Abstract:
An apparatus for providing at least first and second representations of an audio signal for use in a communications system is described. The apparatus comprises a first quantizer for quantizing at least a portion of the signal in accordance with a first multidimensional lattice to generate a first representation. The apparatus further comprises a second quantizer for quantizing at least a portion of the signal in accordance with a second, different multidimensional lattice to generate a second representation. In an illustrative embodiment, the first representation is a core representation containing core audio information. The second representation is an enhancement representation containing enhancement audio information. The core representation is necessary for recovering the audio signal with minimal acceptable quality. Audio quality is enhanced when the core representation, together with the enhancement representation, is used to recover the audio signal. A method for use in such an apparatus is also described.

Description:
This application is a Divisional of U.S. Ser. No. 09/280,785 filed Mar. 29, 1999, now U.S. Pat. No. 6,366,888. 

   FIELD OF THE INVENTION 
   The invention relates to systems and methods for communications of a signal containing information, and more particularly to communications systems and methods for coding the signal to generate multiple representations thereof. 
   BACKGROUND OF THE INVENTION 
   Communications of audio information play an important role in multimedia applications, and Internet applications such as a music-on-demand service, music preview for online compact disk (CD) purchases, etc. To efficiently utilize bandwidth to communicate audio information, a perceptual audio coding (PAC) technique has been developed. For details on the PAC technique, one may refer to U.S. Pat. No. 5,285,498 issued Feb. 8, 1994 to Johnston; and U.S. Pat. No. 5,040,217 issued Aug. 13, 1991 to Brandenburg et al., both of which are hereby incorporated by reference. In accordance with such a PAC technique, each of a succession of time domain blocks of an audio signal representing audio information is coded in the frequency domain. Specifically, the frequency domain representation of each block is divided into coder bands, each of which is individually coded, based on psycho-acoustic criteria, in such a way that the audio information is significantly compressed, thereby requiring a smaller number of bits to represent the audio information than would be the case if the audio information were represented in a more simplistic digital format, such as the PCM format. 
   For example, in providing the aforementioned music-on-demand service, a server connected to the Internet may store PAC compressed versions of each available musical piece to serve client needs. Each version of the musical piece corresponds to a different connection speed at which a client, e.g., a personal computer (PC) having a modem, can afford to communicate over the Internet. The quality, or the lack of distortion, of the version of the musical piece increases with the connection speed corresponding thereto. Thus, for instance, if the server supports (a) a plain old telephone service (POTS) connection speed of about 28.8 kb/sec, (b) an integrated services digital network (ISDN) connection speed of about 64 kb/sec, and (c) a dual ISDN connection speed on the order of 100 kb/sec, three corresponding versions of the musical piece having the respective qualities need to be stored in the server. However, the storage of musical pieces in this manner is undesirably inefficient and occupies much memory space especially when a large number of musical pieces need to be made available. 
   In delivering the service to a client at a given connection speed, the server may packetize the corresponding audio information in the storage, and communicate the resulting packets through a packet switched network, e.g., the Internet. However, in the event that some of the packets are lost in transit because of imperfect network or channel conditions, which is likely, the quality of the received signal representative of a musical piece would be significantly degraded. 
   Accordingly, there exists needs for efficiently storing and distributing information at different rates, and effectively maintaining the minimum acceptable quality of the received signal despite imperfect network or channel conditions. 
   SUMMARY OF THE INVENTION 
   In accordance with the invention, multi-rate coding is implemented to generate multiple subrate representations of a signal containing information, e.g., audio information. These representations are different from one another and may be delivered at rates lower than or equal to the required delivery rates of the information. 
   For example, in providing the music-on-demand service described above, at least one of the subrate representations, referred to as a “C-representation,” may contain core information delivered at a subrate of 28.8 kb/sec. The other subrate representations, referred to as a “E 1 -representation” and “E 2 -representation, each may contain enhancement information delivered at a subrate of 36 kb/sec. Because of the design of the multi-rate coding in accordance with the invention, in this instance recovery of the signal based on the C-representation alone affords the minimum acceptable 28.8 kb/sec signal quality; recovery of the signal based on the C-representation in combination with either E 1 -representation or E 2 -representation affords a higher 64 kb/sec signal quality; and recovery of the signal based on the C-representation in combination with both E 1 -representation and E 2 -representation affords the highest 100 kb/sec signal quality. Advantageously, the server of the aforementioned music-on-demand service needs to store in its memory the subrate representations, i.e., 28.8 kb/sec C-representation, 36 kb/sec E 1 -representation and 36 kb/sec E 2 -representation, of each musical piece, in lieu of the 28.8 kb/sec, 64 kb/sec and 100 kb/sec versions thereof as in prior art, to accommodate the different connection speeds and quality requirements, thereby effectively saving the memory space. 
   In accordance with an aspect of the invention, when the subrate representations are communicated to a client terminal in the form of packets, each packet includes at least an information content derived from one of the representations, and an indicator identifying the representation from which the information content is derived. Despite losses of some packets in transit because of imperfect channel or network conditions, the signal is recovered based on at least the received packets indicated to contain C-representation information to maintain the minimum acceptable signal quality. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
     In the drawing, 
       FIG. 1  illustrates an arrangement embodying the principles of the invention for communicating audio information through a communication network; 
       FIG. 2  is a block diagram of a server in the arrangement of  FIG. 1 ; 
       FIG. 3A  illustrates a homogeneous multidimensional lattice based on which a prior art quantizer performs quantization; 
       FIG. 3B  illustrates a first non-homogeneous multidimensional lattice based on which a first complementary quantizer in the server of  FIG. 2  performs quantization; 
       FIG. 3C  illustrates a second non-homogeneous multidimensional lattice based on which a second complementary quantizer in the server of  FIG. 2  performs quantization; 
       FIG. 4  illustrates a stream of packets generated by the server of  FIG. 2 ; and 
       FIG. 5  is a flow chart depicting the steps whereby a client terminal in the arrangement of  FIG. 1  processes the packets from the server. 
   

   DETAILED DESCRIPTION 
     FIG. 1  illustrates arrangement  100  embodying the principles of the invention for communicating information, e.g., audio information. In this illustrative embodiment, server  105  in arrangement  100  provides a music-on-demand service to client terminals through Internet  120 . One such client terminal is numerically denoted  130  which may be a personal computer (PC). As is well known, Internet  120  is a packet switched network for transporting information in packets in accordance with the standard transmission control protocol/Internet protocol (TCP/IP). 
   Conventional software including browser software, e.g., the NETSCAPE NAVIGATOR or MICROSOFT EXPLORER browser is installed in client terminal  130  for communicating information with server  105 , which is identified by a predetermined uniform resource locator (URL) on Internet  120 . For example, to request the music-on-demand service provided by server  105 , a modem (not shown) in client terminal  130  is used to first establish communication connection  125  with Internet  120 . Depending on the telecommunication facility subscribed by the user of client terminal  130 , communication connection  125  may be limited by different connection speeds. For instance, a plain old telephone service (POTS) connection typically affords a connection speed of about 28.8 kb/sec; an integrated services digital network (ISDN) connection typically affords a connection speed of about 64 kb/sec; and a dual ISDN connection typically affords a connection speed on the order of 100 kb/sec. 
   After the establishment of communication connection  125 , in a conventional manner, client terminal  130  is assigned an IP address for its identification. The user at client  130  may then access the music-on-demand service at the predetermined URL identifying server  105 , and request a selected musical piece from the service. Such a request includes the IP address identifying client terminal  130 , and its connection speed. 
   In prior art, in providing the music-on-demand service, a server needs to store versions of each musical piece corresponding to different connection speeds supported by the server. The audio quality (distortion) of a version of the musical piece increases (decreases) with the corresponding connection speed. Thus, if a prior art server supports three connection speeds, e.g., 28.8 kb/sec, 64 kb/sec and 100 kb/sec, the server needs to store three different versions of each musical piece available having the respective qualities. However, the storage of musical pieces in this manner is undesirably inefficient and occupies much memory space especially when a large number of musical pieces need to be made available. In addition, in delivering the service to a client terminal, the server typically sends the audio information in the form of packets through the Internet. However, in the event that some of the packets are lost in transit because of imperfect network or channel conditions, which is likely, the quality of the received audio information would be significantly degraded. 
   In accordance with the invention, multi-rate audio coding is implemented in server  105  to generate subrate representations of each musical piece to save memory space. Different combinations of the subrate representations of a musical piece correspond to different connection speeds, and audio qualities of the musical piece. In general, the more subrate representations are communicated to a client terminal, the higher the audio quality of the musical piece recovered at the terminal and, of course, the higher the connection speed required of the terminal. For example, in this illustrative embodiment, three subrate representations are used in server  105  to serve each musical piece in accordance with the invention. One of the subrate representations represents core audio information contained in the musical piece, and is referred to as a “C-representation.” The other two subrate representations represent first and second enhancement audio information contained in the musical piece, and are referred to as “E 1 -representation” and “E 2 -representation,” respectively. Because of the design of the multi-rate coding in accordance with the invention, the audio signals recovered based on the C-representation alone, although viable, afford the minimum acceptable quality version of a musical piece; the audio signals recovered based on the C-representation in combination with either E 1 -representation or E 2 -representation afford a relatively high quality version of the musical piece; the audio signals recovered based on the C-representation in combination with both E 1 -representation and E 2 -representation afford the highest quality version of the musical piece. However, any audio signals recovered based only on the E 1 -representation and/or E 2 -representations are not viable. 
   An embedded audio coder in accordance with the invention is used in server  105  to generate the C-representation requiring a bit rate of, say, 28.8 kb/sec for communication thereof; the E 1 -representation requiring a bit rate of, say, 36 kb/sec; and the E 2 -representation requiring a bit rate of, say, 36 kb/sec as well. These bit rates are selected such that if all of the representations are used, the quality of the recovered musical piece version is close to that of a 100 kb/sec version generated by a conventional non-embbeded audio coder. Similarly, the quality of the recovered musical piece version based on a combination of the C-representation with the E 1 -representation or E 2 -representation is close to that of a 64 kb/sec version generated by the conventional non-embedded audio coder. Apparently, the quality of the recovered musical piece version based on the C-representation alone is the same as that of a 28.8 kb/sec version generated by the conventional non-embedded audio coder. Advantageously, server  105  only needs to store in its memory the 28.8 kb/sec C-representation, 36 kb/sec E 1 -representation and 36 kb/sec E 2 -representation of each musical piece, in lieu of the 28.8 kb/sec, 64 kb/sec and 100 kb/sec versions thereof as in prior art, to accommodate different connection speeds (e.g., 28.8 kb/sec, 64 kb/sec and 100 kb/sec), thereby saving the memory space. 
   The aforementioned embbeded audio coder implementing multi-rate coding in accordance with the invention will now be described.  FIG. 2  illustrates one such embbeded audio coder, denoted  203 , in server  105 . An analog signal a(t) representing a musical piece is fed to embedded audio coder  203  in providing the music-on-demand service. In response to such an analog signal, analog-to-digital (A/D) convertor  205  in coder  203  digitizes a(t) in a conventional manner, providing PCM samples of a(t). These PCM samples are fed to both filterbank  209  and perceptual model processor  211 . Filterbank  209  divides the samples into time domain blocks, and performs a modified discrete cosine transform (MDCT) on each block to provide a frequency domain representation therefor. Such a frequency domain representation is bandlimited by low-pass filter (LPF)  213  to the 0 to 10 kHz frequency range in this instance. The resulting MDCT coefficients are grouped by quantizer  215  according to coder bands for quantization. These coder bands approximate the well known critical bands of the human auditory system, although limited to the 0 to 10 kHz frequency range in this instance. Quantizer  215  quantizes the MDCT coefficients corresponding to a given coder band with the same quantizer stepsize. 
   Perceptual model processor  211  analyzes the audio signal samples and determines the appropriate level of quantization (i.e., stepsize) for each coder band. This level of quantization is determined based on an assessment of how well the audio signal in a given coder band masks noise. Quantizer  215  generates quantized MDCT coefficients for application to loss-less compressor  219 , which in this instance performs a conventional Huffman compression process on the quantized coefficients, resulting in the aforementioned C-representation on lead  261 . The output of compressor  219  is fed back to quantizer  215  through rate-loop processor  225 . In a conventional manner, the latter adjusts the output of quantizer  215  to ensure that the bit rate of the C-representation is maintained at its target rate, which in this instance is 28.8 kb/sec. 
   In this illustrative embodiment, the E 1 -representation and E 2 -representation are generated by coder  203  for enhancing the quality of the musical piece which contain spectral information concerning relatively high frequency components of the audio signal, e.g., in the 7 to 20 kHz range. To that end, the quantized MDCT coefficients from quantizer  215  are subtracted by subtracter  229  from the MDCT output of filterbank  209 . The resulting difference signals are duplicated by duplicator  231 , and then bandlimited respectively by band-pass filters (BPFs)  223  and  233  to the 7 to 20 kHz range. Each of quantizers  243  and  253  receives a copy of the filtered difference signals and quantizes the received signals according to predetermined stepsizes. 
   Quantizers  243  and  253  may be scalar quantizers or multidimensional quantizers, and may comprise a complementary quantizer pair. Complementary scalar quantizers are well known in the art, and described, e.g., in V. Vaishampayan, “Design of Multiple Description of Scalar Quantizers,”  IEEE Transactions on Information Theory , Vol. 39, No. 3, May 1993, pp. 821-834. In general, a pair of complementary scalar quantizers may be defined by the following encoding functions f 1  and f 2 , respectively: 
               f   1     ⁢     (   x   )       :   ℜ     -&gt;       {     x   i     }       i   =   1     m1       ,           ⁢   and       
               f   2     ⁡     (   y   )       :   ℜ     -&gt;       {     y   j     }       j   =   1     m2       ,       
 
where  represents the real axis, m 1 =2 S1  and m 2 =2 S2 , where S 1  and S 2  represent the bit rates for quantizers  243  and  253 , respectively. As is well known, associated with each of the quantized values x i  and y j  for f 1 , and f 2 , respectively, is a range or partition [x, y) on the real axis such that all the values in this range are quantized to x i  or y j .
 
   In prior art, to take advantage of the correlation between x i  and y j  from f 1 , and f 2  having a complementary relationship, joint decoding, also known as “center decoding,” on (x i , y j ) is performed in a de-quantizer to realize the optimum decoded value z k  such that the resulting distortion or quantization error is minimized. The center decoding function, {overscore (d)}, performed in the de-quantizer may be expressed as follows: 
             d   _     ⁢     (     x   ,   y     )       :       {     (       x   i     ,     y   j       )     }         i   =   1     ,     j   =   1           i   =   m1     ,     j   =   m2           -&gt;         {     z   k     }       k   =   1       m   _       .         
 
It should be noted that not all (x i , y j ) are valid decodable combinations depending upon the overlap between their associated partitions. Let Q 1 , Q 2  and {overscore (Q)} be the average distortions associated with f 1 , f 2  and center decoding function {overscore (d)}, respectively, and let&#39;s assume that f 1  and f 2  are equivalent, i.e., S 1 =S 2 =S. If Q 1 &lt;2 −2S  and Q 2 &lt;2 −2S , by minimizing {overscore (Q)} subject to the condition Q 1  and Q 2 ≦Q, where Q is a predetermined distortion value, it can be shown that the value of {overscore (Q)} is always greater than the following limit: 
         Q   _     &gt;       1   2     ⁢       2       -   2     ⁢   S       .           
 
That is, use of the complementary scalar quantizers affords at most a 3 dB gain, compared with the case where only an individual scalar quantizer is used.
 
   However, it has been recognized that the average distortion {overscore (Q)} associated with center decoding can be improved if the complementary quantizers used are multidimensional, rather than scalar as in prior art. In this illustrative embodiment, quantizers  243  and  253  are complementary multidimensional quantizers in accordance with the invention. Preferably, they are non-homogeneous multidimensional lattice quantizers. 
   In order to more appreciate the advantages of use of complementary non-homogeneous multidimensional lattice quantizers in accordance with the invention, let&#39;s first consider a prior art homogeneous 2-dimensional lattice quantizer using a square lattice in a 2-dimensional region for quantization.  FIG. 3A  illustrates one such 2-dimensional region which is defined by X 1  and X 2  axes and denoted  360 . Region  360  in this instance has a square lattice and contains Voronoi regions or cells, e.g., cells  367  and  369 , whose length is denoted Δ, where Δ represents a predetermined value. As shown in  FIG. 3A , these cells are homogeneously distributed throughout region  360 , and are each identified by a different code. As is well known, in the quantization process, the prior art quantizer assigns to an input sample point (x 1 , x 2 ) the code identifying the cell in which the sample point falls, where x 1 εX 1  and x 2 εX 2 . For example, sample points having 0≦x 1 &lt;Δ, and 0≦x 2 &lt;Δ are each assigned the code identifying cell  367 . In addition, sample points having Δ≦x 1 &lt;2Δ, and Δ≦x 2 &lt;2Δ are each assigned the code identifying cell  369 . In practice, each code assignment is achieved by looking up a codebook. 
   The above prior art quantizer imposes an average distortion proportional to Δ 2  which in turn is proportional to 2 −2S , where in the multidimensional case here S represents the number of bits/sample/dimension multiplied by the sample rate. 
   As mentioned before, in the preferred embodiment, quantizers  243  and  253  are complementary non-homogeneous multidimensional lattice quantizers. For example, in the 2-dimensional case, quantizers  243  and  253  use non-homogeneous rectangular lattices in 2-dimensional regions  370  and  390 , respectively. In  FIG. 3B , like region  360 , region  370  is defined by X 1  and X 2  axes. However, unlike region  360 , region  370  contains Voronoi regions or cells, e.g., cells  367  and  369 , which are in different shapes and thus non-homogeneous throughout region  370 . By way of example, the vertical boundaries of the rectangular cells in region  370  intersect the X 1  axis at x 1 =0, 0.5Δ, 2.0Δ, 2.5Δ, 4.0Δ . . . , with the separations between successive vertical boundaries alternating between 0.5Δ and 1.5Δ. On the other hand, the horizontal boundaries of the rectangular cells in region  370  intersect the X 2  axis at x 2 =0, 1.5Δ, 2.0Δ, 3.5Δ, 4.0Δ . . . , with the separations between successive horizontal boundaries alternating between 1.5Δ and 0.5Δ. In the quantization process, quantizer  343  assigns to an input sample point (x 1 , x 2 ) the code identifying the cell in which the sample point falls. For example, sample points having 0≦x 1 &lt;0.5Δ, and 0≦x 2 &lt;1.5Δ are each assigned the code identifying cell  377 . In addition, sample points having 0.5Δ≦x 1 &lt;2.0Δ, and 1.5Δ≦x 2 &lt;2.0Δ are each assigned the code identifying cell  379 . 
   A simple way of designing the rectangular lattice in region  390  of quantizer  253 , which is complementary to quantizer  243 , is to adopt the vertical and horizontal boundaries in region  370  as the horizontal and vertical boundaries in region  390 , respectively.  FIG. 3C  illustrates the resulting region  390  containing cells, e.g., cells  391  and  399 , which are in different shapes, and thus non-homogeneous throughout region  390 . In the quantization process, quantizer  253  assigns to an input sample point (x 1 , x 2 ) the code identifying the cell in which the sample point falls. For example, sample points having 0≦x 1 &lt;1.5Δ, and 0≦x 2 &lt;0.5Δ are each assigned the code identifying cell  397 . In addition, sample points having 1.5Δ≦x 1 &lt;2.0Δ, and 0.5Δ≦x 2  &lt;2.0Δ are each assigned the code identifying cell  399 . 
   It can be shown that the average distortion for an individual one of quantizers  243  and  253  equals 1.25ε2 −2S , where ε represents a constant which depends on the probability density function of the input signal to the quantizer, and S in this instance equals 36 kb/s. However, stemming from the fact that quantizers  243  and  253  are complementary quantizers, center decoding on the quantized values from quantizers  243  and  253  respectively can be performed in a de-quantizer. It can be shown that the resulting average distortion {overscore (Q)} associated with 2-dimensional center decoding is no more than 0.25ε2 −2S . That is, complementary quantizers  243  and  253  when implemented with the 2-dimensional center decoding command a 6 dB improvement in terms of distortion over their scalar counterparts. 
   The equivalent lattices of three and higher dimensions of complementary quantizers may be obtained similarly to those of two dimensions described above. However, in three or higher dimensions, it is more advantageous to use a non-homogeneous, non-rectangular (or non-hypercube) lattice in each complementary quantizer. 
   Referring back to  FIG. 2 , the quantized signals from quantizer  243  are fed to loss-less compressor  245  which, like compressor  219 , achieves bit compression on the quantized signals, resulting in the E 1 -representation on lead  263 . The E 1 -representation is fed back to quantizer  243  through rate-loop processor  247  to ensure that the bit rate of the E 1 -representation is maintained at its target rate, which in this instance is S 1 =36 kb/sec. 
   Similarly, the quantized signals from quantizer  253  are fed to loss-less compressor  255  which achieves bit compression on the quantized signals, resulting in the E 2 -representation on lead  265 . The E 2 -representation is fed back to quantizer  253  through rate-loop processor  257  to ensure that the bit rate of E 2 -representation is maintained at its target rate, which in this instance is S 2 =36 kb/sec. 
   Leads  261 ,  263  and  265  extend to storage  270  where the C-representation on lead  261  is stored in memory space  271 , the E 2 -representation on lead  263  is stored in memory space  273 , and the E 2 -representation on lead  265  is stored in memory space  275 . 
   In response to the aforementioned request from client terminal  130  for transmission of the selected musical piece thereto, processor  280  causes packetizer  285  to generate a stream of packets including one or more of the stored representations of the selected musical piece, depending on the given connection speed. Each packet in the stream is destined for client terminal  130  as it contains in its header, as a destination address, the IP address of terminal  130  requesting the music-on-demand service. 
   Specifically, if the given connection speed is 100 kb/sec, packetizer  285  retrieves from memory spaces  271 ,  273  and  275  the C-representation, E 1 -representation and E 2 -representation of the selected musical piece, and packetizes the retrieved representations in accordance with the TCP/IP format. The resulting packet stream is forwarded by processor  280  to Internet  120 . 
     FIG. 4  illustrates such a packet stream, wherein packets  411 ,  413  and  415  generated by packetizer  285  respectively contain C-representation, E 1 -representation and E 2 -representation information corresponding to a first time segment of the musical piece; packets  421 ,  423  and  425  respectively contain C-representation, E 1 -representation and E 2 -representation information corresponding to a second time segment of the musical piece; and so on so forth. To facilitate the assembly of the packets by client terminal  130  when it receives them, the header of each packet contains synchronization information. In particular, the synchronization information in each packet includes a pair of indexes where a sequence index indicating the time segment to which the packet corresponds, followed by a representation index indicating one of the representations with which the packet is associated. For example, field  401  in the header of packet  411  contains the index pair (1, 0), with the sequence index “1” indicating that the packet corresponds to the first time segment, and the representation index “0” indicating that the packet is associated with the C-representation. Similarly, field  403  in the header of packet  413  contains the index pair (1, 1), with the sequence index “1” indicating that the packet corresponds to the first time segment, and the representation index “1” indicating that the packet is associated with the E 1 -representation. Field  405  in the header of packet  415  contains the index pair (1, 2), with the sequence index “1” indicating that the packet corresponds to the first time segment, and the representation index “2” indicating that the packet is associated with the E 2 -representation. 
   Similarly, the sequence index in each of packets  421 ,  423  and  425  has a value “2” indicating that the packet corresponds to the second time segment. In addition, the representation indexes of packets  421 ,  423  and  425  have values “0,” “1,” and “2”, respectively, indicating their respective associations with the C-representation, E 1 -representation and E 2 -representation. 
   Client terminal  130  processes the packet stream from server  105  in accordance with a routine which may be realized using software and/or hardware installed in terminal  130 .  FIG. 5  illustrates such a routine, denoted  500 , where at step  503  terminal  130  receives from server  105  information concerning the indexes identifying the different representations provided thereby to terminal  130 . In this example where the connection speed is 100 kb/sec, as mentioned before terminal  130  is provided with the C-representation, E 1 -representation and E 2 -representation of the musical piece which are identified by representation indexes “0,” “1,” and “2,” respectively. Accordingly, upon receipt of the packet stream of  FIG. 4 , terminal  131  processes the packets on a time segment by time segment basis, and expects to receive three packets associated with the respective representations for each time segment i, 1≦i≦N, where N is the total number of time segments which the musical piece comprises. In this illustrative embodiment, each time segment has the same predetermined length. 
   Specifically, at step  507 , for each time segment i, terminal  130  sets a predetermined time limit within which any packets associated with the time segment are received for processing. Terminal  130  at step  511  examines the aforementioned index pair in the header of each received packet. Based on the sequence index value and the representation index value of the received packets, terminal  130  at step  514  determines whether all of the expected packets for time segment i have been received before the time limit expires. If all of the expected packets have been received, routine  500  proceeds to step  517  where terminal  130  extracts the representation information contents from the respective packets. At step  521 , terminal  130  performs on the extracted information the inverse function to embedded audio coder  203  described above to recover a(t) corresponding to time segment i. In particular, in this example where the extracted information includes C-representation information, E 1 -representation information and E 2 -representation information, respectively, the aforementioned center decoding is performed on the E 1 -representation information and E 2 -representation information based on their correlation to minimize the average distortion in the recovered a(t). 
   Otherwise, if the aforementioned time limit expires before all of the expected packets are received for time segment i, terminal  130  at step  524  determines whether any received packets for the time segment includes the packet containing C-representation information. If it is determined that at least the packet containing C-representation information has been received, terminal  130  extracts representation information content(s) from the received packet(s) for time segment i, and based on the extracted information recovers a(t) corresponding to time segment i, as indicated at step  527 . In that case, the audio recovery may be based on only C-representation information corresponding to 28.8 kb/s quality, or on C-representation information in combination with either E 1 -representation information or E 2 -representation information corresponding to 64 kb/s quality. Otherwise, if no packet containing C-representation information has been received, terminal  130  does not perform any recovery using the received packets for time segment i as any such recovery results in a non-viable a(t). Rather, terminal  130  performs well known audio concealment for time segment i, e.g., interpolation based on the results of audio recovery in neighboring time segments, as indicated at step  531 . 
   If the given connection speed is 64 kb/sec or 28.8 kb/sec instead of 100 kb/sec in the above example, the above-described process similarly follows, although in the 64 kb/sec connection speed case only C-representation information and E 1 -representation information or E 2 -representation information are communicated by server  105  to client terminal  130 , and in the 28.8 kb/sec connection speed case only C-representation information is communicated. 
   The foregoing merely illustrates the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise numerous other arrangements which embody the principles of the invention and are thus within its spirit and scope. 
   For example, in anticipation of packet losses because of imperfect network conditions, server  105  in the illustrative embodiment may implement path diversity by routing streams of packets containing equivalent amounts of audio information through different paths to the same client terminal. Each packet in each stream corresponds to a different time segment of the audio signal to be recovered. For each time segment, the client terminal may use a packet from any one of the streams corresponding to the time segment to recover the audio signal. Thus, despite packet losses, the quality of the recovered signal is maintained as long as the terminal receives one such packet for each time segment. For instance, to deliver an audio signal at 64 kb/sec, server  105  may transmit to the client terminal a first stream of packets containing C-representation information, a second stream of packets containing E 1 -representation information, and a third stream of packets containing E 2 -representation information which is equivalent to E 1 -representation because of use of complementary quantizers  243  and  253 , where the second stream and third stream may be routed through different networks to achieve path diversity. 
   Similarly, server  105  may implement time diversity by transmitting the streams of packets containing equivalent amounts of audio information one-after another through the same network with a predetermined delay. 
   In addition, based on the disclosure heretofore, it is apparent that a person skilled in the art may generate equivalent C-representations, e.g., C 1 -representation and C 2 -representation, using complementary quantizers to achieve path and/or time diversity of such C-representations. 
   Further, the multi-rate coding technique described above is applicable to communications of not only audio information, but also information concerning text, graphics, video, etc. 
   Still further, in the disclosed embodiment, the inventive multi-rate coding technique is illustratively applied to a packet switched communications system. However, the inventive technique equally applies to broadcasting systems including hybrid in-band on channel (IBOC) AM systems, hybrid IBOC FM systems, satellite broadcasting systems, Internet radio systems, TV broadcasting systems, etc. 
   Finally, server  105  is disclosed herein in a form in which various server functions are performed by discrete functional blocks. However, any one or more of these functions could equally well be embodied in an arrangement in which the functions of any one or more of those blocks or indeed, all of the functions thereof, are realized, for example, by one or more appropriately programmed processors.