-processed. Accordingly, an inversely-quantized, rescaled and spectrally pre-processed set of spectral values (e.g., 1024 MDCT coefficients) is obtained. Afterwards, a time-domain representation of an audio frame is derived from the inversely-quantized, rescaled and spectrally pre-processed set of frequency-domain values (e.g. MDCT coefficients). Accordingly, a time-domain representation of an audio frame is obtained. The time-domain representation of a given audio frame may be combined with time-domain representations of previous and/or subsequent audio frames. For example, an overlap-and-add between time-domain representations of subsequent audio frames may be performed in order to smoothen the transitions between the time-domain representations of the adjacent audio frames and in order to obtain an aliasing cancellation. For details regarding the reconstruction of the decoded audio information  212  on the basis of the decoded time-frequency domain audio representation  232 , reference is made, for example, to the International Standard ISO/IEC 14496-3, part 3, sub-part 4 where a detailed discussion is given. However, other more elaborate overlapping and aliasing-cancellation schemes may be used. 
     In the following, some details regarding the arithmetic decoder  230  will be described. The arithmetic decoder  230  comprises a most-significant bit-plane determinator  284 , which is configured to receive the arithmetic codeword acod_m [pki][m] describing the most-significant bit-plane value m. The most-significant bit-plane determinator  284  may be configured to use a cumulative-frequencies table out of a set comprising a plurality of 64 cumulative-frequencies-tables for deriving the most-significant bit-plane value m from the arithmetic codeword “acod_m [pki][m]”. 
     The most-significant bit-plane determinator  284  is configured to derive values  286  of a most-significant bit-plane of spectral values on the basis of the codeword acod_m. The arithmetic decoder  230  further comprises a less-significant bit-plane determinator  288 , which is configured to receive one or more codewords “acod_r” representing one or more less-significant bit-planes of a spectral value. Accordingly, the less-significant bit-plane determinator  288  is configured to provide decoded values  290  of one or more less-significant bit-planes. The audio decoder  200  also comprises a bit-plane combiner  292 , which is configured to receive the decoded values  286  of the most-significant bit-plane of the spectral values and the decoded values  290  of one or more less-significant bit-planes of the spectral values if such less-significant bit-planes are available for the current spectral values. Accordingly, the bit-plane combiner  292  provides decoded spectral values, which are part of the decoded frequency-domain audio representation  232 . Naturally, the arithmetic decoder  230  is typically configured to provide a plurality of spectral values in order to obtain a full set of decoded spectral values associated with a current frame of the audio content. 
     The arithmetic decoder  230  further comprises a cumulative-frequencies-table selector  296 , which is configured to select one of the 64 cumulative-frequencies tables in dependence on a state index  298  describing a state of the arithmetic decoder. The arithmetic decoder  230  further comprises a state tracker  299 , which is configured to track a state of the arithmetic decoder in dependence on the previously-decoded spectral values. The state information may optionally be reset to a default state information in response to the state reset information  224 . Accordingly, the cumulative-frequencies-table selector  296  is configured to provide an index (e.g. ph) of a selected cumulative-frequencies-table, or a selected cumulative-frequencies-table itself, for application in the decoding of the most-significant bit-plane value m in dependence on the codeword “acod_m”. 
     To summarize the functionality of the audio decoder  200 , the audio decoder  200  is configured to receive a bitrate-efficiently-encoded frequency-domain audio representation  222  and to obtain a decoded frequency-domain audio representation on the basis thereof. In the arithmetic decoder  230 , which is used for obtaining the decoded frequency-domain audio representation  232  on the basis of the encoded frequency-domain audio representation  222 , a probability of different combinations of values of the most-significant bit-plane of adjacent spectral values is exploited by using an arithmetic decoder  280 , which is configured to apply a cumulative-frequencies-table. In other words, statistic dependencies between spectral values are exploited by selecting different cumulative-frequencies-tables out of a set comprising 64 different cumulative-frequencies-tables in dependence on a state index  298 , which is obtained by observing the previously-computed decoded spectral values. 
     5. Overview over the Tool of Spectral Noiseless Coding 
     In the following, details regarding the encoding and decoding algorithm, which is performed, for example, by the arithmetic encoder  170  and the arithmetic decoder  230  will be explained. 
     Focus is put on the description of the decoding algorithm. It should be noted, however, that a corresponding encoding algorithm can be performed in accordance with the teachings of the decoding algorithm, wherein mappings are inversed. 
     It should be noted that the decoding, which will be discussed in the following, is used in order to allow for a so-called “spectral noiseless coding” of typically post-processed, scaled and quantized spectral values. The spectral noiseless coding is used in an audio encoding/decoding concept to further reduce the redundancy of the quantized spectrum, which is obtained, for example, by an energy-compacting time-domain to a frequency-domain transformer. 
     The spectral noiseless coding scheme, which is used in embodiments of the invention, is based on an arithmetic coding in conjunction with a dynamically-adapted context. The noiseless coding is fed by (original or encoded representations of) quantized spectral values and uses context-dependent cumulative-frequencies-tables derived, for example, from a plurality of previously-decoded neighboring spectral values. Here, the neighborhood in both time and frequency is taken into account as illustrated in  FIG.  4   . The cumulative-frequencies-tables (which will be explained below) are then used by the arithmetic coder to generate a variable-length binary code and by the arithmetic decoder to derive decoded values from a variable-length binary code. 
     For example, the arithmetic coder  170  produces a binary code for a given set of symbols in dependence on the respective probabilities. The binary code is generated by mapping a probability interval, where the set of symbol lies, to a codeword. 
     In the following, another short overview of the tool of spectral noiseless coding will be given. Spectral noiseless coding is used to further reduce the redundancy of the quantized spectrum. The spectral noiseless coding scheme is based on an arithmetic coding in conjunction with a dynamically adapted context. The noiseless coding is fed by the quantized spectral values and uses context dependent cumulative-frequencies-tables derived from, for example, seven previously-decoded neighboring spectral values 
     Here, the neighborhood in both, time and frequency, is taken into account, as illustrated in  FIG.  4   . The cumulative-frequencies-tables are then used by the arithmetic coder to generate a variable length binary code. 
     The arithmetic coder produces a binary code for a given set of symbols and their respective probabilities. The binary code is generated by mapping a probability interval, where the set of symbols lies to a codeword. 
     6. Decoding Process 
     6.1 Decoding Process Overview 
     In the following, an overview of the process of decoding a spectral value will be given taking reference to  FIG.  3   , which shows a pseudo-program code representation of the process of decoding a plurality of spectral values. 
     The process of decoding a plurality of spectral values comprises an initialization  310  of a context. The initialization  310  of the context comprises a derivation of the current context from a previous context using the function “arith_map_context (1g)”. The derivation of the current context from a previous context may comprise a reset of the context. Both the reset of the context and the derivation of the current context from a previous context will be discussed below. 
     The decoding of a plurality of spectral values also comprises an iteration of a spectral value decoding  312  and a context update  314 , which context update is performed by a function “Arith_update_context(a,i,1g)” which is described below. The spectral value decoding  312  and the context update  314  are repeated 1g times, wherein 1g indicates the number of spectral values to be decoded (e.g. for an audio frame). The spectral value decoding  312  comprises a context-value calculation  312   a , a most-significant bit-plane decoding  312   b , and a less-significant bit-plane addition  312   c.    
     The state value computation  312   a  comprises the computation of a first state value s using the function “arith_get_context(i, 1g, arith_reset_flag, N/2)” which function returns the first state values. The state value computation  312   a  also comprises a computation of a level value “lev0” and of a level value “lev”, which level values “lev0”, “lev” are obtained by shifting the first state value s to the right by 24 bits. The state value computation  312   a  also comprises a computation of a second state value t according to the formula shown in  FIG.  3    at reference numeral  312   a.    
     The most-significant bit-plane decoding  312   b  comprises an iterative execution of a decoding algorithm  312   ba , wherein a variable j is initialized to  0  before a first execution of the algorithm  312   ba.    
     The algorithm  312   ba  comprises a computation of a state index “ph” (which also serves as a cumulative-frequencies-table index) in dependence on the second state value t, and also in dependence on the level values “lev” and lev0, using a function “arith_get_pk( )”, which is discussed below. The algorithm  312   ba  also comprises the selection of a cumulative-frequencies-table in dependence on the state index ph, wherein a variable “cum_freq” may be set to a starting address of one out of 64 cumulative-frequencies-tables in dependence on the state index ph. Also, a variable “cfl” may be initialized to a length of the selected cumulative-frequencies-table, which is, for example, equal to the number of symbols in the alphabet, i.e. the number of different values which can be decoded. The lengths of all the cumulative-frequencies-tables from “arith_cf_m[pki=0][9]” to “arith_cf_m[pki=63][9]” available for the decoding of the most-significant bit-plane value m is 9, as eight different most-significant bit-plane values and an escape symbol can be decoded. Subsequently, a most-significant bit-plane value m may be obtained by executing a function “arith_decode( )”, taking into consideration the selected cumulative-frequencies-table (described by the variable “cum_freq” and the variable “cfl”). When deriving the most-significant bit-plane value m, bits named “acod_m” of the bitstream  210  may be evaluated (see, for example,  FIG.  6   g   ). 
     The algorithm  312   ba  also comprises checking whether the most-significant bit-plane value m is equal to an escape symbol “ARITH_ESCAPE”, or not. If the most-significant bit-plane value m is not equal to the arithmetic escape symbol, the algorithm  312   ba  is aborted (“break”-condition) and the remaining instructions of the algorithm  312   ba  are therefore skipped. Accordingly, execution of the process is continued with the setting of the spectral value a to be equal to the most-significant bit-plane value m (instruction “a=m”). In contrast, if the decoded most-significant bit-plane value m is identical to the arithmetic escape symbol “ARITH_ESCAPE”, the level value “lev” is increased by one. As mentioned, the algorithm  312   ba  is then repeated until the decoded most-significant bit-plane value m is different from the arithmetic escape symbol. 
     As soon as most-significant bit-plane decoding is completed, i.e. a most-significant bit-plane value m different from the arithmetic escape symbol has been decoded, the spectral value variable, a″ is set to be equal to the most-significant bit-plane value m. Subsequently, the less-significant bit-planes are obtained, for example, as shown at reference numeral  312   c  in  FIG.  3   . For each less-significant bit-plane of the spectral value, one out of two binary values is decoded. For example, a less-significant bit-plane value r is obtained. Subsequently, the spectral value variable, a″ is updated by shifting the content of the spectral value variable a″ to the left by 1 bit and by adding the currently-decoded les-significant bit-plane value r as a least-significant bit. However, it should be noted that the concept for obtaining the values of the less-significant bit-planes is not of particular relevance for the present invention. In some embodiments, the decoding of any less-significant bit-planes may even be omitted. Alternatively, different decoding algorithms may be used for this purpose. 
     6.2 Decoding Order According to  FIG.  4     
     In the following, the decoding order of the spectral values will be described. 
     Spectral coefficients are noiselessly coded and transmitted (e.g. in the bitstream) starting from the lowest-frequency coefficient and progressing to the highest-frequency coefficient. 
     Coefficients from an advanced audio coding (for example obtained using a modified-discrete-cosine-transform, as discussed in ISO/IEC 14496, part 3, subpart 4) are stored in an array called “x_ac_quant[g][win][sfb][bin]”, and the order of transmission of the noiseless-coding-codeword (e.g. acod_m, acod_r) is such that when they are decoded in the order received and stored in the array, “bin” (the frequency index) is the most rapidly incrementing index and “g” is the most slowly incrementing index. 
     Spectral coefficients associated with a lower frequency are encoded before spectral coefficients associated with a higher frequency. 
     Coefficients from the transform-coded-excitation (tcx) are stored directly in an array x_tcx_invquant[win][bin], and the order of the transmission of the noiseless coding codewords is such that when they are decoded in the order received and stored in the array, “bin” is the most rapidly incrementing index and “win” is the slowest incrementing index. In other words, if the spectral values describe a transform-coded-excitation of the linear-prediction filter of a speech coder, the spectral values a are associated to adjacent and increasing frequencies of the transform-coded-excitation. 
     Spectral coefficients associated to a lower frequency are encoded before spectral coefficients associated with a higher frequency. 
     Notably, the audio decoder  200  may be configured to apply the decoded frequency-domain audio representation  232 , which is provided by the arithmetic decoder  230 , both for a “direct” generation of a time-domain audio signal representation using a frequency-domain to time-domain signal transform and for an “indirect” provision of an audio signal representation using both a frequency-domain to time-domain decoder and a linear-prediction-filter excited by the output of the frequency-domain to time-domain signal transformer. 
     In other words, the arithmetic decoder  200 , the functionality of which is discussed here in detail, is well-suited for decoding spectral values of a time-frequency-domain representation of an audio content encoded in the frequency-domain and for the provision of a time-frequency-domain representation of a stimulus signal for a linear-prediction-filter adapted to decode a speech signal encoded in the linear-prediction-domain. Thus, the arithmetic decoder is well-suited for use in an audio decoder which is capable of handling both frequency-domain-encoded audio content and linear-predictive-frequency-domain-encoded audio content (transform-coded-excitation linear prediction domain mode). 
     6.3. Context Initialization According to  FIGS.  5   a  and  5   b      
     In the following, the context initialization (also designated as a “context mapping”), which is performed in a step  310 , will be described. 
     The context initialization comprises a mapping between a past context and a current context in accordance with the algorithm “arith_map_context( )”, which is shown in  FIG.  5   a   . As can be seen, the current context is stored in a global variable q[2][n_context] which takes the form of an array having a first dimension of two and a second dimension of n_context. A past context is a stored in a variable qs[n_context], which takes the form of a table having a dimension of n_context. The variable “previous_1g” describes a number of spectral values of a past context. 
     The variable “1g” describes a number of spectral coefficients to decode in the frame. The variable “previous_1g” describes a previous number of spectral lines of a previous frame. 
     A mapping of the context may be performed in accordance with the algorithm “arith_map_context( )”. It should be noted here that the function “arith_map_context( )” sets the entries q[0][i] of the current context array q to the values qs[i] of the past context array qs, if the number of spectral values associated with the current (e.g. frequency-domain-encoded) audio frame is identical to the number of spectral values associated with the previous audio frame for i=0 to i=1g-1. 
     However, a more complicated mapping is performed if the number of spectral values associated to the current audio frame is different from the number of spectral values associated to the previous audio frame. However, details regarding the mapping in this case are not particularly relevant for the key idea of present invention, such that reference is made to the pseudo program code of  FIG.  5   a    for details. 
     6.4 State Value Computation According to  FIGS.  5   b  and  5   c      
     In the following, the state value computation  312   a  will be described in more detail. 
     It should be noted that the first state value s (as shown in  FIG.  3   ) can be obtained as a return value of the function “arith_get_context(i, 1g, arith_reset_flag, N/2)”, a pseudo program code representation of which is shown in  FIGS.  5   b    and  5   c.    
     Regarding the computation of the state value, reference is also made to  FIG.  4   , which shows the context used for a state evaluation.  FIG.  4    shows a two-dimensional representation of spectral values, both over time and frequency. An abscissa  410  describes the time, and an ordinate  412  describes the frequency. As can be seen in  FIG.  4   , a spectral value  420  to decode, is associated with a time index t0 and a frequency index i. As can be seen, for the time index t0, the tuples having frequency indices i−1, i−2 and i−3 are already decoded at the time at which the spectral value  420  having the frequency index i is to be decoded. As can be seen from  FIG.  4   , a spectral value  430  having a time index t0 and a frequency index i−1 is already decoded before the spectral value  420  is decoded, and the spectral value  430  is considered for the context which is used for the decoding of the spectral value  420 . Similarly, a spectral value  434  having a time index t0 and a frequency index i−2, is already decoded before the spectral value  420  is decoded, and the spectral value  434  is considered for the context which is used for decoding the spectral value  420 . Similarly, a spectral value  440  having a time index t-1 and a frequency index of i−2, a spectral value  444  having a time index t-1 and a frequency index i−1, a spectral value  448  having a time index t-1 and a frequency index i, a spectral value  452  having a time index t-1 and a frequency index i+1, and a spectral value  456  having a time index t-1 and a frequency index i+2, are already decoded before the spectral value  420  is decoded, and are considered for the determination of the context, which is used for decoding the spectral value  420 . The spectral values (coefficients) already decoded at the time when the spectral value  420  is decoded and considered for the context are shown by shaded squares. In contrast, some other spectral values already decoded (at the time when the spectral value  420  is decoded), which are represented by squares having dashed lines, and other spectral values, which are not yet decoded (at the time when the spectral value  420  is decoded) and which are shown by circles having dashed lines, are not used for determining the context for decoding the spectral value  420 . 
     However, it should be noted that some of these spectral values, which are not used for the “regular” (or “normal”) computation of the context for decoding the spectral value  420  may, nevertheless, be evaluated for a detection of a plurality of previously-decoded adjacent spectral values which fulfill, individually or taken together, a predetermined condition regarding their magnitudes. 
     Taking reference now to  FIGS.  5   b  and  5   c   , which show the functionality of the function “arith_get_context( )” in the form of a pseudo program code, some more details regarding the calculation of the first context value “s”, which is performed by the function “arith_get_context( )”, will be described. 
     It should be noted that the function “arith_get_context( )” receives, as input variables an index i of the spectral value to decode. The index i is typically a frequency index. An input variable 1g describes a (total) number of expected quantized coefficients (for a current audio frame). A variable N describes a number of lines of the transformation. A flag “arith_reset_flag” indicates whether the context should be reset. The function “arith_get_context” provides, as an output value, a variable, t″, which represents a concatenated state index s and a predicted bit-plane level lev0. 
     The function “arith_get_context( )” uses integer variables a0, c0, c1, c2, c3, c4, c5, c6, lev0, and “region”. 
     The function “arith_get_context( )” comprises as main functional blocks, a first arithmetic reset processing  510 , a detection  512  of a group of a plurality of previously-decoded adjacent zero spectral values, a first variable setting  514 , a second variable setting  516 , a level adaptation  518 , a region value setting  520 , a level adaptation  522 , a level limitation  524 , an arithmetic reset processing  526 , a third variable setting  528 , a fourth variable setting  530 , a fifth variable setting  532 , a level adaptation  534 , and a selective return value computation  536 . 
     In the first arithmetic reset processing  510 , it is checked whether the arithmetic reset flag “arith_reset_flag” is set, while the index of the spectral value to decode is equal to zero. In this case, a context value of zero is returned, and the function is aborted. 
     In the detection  512  of a group of a plurality of previously-decoded zero spectral values, which is only performed if the arithmetic reset flag is inactive and the index i of the spectral value to decode is different from zero, a variable named “flag” is initialized to 1, as shown at reference numeral  512   a , and a region of spectral value that is to be evaluated is determined, as shown at reference numeral  512   b . Subsequently, the region of spectral values, which is determined as shown at reference number  512   b , is evaluated as shown at reference numeral  512   c . If it is found that there is a sufficient region of previously-decoded zero spectral values, a context value of 1 is returned, as shown at reference numeral  512   d . For example, an upper frequency index boundary “lim_max” is set to i+6, unless index i of the spectral value to be decoded is close to a maximum frequency index 1g−1, in which case a special setting of the upper frequency index boundary is made, as shown at reference numeral  512   b . Moreover, a lower frequency index boundary “lim_min” is set to −5, unless the index i of the spectral value to decode is close to zero (i+lim_min&lt;0), in which case a special computation of the lower frequency index boundary lim_min is performed, as shown at reference numeral  512   b.    
     When evaluating the region of spectral values determined in step  512   b , an evaluation is first performed for negative frequency indices k between the lower frequency index boundary lim_min and zero. For frequency indices k between lim_min and zero, it is verified whether at least one out of the context values q[0][k].c and q[1][k].c is equal to zero. If, however, both of the context values q[0][k].c and q[1][k].c are different from zero for any frequency indices k between lim_min and zero, it is concluded that there is no sufficient group of zero spectral values and the evaluation  512   c  is aborted. Subsequently, context values q[0][k].c for frequency indices between zero and lim_max are evaluated. If it found that any of the context values q[0][k].c for any of the frequency indices between zero and lim_max is different from zero, it is concluded that there is no sufficient group of previously-decoded zero spectral values, and the evaluation  512   c  is aborted. If, however, it is found that for every frequency indices k between lim_min and zero, there is at least one context value q[0][k].c or q[1][k].c which is equal to zero and if there is a zero context value q[0][k].c for every frequency index k between zero and lim_max, it is concluded that there is a sufficient group of previously-decoded zero spectral values. Accordingly, a context value of 1 is returned in this case to indicate this condition, without any further calculation. In other words, calculations  514 ,  516 ,  518 ,  520 ,  522 ,  524 ,  526 ,  528 ,  530 ,  532 ,  534 ,  536  are skipped, if a sufficient group of a plurality of context values q[0] [k].c, q[1] [k].c having a value of zero is identified. In other words, the returned context value, which describes the context state (s), is determined independent from the previously decoded spectral values in response to the detection that the predetermined condition is fulfilled. 
     Otherwise, i.e. if there is no sufficient group of context values [q] [0] [k].c, [q][1][k].c, which are zero at least some of the computations  514 ,  516 ,  518 ,  520 ,  522 ,  524 , 526 ,  528 ,  530 ,  532 ,  534 ,  536  are executed. 
     In the first variable setting  514 , which is selectively executed if (and only if) index i of the spectral value to be decoded is less than 1, the variable a0 is initialized to take the context value q[1][i−1], and the variable c0 is initialized to take the absolute value of the variable a0. The variable, lev0″ is initialized to take the value of zero. Subsequently, the variables, lev0″ and c0 are increased if the variable a0 comprises a comparatively large absolute value, i.e. is smaller than −4, or larger or equal to 4. The increase of the variables, lev0″ and c0 is performed iteratively, until the value of the variable a0 is brought into a range between −4 and 3 by a shift-to-the-right operation (step  514   b ). 
     Subsequently, the variables c0 and, lev0″ are limited to maximum values of 7 and 3, respectively (step  514   c ). 
     If the index i of the spectral value to be decoded is equal to 1 and the arithmetic reset flag (“arith_reset_flag”) is active, a context value is returned, which is computed merely on the basis of the variables c0 and lev( )(step  514   d ). Accordingly, only a single previously-decoded spectral value having the same time index as the spectral value to decode and having a frequency index which is smaller, by 1, than the frequency index i of the spectral value to be decoded, is considered for the context computation (step  514   d ). Otherwise, i.e. if there is no arithmetic reset functionality, the variable c4 is initialized (step  514   e ). 
     To conclude, in the first variable setting  514 , the variables c0 and, lev0″ are initialized in dependence on a previously-decoded spectral value, decoded for the same frame as the spectral value to be currently decoded and for a preceding spectral bin i−1. The variable c4 is initialized in dependence on a previously-decoded spectral value, decoded for a previous audio frame (having time index t-1) and having a frequency which is lower (e.g., by one frequency bin) than the frequency associated with the spectral value to be currently decoded. 
     The second variable setting  516  which is selectively executed if (and only if) the frequency index of the spectral value to be currently decoded is larger than 1, comprises an initialization of the variables c1 and c6 and an update of the variable lev0. The variable c1 is updated in dependence on a context value q[1][i−2].c associated with a previously-decoded spectral value of the current audio frame, a frequency of which is smaller (e.g. by two frequency bins) than a frequency of a spectral value currently to be decoded. Similarly, variable c6 is initialized in dependence on a context value q[0][i−2].c, which describes a previously-decoded spectral value of a previous frame (having time index t-1), an associated frequency of which is smaller (e.g. by two frequency bins) than a frequency associated with the spectral value to currently be decoded. In addition, the level variable, lev0″ is set to a level value q[1][i−2].1 associated with a previously-decoded spectral value of the current frame, an associated frequency of which is smaller (e.g. by two frequency bins) than a frequency associated with the spectral value to currently be decoded, if q[ 1 ][i−2].1 is larger than lev0. 
     The level adaptation  518  and the region value setting  520  are selectively executed, if (and only if) the index i of the spectral value to be decoded is larger than 2. In the level adaptation  518 , the level variable, lev0″ is increased to a value of q[1][i−3].1, if the level value q[1][i−3].1 which is associated to a previously-decoded spectral value of the current frame, an associated frequency of which is smaller (e.g. by three frequency bins) than the frequency associated with the spectral value to currently be decoded, is larger than the level value lev0. 
     In the region value setting  520 , a variable “region” is set in dependence on an evaluation, in which spectral region, out of a plurality of spectral regions, the spectral value to currently be decoded is arranged. For example, if it is found that the spectral value to be currently decoded is associated to a frequency bin (having frequency bin index i) which is in the first (lower most) quarter of the frequency bins (0≤i&lt;N/4), the region variable “region” is set to zero. Otherwise, if the spectral value currently to be decoded is associated to a frequency bin which is in a second quarter of the frequency bins associated to the current frame (N/4&lt;i&lt;N/2), the region variable is set to a value of 1. Otherwise, i.e. if the spectral value currently to be decoded is associated to a frequency bin which is in the second (upper) half of the frequency bins (N/2&lt;i&lt;N), the region variable is set to 2. Thus, a region variable is set in dependence on an evaluation to which frequency region the spectral value currently to be decoded is associated. Two or more frequency regions may be distinguished. 
     An additional level adaptation  522  is executed if (and only if) the spectral value currently to be decoded comprises a spectral index which is larger than 3. In this case, the level variable lev0″ is increased (set to the value q[1][i−4].1) if the level value q[i][i−4].1, which is associated to a previously-decoded spectral value of the current frame, which is associated to a frequency which is smaller, for example, by four frequency bins, than a frequency associated to the spectral value currently to be decoded is larger than the current level, lev0″ (step  522 ). The level variable, lev0″ is limited to a maximum value of 3 (step  524 ). 
     If an arithmetic reset condition is detected and the index i of the spectral value currently to be decoded is larger than 1, the state value is returned in dependence on the variables c0, c1, lev0, as well as in dependence on the region variable “region” (step  526 ). Accordingly, previously-decoded spectral values of any previous frames are left out of consideration if an arithmetic reset condition is given. 
     In the third variable setting  528 , the variable c2 is set to the context value q[0][i].c, which is associated to a previously-decoded spectral value of the previous audio frame (having time index t-1), which previously-decoded spectral value is associated with the same frequency as the spectral value currently to be decoded. 
     In the fourth variable setting  530 , the variable c3 is set to the context value q[0][i+1].c, which is associated to a previously-decoded spectral value of the previous audio frame having a frequency index i+1, unless the spectral value currently to be decoded is associated with the highest possible frequency index 1g-1. 
     In the fifth variable setting  532 , the variable c5 is set to the context value q[0][i+2].c, which is associated with a previously-decoded spectral value of the previous audio frame having frequency index i+2, unless the frequency index i of the spectral value currently to be decoded is too close to the maximum frequency index value (i.e. takes the frequency index value 1g-2 or 1g-1). 
     An additional adaptation of the level variable, lev0″ is performed if the frequency index i is equal to zero (i.e. if the spectral value currently to be decoded is the lowermost spectral value). In this case, the level variable, lev0″ is increased from zero to 1, if the variable c2 or c3 takes a value of 3, which indicates that a previously-decoded spectral value of a previous audio frame, which is associated with the same frequency or even a higher frequency, when compared to the frequency associated with the spectral value currently to be encoded, takes a comparatively large value. 
     In the selective return value computation  536 , the return value is computed in dependence on whether the index i of the spectral values currently to be decoded takes the value zero, 1, or a larger value. The return value is computed in dependence on the variables c2, c3, c5 and lev0, as indicated at reference numeral  536   a , if index i takes the value of zero. The return value is computed in dependence on the variables c0, c2, c3, c4, c5, and, lev0″ as shown at reference numeral  536   b , if index i takes the value of 1. The return value is computed in dependence on the variable c0, c2, c3, c4, c1, c5, c6, “region”, and lev0, if the index i takes a value which is different from zero or 1 (reference numeral  536   c ). 
     To summarize the above, the context value computation “arith_get_context( )” comprises a detection  512  of a group of a plurality of previously-decoded zero spectral values (or at least, sufficiently small spectral values). If a sufficient group of previously-decoded zero spectral values is found, the presence of a special context is indicated by setting the return value to 1. Otherwise, the context value computation is performed. It can generally be said that in the context value computation, the index value i is evaluated in order to decide how many previously-decoded spectral values should be evaluated. For example, a number of evaluated previously-decoded spectral values is reduced if a frequency index i of the spectral value currently to be decoded is close to a lower boundary (e.g. zero), or close to an upper boundary (e.g. 1g-1). In addition, even if the frequency index i of the spectral value currently to be decoded is sufficiently far away from a minimum value, different spectral regions are distinguished by the region value setting  520 . Accordingly, different statistical properties of different spectral regions (e.g. first, low frequency spectral region, second, medium frequency spectral region, and third, high frequency spectral region) are taken into consideration. The context value, which is calculated as a return value, is dependent on the variable “region”, such that the returned context value is dependent on whether a spectral value currently to be decoded is in a first predetermined frequency region or in a second predetermined frequency region (or in any other predetermined frequency region). 
     6.5 Mapping Rule Selection 
     In the following, the selection of a mapping rule, for example, a cumulative-frequencies-table, which describes a mapping of a code value onto a symbol code, will be described. The selection of the mapping rule is made in dependence on the context state, which is described by the state value s or t. 
     6.5.1 Mapping Rule Selection Using the Algorithm According to  FIG.  5   d      
     In the following, the selection of a mapping rule using the function “get_pk” according to  FIG.  5   d    will be described. It should be noted that the function “get_pk” may be performed to obtain the value of “pki” in the sub-algorithm  312   ba  of the algorithm of  FIG.  3   . Thus, the function “get_pk” may take the place of the function “arith_get_pk” in the algorithm of  FIG.  3   . 
     It should also be noted that a function “get_pk” according to  FIG.  5   d    may evaluate the table “ari_s_hash[387]” according to  FIGS.  17   ( 1 ) and  17 ( 2 ) and a table “ari_gs_hash”[225] according to  FIG.  18   . 
     The function “get_pk” receives, as an input variable, a state value s, which may be obtained by a combination of the variable, t″ according to  FIG.  3    and the variables “led”, “lev0” according to  FIG.  3   . The function “get_pk” is also configured to return, as a return value, a value of a variable “pki”, which designates a mapping rule or a cumulative-frequencies-table. The function “get_pk” is configured to map the state value s onto a mapping rule index value “pki”. 
     The function “get_pk” comprises a first table evaluation  540 , and a second table evaluation  544 . The first table evaluation  540  comprises a variable initialization  541  in which the variables i_min, i_max, and i are initialized, as shown at reference numeral  541 . The first table evaluation  540  also comprises an iterative table search  542 , in the course of which a determination is made as to whether there is an entry of the table “ari_s_hash” which matches the state value s. If such a match is identified during the iterative table search  542 , the function get_pk is aborted, wherein a return value of the function is determined by the entry of the table “ari_s_hash” which matches the state value s, as will be explained in more detail. If, however, no perfect match between the state value s and an entry of the table “ari_s_hash” is found during the course of the iterative table search  542 , a boundary entry check  543  is performed. 
     Turning now to the details of the first table evaluation  540 , it can be seen that a search interval is defined by the variables i_min and i_max. The iterative table search  542  is repeated as long as the interval defined by the variables i_min and i_max is sufficiently large, which may be true if the condition i_max−i_min&gt;1 is fulfilled. Subsequently, the variable i is set, at least approximately, to designate the middle of the interval (i=i_min+(i_max−i_min)/2). Subsequently, a variable j is set to a value which is determined by the array “ari_s_hash” at an array position designated by the variable i (reference numeral  542 ). It should be noted here that each entry of the table “ari_s_hash” describes both, a state value, which is associated to the table entry, and a mapping rule index value which is associated to the table entry. The state value, which is associated to the table entry, is described by the more-significant bits (bits 8-31) of the table entry, while the mapping rule index values are described by the lower bits (e.g. bits 0-7) of said table entry. The lower boundary i_min or the upper boundary i_max are adapted in dependence on whether the state value s is smaller than a state value described by the most-significant 24 bits of the entry “ari_s_hash[i]” of the table “ari_s_hash” referenced by the variable i. For example, if the state value s is smaller than the state value described by the most-significant 24 bits of the entry “ari_s_hash[i]”, the upper boundary i_max of the table interval is set to the value i. Accordingly, the table interval for the next iteration of the iterative table search  542  is restricted to the lower half of the table interval (from i_min to i_max) used for the present iteration of the iterative table search  542 . If, in contrast, the state value s is larger than the state values described by the most-significant 24 bits of the table entry “ari_s_hash[i]”, then the lower boundary i_min of the table interval for the next iteration of the iterative table search  542  is set to value i, such that the upper half of the current table interval (between i_min and i_max) is used as the table interval for the next iterative table search. If, however, it is found that the state value s is identical to the state value described by the most-significant 24 bits of the table entry “ari_s_hash[i]”, the mapping rule index value described by the least-significant 8-bits of the table entry “ari_s_hash[i]” is returned by the function “get_pk”, and the function is aborted. 
     The iterative table search  542  is repeated until the table interval defined by the variables i_min and i_max is sufficiently small. 
     A boundary entry check  543  is (optionally) executed to supplement the iterative table search  542 . If the index variable i is equal to index variable i_max after the completion of the iterative table search  542 , a final check is made whether the state value s is equal to a state value described by the most-significant 24 bits of a table entry “ari_s_hash[i_min]”, and a mapping rule index value described by the least-significant 8 bits of the entry “ari_s_hash[i_min]” is returned, in this case, as a result of the function “get_pk”. In contrast, if the index variable i is different from the index variable i_max, then a check is performed as to whether a state value s is equal to a state value described by the most-significant 24 bits of the table entry “ari_s_hash[i_max]”, and a mapping rule index value described by the least-significant 8 bits of said table entry “ari_s_hash[i_max]” is returned as a return value of the function “get_pk” in this case. 
     However, it should be noted that the boundary entry check  543  may be considered as optional in its entirety. 
     Subsequent to the first table evaluation  540 , the second table evaluation  544  is performed, unless a “direct hit” has occurred during the first table evaluation  540 , in that the state value s is identical to one of the state values described by the entries of the table “ari_s_hash” (or, more precisely, by the 24 most-significant bits thereof). 
     The second table evaluation  544  comprises a variable initialization  545 , in which the index variables i_min, i and i_max are initialized, as shown at reference numeral  545 . The second table evaluation  544  also comprises an iterative table search  546 , in the course of which the table “ari_gs_hash” is searched for an entry which represents a state value identical to the state value s. Finally, the second table search  544  comprises a return value determination  547 . 
     The iterative table search  546  is repeated as long as the table interval defined by the index variables i_min and i_max is large enough (e.g. as long as i_max−i_min&gt;1). In the iteration of the iterative table search  546 , the variable i is set to the center of the table interval defined by i_min and i_max (step  546   a ). Subsequently, an entry j of the table “ari_gs_hash” is obtained at a table location determined by the index variable i ( 546   b ). In other words, the table entry “ari_gs_hash[i]” is a table entry at the center of the current table interval defined by the table indices i_min and i_max. Subsequently, the table interval for the next iteration of the iterative table search  546  is determined. For this purpose, the index value i_max describing the upper boundary of the table interval is set to the value i, if the state value s is smaller than a state value described by the most-significant 24 bits of the table entry “j=ari_gs_hash[i]” ( 546   c ). In other words, the lower half of the current table interval is selected as the new table interval for the next iteration of the iterative table search  546  (step  546   c ). Otherwise, if the state value s is larger than a state value described by the most-significant 24 bits of the table entry “j=ari_gs_hash[i]”, the index value i_min is set to the value i. Accordingly, the upper half of the current table interval is selected as the new table interval for the next iteration of the iterative table search  546  (step  546   d ). If, however, it is found that the state value s is identical to a state value described by the uppermost 24 bits of the table entry “j=ari_gs_hash[i]”, the index variable i_max is set to the value i+1 or to the value  224  (if i+1 is larger than 224), and the iterative table search  546  is aborted. However, if the state value s is different from the state value described by the 24 most-significant bits of “j=ari_gs_hash[i]”, the iterative table search  546  is repeated with the newly set table interval defined by the updated index values i_min and i_max, unless the table interval is too small (i_max−i_min&lt;1). Thus, the interval size of the table interval (defined by i_min and i_max) is iteratively reduced until a “direct hit” is detected (s==(j&gt;&gt;8)) or the interval reaches a minimum allowable size (i_max−i_min≤1). Finally, following an abortion of the iterative table search  546 , a table entry “j=ari_gs_hash[i_max]” is determined and a mapping rule index value, which is described by the 8 least-significant bits of said table entry “j=ari_gs_hash[i_max]” is returned as the return value of the function “get_pk”. Accordingly, the mapping rule index value is determined in dependence on the upper boundary i_max of the table interval (defined by i_min and i_max) after the completion or abortion of the iterative table search  546 . 
     The above-described table evaluations  540 ,  544 , which both use iterative table search  542 ,  546 , allow for the examination of tables “ari_s_hash” and “ari_gs_hash” for the presence of a given significant state with very high computational efficiency. In particular, a number of table access operations can be kept reasonably small, even in a worst case. It has been found that a numeric ordering of the table “ari_s_hash” and “ari_gs_hash” allows for the acceleration of the search for an appropriate hash value. In addition, a table size can be kept small as the inclusion of escape symbols in tables “ari_s_hash” and “ari_gs_hash” is not required. Thus, an efficient context hashing mechanism is established even though there are a large number of different states: In a first stage (first table evaluation  540 ), a search for a direct hit is conducted (s==(j&gt;&gt; 8 )). 
     In the second stage (second table evaluation  544 ) ranges of the state value s can be mapped onto mapping rule index values. Thus, a well-balanced handling of particularly significant states, for which there is an associated entry in the table “ari_s_hash”, and less-significant states, for which there is a range-based handling, can be performed. Accordingly, the function “get_pk” constitutes an efficient implementation of a mapping rule selection. 
     For any further details, reference is made to the pseudo program code of  FIG.  5   d   , which represents the functionality of the function “get_pk” in a representation in accordance with the well-known programming language C. 
     6.5.2 Mapping Rule Selection Using the Algorithm According to  FIG.  5   e      
     In the following, another algorithm for a selection of the mapping rule will be described taking reference to  FIG.  5   e   . It should be noted that the algorithm “arith_get_pk” according to  FIG.  5   e    receives, as an input variable, a state value s describing a state of the context. The function “arith_get_pk” provides, as an output value, or return value, an index “pki” of a probability model, which may be an index for selecting a mapping rule, (e.g., a cumulative-frequencies-table). 
     It should be noted that the function “arith_get_pk” according to  FIG.  5   e    may take the functionality of the function “arith_get_pk” of the function “value_decode” of  FIG.  3   . 
     It should also be noted that the function “arith_get_pk” may, for example, evaluate the table ari_s_hash according to  FIG.  20   , and the table ari_gs_hash according to  FIG.  18   . 
     The function “arith_get_pk” according to  FIG.  5   e    comprises a first table evaluation  550  and a second table evaluation  560 . In the first table evaluation  550 , a linear scan is made through the table ari_s_hash, to obtain an entry j=ari_s_hash[i] of said table. If a state value described by the most-significant 24 bits of a table entry j=ari_s_hash[i] of the table ari_s_hash is equal to the state value s, a mapping rule index value “pki” described by the least-significant 8 bits of said identified table entry j=ari_s_hash[i] is returned and the function “arith_get_pk” is aborted. Accordingly, all 387 entries of the table ari_s_hash are evaluated in an ascending sequence unless a “direct hit” (state value s equal to the state value described by the most-significant 24 bits of a table entry j) is identified. 
     If a direct hit is not identified within the first table evaluation  550 , a second table evaluation  560  is executed. In the course of the second table evaluation, a linear scan with entry indices i increasing linearly from zero to a maximum value of 224 is performed. During the second table evaluation, an entry “ari_gs_hash[i]” of the table “ari_gs_hash” for table i is read, and the table entry “j=ari_gs_hash[i] is evaluated in that it is determined whether the state value represented by the 24 most-significant bits of the table entry j is larger than the state value s. If this is the case, a mapping rule index value described by the 8 least-significant bits of said table entry j is returned as the return value of the function “arith_get_pk”, and the execution of the function “arith_get_pk” is aborted. If, however, the state value s is not smaller than the state value described by the 24 most-significant bits of the current table entry j=ari_gs_hash[i], the scan through the entries of the table ari_gs_hash is continued by increasing the table index i. If, however, the state value s is larger than or equal to any of the state values described by the entries of the table ari_gs_hash, a mapping rule index value pki” defined by the 8 least-significant bits of the last entry of the table ari_gs_hash is returned as the return value of the function “arith_get_pk”. 
     To summarize, the function “arith_get_pk” according to  FIG.  5   e    performs a two-step hashing. In a first step, a search for a direct hit is performed, wherein it is determined whether the state value s is equal to the state value defined by any of the entries of a first table “ari_s_hash”. If a direct hit is identified in the first table evaluation  550 , a return value is obtained from the first table “ari_s_hash” and the function “arith_get_pk” is aborted. If, however, no direct hit is identified in the first table evaluation  550 , the second table evaluation  560  is performed. In the second table evaluation, a range-based evaluation is performed. Subsequent entries of the second table “ari_gs_hash” define ranges. If it is found that the state value s lies within such a range (which is indicated by the fact that the state value described by the 24 most-significant bits of the current table entry “j=ari_gs_hash[i] is larger than the state value s, the mapping rule index value “pki” described by the 8 least-significant bits of the table entry j=ari_gs_hash[i] is returned. 
     6.5.3 Mapping Rule Selection Using the Algorithm According to  FIG.  5   f      
     The function “get_pk” according to  FIG.  5   f    is substantially equivalent to the function “arith_get_pk” according to  FIG.  5   e   . Accordingly, reference is made to the above discussion. For further details, reference is made to the pseudo program representation in  FIG.  5     f.    
     It should be noted that the function, get_pk” according to  FIG.  5   f    may take the place of the function “arith_get_pk” called in the function “value_decode” of  FIG.  3   . 
     6.6. Function “Arith_Decode( )” According to  FIG.  5   g      
     In the following, the functionality of the function “arith_decode( )” will be discussed in detail taking reference to  FIG.  5   g   . It should be noted that the function “arith_decode( )” uses the helper function “arith_first_symbol (void)”, which returns TRUE, if it is the first symbol of the sequence and FALSE otherwise. The function “arith_decode( )” also uses the helper function “arith_get_next_bit(void)”, which gets and provides the next bit of the bitstream. 
     In addition, the function “arith_decode( )” uses the global variables “low”, “high” and “value”. Further, the function “arith_decode( )” receives, as an input variable, the variable “cum_freq[ ]”, which points towards a first entry or element (having element index or entry index 0) of the selected cumulative-frequencies-table. Also, the function “arith_decode( )” uses the input variable “cfl”, which indicates the length of the selected cumulative-frequencies-table designated by the variable “cum_freq[ ]”. 
     The function “arith_decode( )” comprises, as a first step, a variable initialization  570   a , which is performed if the helper function “arith_first_symbol( )” indicates that the first symbol of a sequence of symbols is being decoded. The value initialization  550   a  initializes the variable “value” in dependence on a plurality of, for example, 20 bits, which are obtained from the bitstream using the helper function “arith_get_next_bit”, such that the variable “value” takes the value represented by said bits. Also, the variable “low” is initialized to take the value of 0, and the variable “high” is initialized to take the value of 1048575. 
     In a second step  570   b , the variable “range” is set to a value, which is larger, by 1, than the difference between the values of the variables “high” and “low”. The variable “cum” is set to a value which represents a relative position of the value of the variable “value” between the value of the variable “low” and the value of the variable “high”. Accordingly, the variable “cum” takes, for example, a value between 0 and 2 16  in dependence on the value of the variable “value”. 
     The pointer p is initialized to a value which is smaller, by 1, than the starting address of the selected cumulative-frequencies-table. 
     The algorithm “arith_decode( )” also comprises an iterative cumulative-frequencies-table-search  570   c . The iterative cumulative-frequencies-table-search is repeated until the variable cfl is smaller than or equal to 1. In the iterative cumulative-frequencies-table-search  570   c , the pointer variable q is set to a value, which is equal to the sum of the current value of the pointer variable p and half the value of the variable “cfl”. If the value of the entry *q of the selected cumulative-frequencies-table, which entry is addressed by the pointer variable q, is larger than the value of the variable “cum”, the pointer variable p is set to the value of the pointer variable q, and the variable “cfl” is incremented. Finally, the variable “cfl” is shifted to the right by one bit, thereby effectively dividing the value of the variable “cfl” by 2 and neglecting the modulo portion. 
     Accordingly, the iterative cumulative-frequencies-table-search  570   c  effectively compares the value of the variable “cum” with a plurality of entries of the selected cumulative-frequencies-table, in order to identify an interval within the selected cumulative-frequencies-table, which is bounded by entries of the cumulative-frequencies-table, such that the value cum lies within the identified interval. Accordingly, the entries of the selected cumulative-frequencies-table define intervals, wherein a respective symbol value is associated to each of the intervals of the selected cumulative-frequencies-table. Also, the widths of the intervals between two adjacent values of the cumulative-frequencies-table define probabilities of the symbols associated with said intervals, such that the selected cumulative-frequencies-table in its entirety defines a probability distribution of the different symbols (or symbol values). Details regarding the available cumulative-frequencies-tables will be discussed below taking reference to  FIG.  19   . 
     Taking reference again to  FIG.  5   g   , the symbol value is derived from the value of the pointer variable p, wherein the symbol value is derived as shown at reference numeral  570   d . Thus, the difference between the value of the pointer variable p and the starting address “cum_freq” is evaluated in order to obtain the symbol value, which is represented by the variable “symbol”. 
     The algorithm “arith_decode” also comprises an adaptation  570   e  of the variables “high” and “low”. If the symbol value represented by the variable “symbol” is different from 0, the variable “high” is updated, as shown at reference numeral  570   e . Also, the value of the variable “low” is updated, as shown at reference numeral  570   e . The variable “high” is set to a value which is determined by the value of the variable “low”, the variable “range” and the entry having the index “symbol — 1 ” of the selected cumulative-frequencies-table. The variable “low” is increased, wherein the magnitude of the increase is determined by the variable “range” and the entry of the selected cumulative-frequencies-table having the index “symbol”. Accordingly, the difference between the values of the variables “low” and “high” is adjusted in dependence on the numeric difference between two adjacent entries of the selected cumulative-frequencies-table. 
     Accordingly, if a symbol value having a low probability is detected, the interval between the values of the variables “low” and “high” is reduced to a narrow width. In contrast, if the detected symbol value comprises a relatively large probability, the width of the interval between the values of the variables “low” and “high” is set to a comparatively large value. Again, the width of the interval between the values of the variable “low” and “high” is dependent on the detected symbol and the corresponding entries of the cumulative-frequencies-table. 
     The algorithm “arith_decode( )” also comprises an interval renormalization  570   f , in which the interval determined in the step  570   e  is iteratively shifted and scaled until the “break”-condition is reached. In the interval renormalization  570   f , a selective shift-downward operation  570   fa  is performed. If the variable “high” is smaller than 524286, nothing is done, and the interval renormalization continues with an interval-size-increase operation  570   fb . If, however, the variable “high” is not smaller than 524286 and the variable “low” is greater than or equal to 524286, the variables “values”, “low” and “high” are all reduced by  524286 , such that an interval defined by the variables “low” and “high” is shifted downwards, and such that the value of the variable “value” is also shifted downwards. If, however, it is found that the value of the variable “high” is not smaller than 524286, and that the variable “low” is not greater than or equal to 524286, and that the variable “low” is greater than or equal to 262143 and that the variable “high” is smaller than 786429, the variables “value”, “low” and “high” are all reduced by  262143 , thereby shifting down the interval between the values of the variables “high” and “low” and also the value of the variable “value”. If, however, neither of the above conditions is fulfilled, the interval renormalization is aborted. 
     If, however, any of the above-mentioned conditions, which are evaluated in the step  570   fa , is fulfilled, the interval-increase-operation  570   fb  is executed. In the interval-increase-operation  570   fb , the value of the variable “low” is doubled. Also, the value of the variable “high” is doubled, and the result of the doubling is increased by 1. Also, the value of the variable “value” is doubled (shifted to the left by one bit), and a bit of the bitstream, which is obtained by the helper function “arith_get_next_bit” is used as the least-significant bit. Accordingly, the size of the interval between the values of the variables “low” and “high” is approximately doubled, and the precision of the variable “value” is increased by using a new bit of the bitstream. As mentioned above, the steps  570   fa  and  570   fb  are repeated until the “break” condition is reached, i.e. until the interval between the values of the variables “low” and “high” is large enough. 
     Regarding the functionality of the algorithm “arith_decode( )”, it should be noted that the interval between the values of the variables “low” and “high” is reduced in the step  570   e  in dependence on two adjacent entries of the cumulative-frequencies-table referenced by the variable “cum_freq”. If an interval between two adjacent values of the selected cumulative-frequencies-table is small, i.e. if the adjacent values are comparatively close together, the interval between the values of the variables “low” and “high”, which is obtained in the step  570   e , will be comparatively small. In contrast, if two adjacent entries of the cumulative-frequencies-table are spaced further, the interval between the values of the variables “low” and “high”, which is obtained in the step  570   e , will be comparatively large. 
     Consequently, if the interval between the values of the variables “low” and “high”, which is obtained in the step  570   e , is comparatively small, a large number of interval renormalization steps will be executed to re-scale the interval to a “sufficient” size (such that neither of the conditions of the condition evaluation  570   fa  is fulfilled). Accordingly, a comparatively large number of bits from the bitstream will be used in order to increase the precision of the variable “value”. If, in contrast, the interval size obtained in the step  570   e  is comparatively large, only a smaller number of repetitions of the interval normalization steps  570   fa  and  570   fb  may be used in order to renormalize the interval between the values of the variables “low” and “high” to a “sufficient” size. Accordingly, only a comparatively small number of bits from the bitstream will be used to increase the precision of the variable “value” and to prepare a decoding of a next symbol. 
     To summarize the above, if a symbol is decoded, which comprises a comparatively high probability, and to which a large interval is associated by the entries of the selected cumulative-frequencies-table, only a comparatively small number of bits will be read from the bitstream in order to allow for the decoding of a subsequent symbol. In contrast, if a symbol is decoded, which comprises a comparatively small probability and to which a small interval is associated by the entries of the selected cumulative-frequencies-table, a comparatively large number of bits will be taken from the bitstream in order to prepare a decoding of the next symbol. 
     Accordingly, the entries of the cumulative-frequencies-tables reflect the probabilities of the different symbols and also reflect a number of bits that may be used for decoding a sequence of symbols. By varying the cumulative-frequencies-table in dependence on a context, i.e. in dependence on previously-decoded symbols (or spectral values), for example, by selecting different cumulative-frequencies-tables in dependence on the context, stochastic dependencies between the different symbols can be exploited, which allows for a particular bitrate-efficient encoding of the subsequent (or adjacent) symbols. 
     To summarize the above, the function “arith_decode( )”, which has been described with reference to  FIG.  5   g   , is called with the cumulative-frequencies-table “arith_cf_m[pki][ ]”, corresponding to the index “pki” returned by the function “arith_get_pk( )” to determine the most-significant bit-plane value m (which may be set to the symbol value represented by the return variable “symbol”). 
     6.7 Escape Mechanism 
     While the decoded most-significant bit-plane value m (which is returned as a symbol value by the function “arith_decode( )” is the escape symbol “ARITH_ESCAPE”, an additional most-significant bit-plane value m is decoded and the variable “led” is incremented by 1. 
     Accordingly, an information is obtained about the numeric significance of the most-significant bit-plane value m as well as on the number of less-significant bit-planes to be decoded. 
     If an escape symbol “ARITH_ESCAPE” is decoded, the level variable “led” is increased by 1. Accordingly, the state value which is input to the function “arith_get_pk” is also modified in that a value represented by the uppermost bits (bits 24 and up) is increased for the next iterations of the algorithm  312   ba.    
     6.8 Context Update According to  FIG.  5   h      
     Once the spectral value is completely decoded (i.e. all of the least-significant bit-planes have been added, the context tables q and qs are updated by calling the function “arith_update_context(a,i,1g))”. In the following, details regarding the function “arith_update_context(a,i,1g)” will be described taking reference to  FIG.  5   h   , which shows a pseudo program code representation of said function. 
     The function “arith_update_context( )” receives, as input variables, the decoded quantized spectral coefficient a, the index i of the spectral value to be decoded (or of the decoded spectral value) and the number 1g of spectral values (or coefficients) associated with the current audio frame. 
     In a step  580 , the currently decoded quantized spectral value (or coefficient) a is copied into the context table or context array q. Accordingly, the entry q[1] [i] of the context table q is set to a. Also, the variable “a0” is set to the value of “a”. 
     In a step  582 , the level value q[1][i]0.1 of the context table q is determined. By default, the level value q[1][i]0.1 of the context table q is set to zero. However, if the absolute value of the currently coded spectral value a is larger than 4, the level value q[1][i]0.1 is incremented. With each increment, the variable “a” is shifted to the right by one bit. The increment of the level value q[1][i]0.1 is repeated until the absolute value of the variable a0 is smaller than, or equal to, 4. 
     In a step  584 , a 2-bit context value q[1][i].c of the context table q is set. The 2-bit context value q[1] [i].c is set to the value of zero if the currently decoded spectral value a is equal to zero. Otherwise, if the absolute value of the decoded spectral value a is smaller than, or equal to, 1, the 2-bit context value q[1][i].c is set to 1. Otherwise, if the absolute value of the currently decoded spectral value a is smaller than, or equal to, 3, the 2-bit context value q[1][i].c is set to 2. Otherwise, i.e. if the absolute value of the currently decoded spectral value a is larger than 3, the 2-bit context value q[1][i].c is set to 3. Accordingly, the 2-bit context value q[1][i].c is obtained by a very coarse quantization of the currently decoded spectral coefficient a. 
     In a subsequent step  586 , which is only performed if the index i of the currently decoded spectral value is equal to the number 1g of coefficients (spectral values) in the frame, that is, if the last spectral value of the frame has been decoded) and the core mode is a linear-prediction-domain core mode (which is indicated by “core_mode==1”), the entries q[1][j].c are copied into the context table qs [k]. The copying is performed as shown at reference numeral  586 , such that the number 1g of spectral values in the current frame is taken into consideration for the copying of the entries q[1][j].c to the context table qs [k]. In addition, the variable “previous_1g” takes the value  1024 . 
     Alternatively, however, the entries q[1][j].c of the context table q are copied into the context table qs[j] if the index i of the currently decoded spectral coefficient reaches the value of 1g and the core mode is a frequency-domain core mode (indicated by “core_mode==0”). 
     In this case, the variable “previous_1g” is set to the minimum between the value of 1024 and the number 1g of spectral values in the frame. 
     6.9 Summary of the Decoding Process 
     In the following, the decoding process will briefly be summarized. For details, reference is made to the above discussion and also to  FIGS.  3 ,  4  and  5     a  to  5   i.    
     The quantized spectral coefficients a are noiselessly coded and transmitted, starting from the lowest frequency coefficient and progressing to the highest frequency coefficient. 
     The coefficients from the advanced-audio coding (AAC) are stored in the array “x_ac_quant[g][win][sfb][bin]”, and the order of transmission of the noiseless coding codewords is such, that when they are decoded in the order received and stored in the array, bin is the most rapidly incrementing index and g is the most slowly incrementing index. Index bin designates frequency bins. The index “sfb” designates scale factor bands. The index “win” designates windows. The index “g” designates audio frames. 
     The coefficients from the transform-coded-excitation are stored directly in an array “x_tcx_invquant[win][bin]”, and the order of the transmission of the noiseless coding codewords is such that when they are decoded in the order received and stored in the array, “bin” is the most rapidly incrementing index and “win” is the most slowly incrementing index. 
     First, a mapping is done between the saved past context stored in the context table or array “qs” and the context of the current frame q (stored in the context table or array q). The past context “qs” is stored onto 2-bits per frequency line (or per frequency bin). 
     The mapping between the saved past context stored in the context table “qs” and the context of the current frame stored in the context table “q” is performed using the function “arith_map_context( )”, a pseudo-program-code representation of which is shown in  FIG.  5     a.    
     The noiseless decoder outputs signed quantized spectral coefficients “a”. 
     At first, the state of the context is calculated based on the previously-decoded spectral coefficients surrounding the quantized spectral coefficients to decode. The state of the context s corresponds to the 24 first bits of the value returned by the function “arith_get_context( )”. The bits beyond the 24 th  bit of the returned value correspond to the predicted bit-plane-level lev0. The variable “lev” is initialized to lev0. A pseudo program code representation of the function “arith_get_context” is shown in  FIGS.  5   b    and  5   c.    
     Once the state s and the predicted level “lev0” are known, the most-significant 2-bits wise plane m is decoded using the function “arith_decode( )”, fed with the appropriated cumulative-frequencies-table corresponding to the probability model corresponding to the context state. 
     The correspondence is made by the function “arith_get_pk( )”. 
     A pseudo-program-code representation of the function “arith_get_pk( )” is shown in  FIG.  5     e.    
     A pseudo program code of another function “get_pk” which may take the place of the function “arith_get_pk( )” is shown in  FIG.  5   f   . A pseudo program code of another function “get_pk”, which may take over the place of the function “arith_get_pk( )” is shown in  FIG.  5     d.    
     The value m is decoded using the function “arith_decode( )” called with the cumulative-frequencies-table, “arith_cf_m[pki][ ], where, pki” corresponds to the index returned by the function “arith_get_pk( )” (or, alternatively, by the function “get_pk( )”). 
     The arithmetic coder is an integer implementation using the method of tag generation with scaling (see, e.g., K. Sayood “Introduction to Data Compression” third edition, 2006, Elsevier Inc.). The pseudo-C-code shown in  FIG.  5   g    describes the used algorithm. 
     When the decoded value m is the escape symbol, “ARITH_ESCAPE”, another value m is decoded and the variable “lev” is incremented by 1. Once the value m is not the escape symbol, “ARITH_ESCAPE”, the remaining bit-planes are then decoded from the most-significant to the least-significant level, by calling “lev” times the function “arith_decode( )” with the cumulative-frequencies-table “arith_cf_r[ ]”. Said cumulative-frequencies-table “arith_cf_r[ ]” may, for example, describe an even probability distribution. 
     The decoded bit planes r permit the refining of the previously-decoded value m in the following manner 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 a = m; 
               
               
                   
                 for (i=0; i&lt;lev;i++) { 
               
               
                   
                  r = arith_decode (arith_cf_r,2); 
               
               
                   
                  a = (a&lt;&lt;1) | (r&amp;1); 
               
               
                   
                 } 
               
               
                   
                   
               
            
           
         
       
     
     Once the spectral quantized coefficient a is completely decoded, the context tables q, or the stored context qs, is updated by the function “arith_update_context( )”, for the next quantized spectral coefficients to decode. 
     A pseudo program code representation of the function “arith_update_context( )” is shown in  FIG.  5     h.    
     In addition, a legend of the definitions is shown in  FIG.  5     i.    
     7. Mapping Tables 
     In an embodiment according to the invention, particularly advantageous tables “ari_s_hash” and “ari_gs_hash” and “ari_cf_m” are used for the execution of the function “get_pk”, which has been discussed with reference to  FIG.  5   d   , or for the execution of the function “arith_get_pk”, which has been discussed with reference to  FIG.  5   e   , or for the execution of the function “get_pk”, which was discussed with reference  5   f , and for the execution of the function “arith_decode” which was discussed with reference to  FIG.  5     g.    
     7.1. Table “Ari_s_Hash[387]” According to  FIG.  17     
     A content of a particularly advantageous implementation of the table “ari_s_hash”, which is used by the function “get_pk” which was described with reference to  FIG.  5   d   , is shown in the table of  FIG.  17   . It should be noted that the table of  FIG.  17    lists the 387 entries of the table “ari_s_hash[387]”. It should also be noted that the table representation of  FIG.  17    shows the elements in the order of the element indices, such that the first value “0x00000200” corresponds to a table entry “ari_s_hash[0]” having element index (or table index)  0 , such that the last value “0x03D0713D” corresponds to a table entry “ari_s_hash[386]” having element index or table index  386 . It should further be noted her that “0x” indicates that the table entries of the table “ari_s_hash” are represented in a hexadecimal format. Furthermore, the table entries of the table “ari_s_hash” according to  FIG.  17    are arranged in numeric order in order to allow for the execution of the first table evaluation  540  of the function “get_pk”. 
     It should further be noted that the most-significant 24 bits of the table entries of the table “ari_s_hash” represent state values, while the least-significant 8-bits represent mapping rule index values pki. 
     Thus, the entries of the table “ari_s_hash” describe a “direct hit” mapping of a state value onto a mapping rule index value “pki”. 
     7.2 Table “Ari_Gs_Hash” According to  FIG.  18     
     A content of a particularly advantageous embodiment of the table “ari_gs_hash” is shown in the table of  FIG.  18   . It should be noted here that the table of table  18  lists the entries of the table “ari_gs_hash”. Said entries are referenced by a one-dimensional integer-type entry index (also designated as “element index” or “array index” or “table index”), which is, for example, designated with “i”. It should be noted that the table “ari_gs_hash” which comprises a total of 225 entries, is well-suited for the use by the second table evaluation  544  of the function “get_pk” described in  FIG.  5     d.    
     It should be noted that the entries of the table “ari_gs_hash” are listed in an ascending order of the table index i for table index values i between zero and 224. The term “0x” indicates that the table entries are described in a hexadecimal format. Accordingly, the first table entry “0X00000401” corresponds to table entry “ari_gs_hash[0]” having table index 0 and the last table entry “0Xffffff3f” corresponds to table entry “ari_gs_hash[224]” having table index  224 . 
     It should also be noted that the table entries are ordered in a numerically ascending manner, such that the table entries are well-suited for the second table evaluation  544  of the function “get_pk”. The most-significant 24 bits of the table entries of the table “ari_gs_hash” describe boundaries between ranges of state values, and the 8 least-significant bits of the entries describe mapping rule index values “pki” associated with the ranges of state values defined by the 24 most-significant bits. 
     7.3 Table “Ari_Cf_m” According to  FIG.  19     
       FIG.  19    shows a set of 64 cumulative-frequencies-tables “ari_cf_m[pki][9]”, one of which is selected by an audio encoder  100 ,  700 , or an audio decoder  200 ,  800 , for example, for the execution of the function “arith_decode”, i.e. for the decoding of the most-significant bit-plane value. The selected one of the 64 cumulative-frequencies-tables shown in  FIG.  19    takes the function of the table “cum_freq[ ]” in the execution of the function “arith_decode( )”. 
     As can be seen from  FIG.  19   , each line represents a cumulative-frequencies-table having 9 entries. For example, a first line  1910  represents the 9 entries of a cumulative-frequencies-table for “pki=0”. A second line  1912  represents the 9 entries of a cumulative-frequencies-table for “pki=1”. Finally, a 64 th  line  1964  represents the 9 entries of a cumulative-frequencies-table for “pki=63”. Thus,  FIG.  19    effectively represents 64 different cumulative-frequencies-tables for “pki=0” to a “pki=63”, wherein each of the 64 cumulative-frequencies-tables is represented by a single line and wherein each of said cumulative-frequencies-tables comprises 9 entries. 
     Within a line (e.g. a line  1910  or a line  1912  or a line  1964 ), a leftmost value describes a first entry of a cumulative-frequencies-table and a rightmost value describes the last entry of a cumulative-frequencies-table. 
     Accordingly, each line  1910 ,  1912 ,  1964  of the table representation of  FIG.  19    represents the entries of a cumulative-frequencies-table for use by the function “arith_decode” according to  FIG.  5   g   . The input variable “cum_freq[ ]” of the function “arith_decode” describes which of the 64 cumulative-frequencies-tables (represented by individual lines of 9 entries) of the table “ari_cf_m” should be used for the decoding of the current spectral coefficients. 
     7.4 Table “Ari_s_Hash” According to  FIG.  20     
       FIG.  20    shows an alternative for the table “ari_s_hash”, which may be used in combination with the alternative function “arith_get_pk( )” or “get_pk( )” according to  FIG.  5   e    or  5   f.    
     The table “ari_s_hash” according to  FIG.  20    comprises 386 entries, which are listed in  FIG.  20    in an ascending order of the table index. Thus, the first table value “0x0090D52E” corresponds to the table entry “ari_s_hash[0]” having table index 0, and the last table entry “0x03D0513C” corresponds to the table entry “ari_s_hash[386]” having table index  386 . 
     The “0x” indicates that the table entries are represented in a hexadecimal form. The 24 most-significant bits of the entries of the table “ari_s_hash” describe significant states, and the 8 least-significant bits of the entries of the table “ari_s_hash” describe mapping rule index values. 
     Accordingly, the entries of the table “ari_s_hash” describe a mapping of significant states onto mapping rule index values “pki”. 
     8. Performance Evaluation and Advantages 
     The embodiments according to the invention use updated functions (or algorithms) and an updated set of tables, as discussed above, in order to obtain an improved tradeoff between computation complexity, memory requirements, and coding efficiency. 
     Generally speaking, the embodiments according to the invention create an improved spectral noiseless coding. 
     The present description describes embodiments for the CE on improved spectral noiseless coding of spectral coefficients. The proposed scheme is based on the “original” context-based arithmetic coding scheme, as described in the working draft 4 of the USAC draft standard, but significantly reduces memory requirements (RAM, ROM), while maintaining a noiseless coding performance A lossless transcoding of WD3 (i.e. of the output of an audio encoder providing a bitstream in accordance with the working draft 3 of the USAC draft standard) was proven to be possible. The scheme described herein is, in general, scalable, allowing further alternative tradeoffs between memory requirements and encoding performance. Embodiments according to the invention aim at replacing the spectral noiseless coding scheme as used in the working draft 4 of the USAC draft standard. 
     The arithmetic coding scheme described herein is based on the scheme as in the reference model 0 (RM0) or the working draft 4 (WD4) of the USAC draft standard. Spectral coefficients previous in frequency or in time model a context. This context is used for the selection of cumulative-frequencies-tables for the arithmetic coder (encoder or decoder). Compared to the embodiment according to WD4, the context modeling is further improved and the tables holding the symbol probabilities were retrained. The number of different probability models was increased from 32 to 64. 
     Embodiments according to the invention reduce the table sizes (data ROM demand) to 900 words of length 32-bits or 3600 bytes. In contrast, embodiments according to WD4 of the USAC draft standard may use 16894.5 words or 76578 bytes. The static RAM demand is reduced, in some embodiments according to the invention, from 666 words (2664 bytes) to 72 (288 bytes) per core coder channel. At the same time, it fully preserves the coding performance and can even reach a gain of approximately 1.04% to 1.39%, compared to the overall data rate over all 9 operating points. All working draft 3 (WD3) bitstreams can be transcoded in a lossless manner without affecting the bit reservoir constraints. 
     The proposed scheme according to the embodiments of the invention is scalable: flexible tradeoffs between memory demand and coding performance are possible. By increasing the table sizes to the coding gain can be further increased. 
     In the following, a brief discussion of the coding concept according to WD4 of the USAC draft standard will be provided to facilitate the understanding of the advantages of the concept described herein. In USAC WD4, a context based arithmetic coding scheme is used for noiseless coding of quantized spectral coefficients. As context, the decoded spectral coefficients are used, which are previous in frequency and time. According to WD4, a maximum number of 16 spectral coefficients are used as context, 12 of which are previous in time. Both, spectral coefficients used for the context and to be decoded, are grouped as 4-tuples (i.e. four spectral coefficients neighbored in frequency, see  FIG.  10   a   ). The context is reduced and mapped on a cumulative-frequencies-table, which is then used to decode the next 4-tuple of spectral coefficients. 
     For the complete WD4 noiseless coding scheme, a memory demand (ROM) of 16894.5 words (67578 bytes) may be used. Additionally, 666 words (2664 byte) of static ROM per core-coder channel may be used to store the states for the next frame. 
     The table representation of  FIG.  11   a    describes the tables as used in the USAC WD4 arithmetic coding scheme. 
     A total memory demand of a complete USAC WD4 decoder is estimated to be 37000 words (148000 byte) for data ROM without a program code and 10000 to 17000 words for the static RAM. It can clearly be seen that the noiseless coder tables consume approximately 45% of the total data ROM demand. The largest individual table already consumes 4096 words (16384 byte). 
     It has been found that both, the size of the combination of all tables and the large individual tables exceed typical cache sizes as provided by fixed point chips for low-budget portable devices, which is in a typical range of 8-32 kByte (e.g. ARM9e, TIC64xx, etc.). This means that the set of tables can probably not be stored in the fast data RAM, which enables a quick random access to the data. This causes the whole decoding process to slow down. 
     In the following, the proposed new scheme will briefly be described. 
     To overcome the problems mentioned above, an improved noiseless coding scheme is proposed to replace the scheme as in WD4 of the USAC draft standard. As a context based arithmetic coding scheme, it is based on the scheme of WD4 of the USAC draft standard, but features a modified scheme for the derivation of cumulative-frequencies-tables from the context. Further on, context derivation and symbol coding is performed on granularity of a single spectral coefficient (opposed to 4-tuples, as in WD4 of the USAC draft standard). In total, 7 spectral coefficients are used for the context (at least in some cases). By reduction in mapping, one of in total 64 probability models or cumulative frequency tables (in WD4: 32) is selected. 
       FIG.  10   b    shows a graphical representation of a context for the state calculation, as used in the proposed scheme (wherein a context used for the zero region detection is not shown in  FIG.  10   b   ). 
     In the following, a brief discussion will be provided regarding the reduction of the memory demand, which can be achieved by using the proposed coding scheme. The proposed new scheme exhibits a total ROM demand of 900 words (3600 Bytes) (see the table of  FIG.  11   b    which describes the tables as used in the proposed coding scheme). 
     Compared to the ROM demand of the noiseless coding scheme in WD4 of the USAC draft standard, the ROM demand is reduced by 15994.5 words (64978 Bytes)(see also  FIG.  12   a   , which figure shows a graphical representation of the ROM demand of the noiseless coding scheme as proposed and of the noiseless coding scheme in WD4 of the USAC draft standard). This reduces the overall ROM demand of a complete USAC decoder from approximately 37000 words to approximately 21000 words, or by more than 43% (see  FIG.  12   b   , which shows a graphical representation of a total USAC decoder data ROM demand in accordance with WD4 of the USAC draft standard, as well as in accordance with the present proposal). 
     Further on, the amount of information needed for the context derivation in the next frame (static RAM) is also reduced. According to WD4, the complete set of coefficients (maximally 1152) with a resolution of typically 16-bits additional to a group index per 4-tuple of resolution 10-bits needed to be stored, which sums up to 666 words (2664 Bytes) per core-coder channel (complete USAC WD4 decoder: approximately 10000 to 17000 words). 
     The new scheme, which is used in embodiments according to the invention, reduces the persistent information to only 2-bits per spectral coefficient, which sums up to 72 words (288 Bytes) in total per core-coder channel. The demand on static memory can be reduced by 594 words (2376 Bytes). 
     In the following, some details regarding a possible increase of coding efficiency will be described. The coding efficiency of embodiments according to the new proposal was compared against the reference quality bitstreams according to WD3 of the USAC draft standard. The comparison was performed by means of a transcoder, based on a reference software decoder. For details regarding the comparison of the noiseless coding according to WD3 of the USAC draft standard and the proposed coding scheme, reference is made to  FIG.  9   , which shows a schematic representation of a test arrangement. 
     Although the memory demand is drastically reduced in embodiments according to the invention when compared to embodiments according to WD3 or WD4 of the USAC draft standard, the coding efficiency is not only maintained, but slightly increased. The coding efficiency is on average increased by 1.04% to 1.39%. For details, reference is made to the table of  FIG.  13   a   , which shows a table representation of average bitrates produced by the USAC coder using the working draft arithmetic coder and an audio coder (e.g., USAC audio coder) according to an embodiment of the invention. 
     By measurement of the bit reservoir fill level, it was shown that the proposed noiseless coding is able to losslessly transcode the WD3 bitstream for every operating point. For details, reference is made to the table of  FIG.  13   b    which shows a table representation of a bit reservoir control for an audio coder according to the USAC WD3 and an audio coder according to an embodiment of the present invention. 
     Details on average bitrates per operating mode, minimum, maximum and average bitrates on a frame basis and a best/worst case performance on a frame basis can be found in the tables of  FIGS.  14 ,  15 , and  16   , wherein the table of  FIG.  14    shows a table representation of average bitrates for an audio coder according to the USAC WD3 and for an audio coder according to an embodiment of the present invention, wherein the table of  FIG.  15    shows a table representation of minimum, maximum, and average bitrates of a USAC audio coder on a frame basis, and wherein the table of  FIG.  16    shows a table representation of best and worst cases on a frame basis. 
     In addition, it should be noted that embodiments according to the present invention provide a good scalability. By adapting the table size, a tradeoff between memory requirements, computational complexity and coding efficiency can be adjusted in accordance with the requirements. 
     9. Bitstream Syntax 
     9.1. Payloads of the Spectral Noiseless Coder 
     In the following, some details regarding the payloads of the spectral noiseless coder will be described. In some embodiments, there is a plurality of different coding modes, such as for example, a so-called linear-prediction-domain, “coding mode” and a “frequency-domain” coding mode. In the linear-prediction-domain coding mode, a noise shaping is performed on the basis of a linear-prediction analysis of the audio signal, and a noise-shaped signal is encoded in the frequency-domain. In the frequency-domain mode, a noise shaping is performed on the basis of a psychoacoustic analysis and a noise-shaped version of the audio content is encoded in the frequency-domain 
     Spectral coefficients from both, a “linear-prediction domain” coded signal and a “frequency-domain” coded signal are scalar quantized and then noiselessly coded by an adaptively context dependent arithmetic coding. The quantized coefficients are transmitted from the lowest-frequency to the highest-frequency. Each individual quantized coefficient is split into the most significant 2-bits-wise plane m, and the remaining less-significant bit-planes r. The value m is coded according to the coefficient&#39;s neighborhood. The remaining less-significant bit-planes r are entropy-encoded, without considering the context. The values m and r form the symbols of the arithmetic coder. 
     A detailed arithmetic decoding procedure is described herein. 
     9.2. Syntax Elements 
     In the following, the bitstream syntax of a bitstream carrying the arithmetically-encoded spectral information will be described taking reference to  FIGS.  6   a    to  6   h.    
       FIG.  6   a    shows a syntax representation of so-called USAC raw data block (“usac_raw_data_block( )”). 
     The USAC raw data block comprises one or more single channel elements (“single_channel_element( )”) and/or one or more channel pair elements (“channel_pair_element( )”). 
     Taking reference now to  FIG.  6   b   , the syntax of a single channel element is described. The single channel element comprises a linear-prediction-domain channel stream (“lpd_channel_stream( )”) or a frequency-domain channel stream (“fd_channel_stream( )”) in dependence on the core mode. 
       FIG.  6   c    shows a syntax representation of a channel pair element. A channel pair element comprises core mode information (“core_mode0”, “core_mode1”). In addition, the channel pair element may comprise a configuration information “ics_info( )”. Additionally, depending on the core mode information, the channel pair element comprises a linear-prediction-domain channel stream or a frequency-domain channel stream associated with a first of the channels, and the channel pair element also comprises a linear-prediction-domain channel stream or a frequency-domain channel stream associated with a second of the channels. 
     The configuration information “ics_mfo( )”, a syntax representation of which is shown in  FIG.  6   d   , comprises a plurality of different configuration information items, which are not of particular relevance for the present invention. 
     A frequency-domain channel stream (“fd_channel_stream( )”), a syntax representation of which is shown in  FIG.  6   e   , comprises a gain information (“global_gain”) and a configuration information (“ics_info( )”). In addition, the frequency-domain channel stream comprises scale factor data (“scale_factor_data( )”), which describes scale factors used for the scaling of spectral values of different scale factor bands, and which is applied, for example, by the scaler  150  and the rescaler  240 . The frequency-domain channel stream also comprises arithmetically-coded spectral data (“ac_spectral_data( )”), which represents arithmetically-encoded spectral values. 
     The arithmetically-coded spectral data (“ac_spectral_data( )”), a syntax representation of which is shown in  FIG.  6   f   , comprises an optional arithmetic reset flag (“arith_reset_flag”), which is used for selectively resetting the context, as described above. In addition, the arithmetically-coded spectral data comprise a plurality of arithmetic-data blocks (“arith_data”), which carry the arithmetically-coded spectral values. The structure of the arithmetically-coded data blocks depends on the number of frequency bands (represented by the variable “num_bands”) and also on the state of the arithmetic reset flag, as will be discussed in the following. 
     The structure of the arithmetically-encoded data block will be described taking reference to  FIG.  6   g   , which shows a syntax representation of said arithmetically-coded data blocks. The data representation within the arithmetically-coded data block depends on the number 1g of spectral values to be encoded, the status of the arithmetic reset flag and also on the context, i.e. the previously-encoded spectral values. 
     The context for the encoding of the current set of spectral values is determined in accordance with the context determination algorithm shown at reference numeral  660 . Details with respect to the context determination algorithm have been discussed above taking reference to  FIG.  5   a   . The arithmetically-encoded data block comprises 1g sets of codewords, each set of codewords representing a spectral value. A set of codewords comprises an arithmetic codeword “acod_m [pki] [m]” representing a most-significant bit-plane value m of the spectral value using between 1 and 20 bits. In addition, the set of codewords comprises one or more codewords “acod_r[r]” if the spectral value uses more bit planes than the most-significant bit plane for a correct representation. The codeword “acod_r [r]” represents a less-significant bit plane using between 1 and 20 bits. 
     If, however, one or more less-significant bit-planes may be used (in addition to the most-significant bit plane) for a proper representation of the spectral value, this is signaled by using one or more arithmetic escape codewords (“ARITH_ESCAPE”). Thus, it can be generally said that for a spectral value, it is determined how many bit planes (the most-significant bit plane and, possibly, one or more additional less-significant bit planes) may be used. If one or more less-significant bit planes may be used, this is signaled by one or more arithmetic escape codewords “acod_m [ph] [ARITH_ESCAPE]”, which are encoded in accordance with a currently-selected cumulative-frequencies-table, a cumulative-frequencies-table-index of which is given by the variable pki. In addition, the context is adapted, as can be seen at reference numerals  664 ,  662 , if one or more arithmetic escape codewords are included in the bitstream. Following the one or more arithmetic escape codewords, an arithmetic codeword “acod_m [ph] [m]” is included in the bitstream, as shown at reference numeral  663 , wherein pki designates the currently-valid probability model index (taking into consideration the context adaptation caused by the inclusion of the arithmetic escape codewords), and wherein m designates the most-significant bit-plane value of the spectral value to be encoded or decoded. 
     As discussed above, the presence of any less-significant-bit planes results in the presence of one or more codewords “acod_r [r]”, each of which represents one bit of the least-significant bit plane. The one or more codewords “acod_r[r]” are encoded in accordance with a corresponding cumulative-frequencies-table, which is constant and context-independent. 
     In addition, it should be noted that the context is updated after the encoding of each spectral value, as shown at reference numeral  668 , such that the context is typically different for encoding of two subsequent spectral values. 
       FIG.  6   h    shows a legend of definitions and help elements defining the syntax of the arithmetically-encoded data block. 
     To summarize the above, a bitstream format has been described, which may be provided by the audio coder  100 , and which may be evaluated by the audio decoder  200 . The bitstream of the arithmetically-encoded spectral values is encoded such that it fits the decoding algorithm discussed above. 
     In addition, it should be generally noted that the encoding is the inverse operation of the decoding, such that it can generally be assumed that the encoder performs a table lookup using the above-discussed tables, which is approximately inverse to the table lookup performed by the decoder. Generally, it can be said that a man skilled in the art who knows the decoding algorithm and/or the desired bitstream syntax will easily be able to design an arithmetic encoder, which provides the data that is defined in the bitstream syntax and may be used by the arithmetic decoder. 
     10. Implementation Alternatives 
     Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus. Some or all of the method steps may be executed by (or using) a hardware apparatus, like for example, a microprocessor, a programmable computer or an electronic circuit. In some embodiments, some one or more of the most important method steps may be executed by such an apparatus. 
     The inventive encoded audio signal can be stored on a digital storage medium or can be transmitted on a transmission medium such as a wireless transmission medium or a wired transmission medium such as the Internet. 
     Depending on certain implementation requirements, embodiments of the invention can be implemented in hardware or in software. The implementation can be performed using a digital storage medium, for example a floppy disk, a DVD, a Blue-Ray, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed. Therefore, the digital storage medium may be computer readable. 
     Some embodiments according to the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed. 
     Generally, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may for example be stored on a machine readable carrier. 
     Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier. 
     In other words, an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer. 
     A further embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, recorded thereon, the computer program for performing one of the methods described herein. 
     A further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein. The data stream or the sequence of signals may for example be configured to be transferred via a data communication connection, for example via the Internet. 
     A further embodiment comprises a processing means, for example a computer, or a programmable logic device, configured to or adapted to perform one of the methods described herein. 
     A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein. 
     In some embodiments, a programmable logic device (for example a field programmable gate array) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein. Generally, the methods are advantageously performed by any hardware apparatus. 
     The above described embodiments are merely illustrative for the principles of the present invention. It is understood that modifications and variations of the arrangements and the details described herein will be apparent to others skilled in the art. It is the intent, therefore, to be limited only by the scope of the impending patent claims and not by the specific details presented by way of description and explanation of the embodiments herein. 
     While the foregoing has been particularly shown and described with reference to particular embodiments above, it will be understood by those skilled in the art that various other changes in the forms and details may be made without departing from the sprit and cope thereof. It is to be understood that various changes may be made in adapting to different embodiments without departing from the broader concept disclosed herein and comprehended by the claims that follow. 
     11. Conclusion 
     To conclude, it can be noted that embodiments according to the invention create an improved spectral noiseless coding scheme. Embodiments according to the new proposal allows for the significant reduction of the memory demand from 16894.5 words to 900 words (ROM) and from 666 words to 72 (static RAM per core-coder channel). This allows for the reduction of the data ROM demand of the complete system by approximately 43% in one embodiment. Simultaneously, the coding performance is not only fully maintained, but on average even increased. A lossless transcoding of WD3 (or of a bitstream provided in accordance with WD3 of the USAC draft standard) was proven to be possible. Accordingly, an embodiment according to the invention is obtained by adopting the noiseless decoding described herein into the upcoming working draft of the USAC draft standard. 
     To summarize, in an embodiment the proposed new noiseless coding may engender the modifications in the MPEG USAC working draft with respect to the syntax of the bitstream element “arith_data( )” as shown in  FIG.  6   g   , with respect to the payloads of the spectral noiseless coder as described above and as shown in  FIG.  5   h   , with respect to the spectral noiseless coding, as described above, with respect to the context for the state calculation as shown in  FIG.  4   , with respect to the definitions as shown in  FIG.  5   i   , with respect to the decoding process as described above with reference to  FIGS.  5   a ,  5   b ,  5   c ,  5   e ,  5   g ,  5   h   , and with respect to the tables as shown in  FIGS.  17 ,  18 ,  20   , and with respect to the function “get_pk” as shown in  FIG.  5   d   . Alternatively, however, the table “ari_s_hash” according to  FIG.  20    may be used instead of the table “ari_s_hash” of  FIG.  17   , and the function “get_pk” of  FIG.  5   f    may be used instead of the function “get_pk” according to  FIG.  5     d.    
     While this invention has been described in terms of several embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations and equivalents as fall within the true spirit and scope of the present invention.