Abstract:
A system and method employing a rate matching algorithm for providing an optimized pattern for puncturing parity bits of a turbo encoded data word of a given rate to produce a turbo encoded data word of a desired lower rate, to thus eliminate bits from said turbo encoded data word to be transmitted by a transmitter. The system and method determine a final amount of bits to be transmitted in the encoded data word, and determine, based on the final amount of bits in relation to the original number of bits in the encoded data word, the number of parity bits to be eliminated from transmission in the encoded data word. Because the parity bits typically have been inserted into the encoded data word by different encoders, the system and method uses a rate matching algorithm to provide an optimized pattern for puncturing the parity bits so that substantially the same number of parity bits provided by each encoder are punctured.

Description:
The present invention claims benefit under 35 U.S.C. §119(e) of a U.S. provisional application of A Roger Hammons entitled “Rate Matching Algorithm Providing Near Optimal Puncturing Patterns for Turbo Codes”, Ser. No. 60/131,315, filed Apr. 27, 1999, the entire contents of which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a system and method employing a rate matching algorithm for providing optimized puncturing patterns for turbo encoded data in a communications network. More particularly, the present invention relates to a system and method employing a rate matching algorithm for providing an optimized pattern for puncturing parity bits of a turbo encoded data word of a given rate to produce a turbo encoded data word of a desired lower rate. 
     2. Description of the Related Art 
     Many communications devices, such as those used in satellite-based or terrestrial telecommunications networks, employ encoders for encoding data prior to transmission to increase the integrity of the transmitted data and thus reduce data receipt errors. One type of encoder suitable for use in data transmitters is referred to as a turbo encoder. A turbo encoder typically includes one or more constituent encoders which insert in the outgoing data stream one or more parity bits for each information-bearing data bit (information bit). 
     The number of parity bits per data bit in the outgoing data stream indicates the rate at which the outgoing data stream is encoded. For example, a rate ⅓ systematically-encoded data stream includes the input information-bearing data bits, as well as two parity bits per each information bit. In other words, the length of a data stream that is rate ⅓ encoded is increased by a factor of three. Similarly, a rate ½ systematically-encoded data stream includes one parity bit per each real information bit in the data stream. Hence, the length of a data stream that is rate ½ encoded is increased by a factor of two. 
     Due to data capacity limitations that may be present in certain communications networks, it is often necessary to decrease the rate and hence, the length, of a rate encoded data stream. For example, many communications networks transmit data in data packets or frames of a fixed size, which are transmitted in a time-division multiple access (TDMA) transmission scheme. Due to the fixed length of a data frame, a rate ⅓ data stream may be too long to fit within one data frame. However, the length of a data frame may be sufficient to contain a shorter rate ½ data stream. Hence, it may be desirable to decrease a rate ⅓ data stream to a rate ½ data stream so the data stream can be transmitted within one data frame. 
     One method of decreasing the rate of a data stream is referred to as puncturing the data stream. When a data stream is punctured, certain bits of the data stream are eliminated from the data stream transmission. For example, if a rate ⅓ data stream having a length of 3000 bits is punctured to a rate ½ data stream having a length of 2000 bits, 1000 bits of the rate ⅓ data stream are not transmitted. 
     In many systems employing convolutional coding, puncturing is ordinarily performed as a part of channel encoding so that optimal or nearly optimal puncturing patterns can be applied. In certain code-division multiple access (CDMA) systems employing convolutional encoding, the puncturing is performed by a generic “rate matching” function apart from the encoder, in order to simplify multiplexing of many disparate data streams onto a common set of physical channels. In such an environment, the available payload would not be known at the encoder and the required puncturing patterns would be complex. For rate ⅓ turbo codes, in which the turbo encoder produces two parity bits for every systematic information bit as discussed above, it is preferable to avoid puncturing any of the systematic bits and to spread the puncturing between constituent encoders as evenly as possible. However, known rate matching algorithms for systems using convolutional codes fail to meet the above mentioned turbo code puncturing guidelines. 
     Therefore, a need exists for a method and system for providing an algorithm for evenly puncturing parity bits of a turbo encoded data stream without puncturing any systematic data bits of the data stream. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a system and method employing a rate matching algorithm for providing optimized puncturing patterns for turbo encoded data in a communications network. 
     Another object of the present invention is to provide a system and method employing a rate matching algorithm for providing an optimized pattern for puncturing parity bits of a turbo encoded data word of a given rate to produce a turbo encoded data word of a desired lower rate, to thus eliminate bits from said turbo encoded data word to be transmitted by a transmitter. 
     A further object of the present invention is to provide a system and method employing a rate matching algorithm for providing optimized patterns for puncturing parity bits that have been inserted into a turbo encoded data word by different encoders so that substantially the same amount of parity bits provided by each encoder are punctured. 
     These and other objects of the present invention are substantially achieved by providing a system and method for puncturing bits of an encoded data word to reduce a total number of bits in the encoded data word to be transmitted by a transmitter of a communications system. The bits include information bits and parity bits. The system and method operate to determine a final desired number of bits to be transmitted in the encoded data word, and to determine a respective number of parity bits associated with each respective number of information bits. The system and method establish a first variable for identifying positions of the information bits in the data word, and establish a respective parity variable associated with each respective number of parity bits. For example, if the encoded data word is rate ⅓ encoded, two parity bits are associated with each information bit. Therefore, the system and method will establish two parity variables. 
     The system and method then operate to eliminate certain parity bits from transmission in the encoded word based on values of the first variable and each respective parity variable so that the final desired number of bits remain in the encoded data word. In doing so, the system and method organizes the bits into a systematic group and one or more parity groups. The system and method selects certain groups based on the final number of bits and eliminates at least one parity bit from each of the selected groups. To do this, the system and method periodically changes the values of the first variable and each respective parity variable based on at least one constant which has been determined based on the final amount, and determines whether to eliminate any of the parity bits of a particular group during each period in which the values of the first variable and each respective parity variable are changed. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other objects, advantages and novel features of the invention will be more readily appreciated from the following detailed description when read in conjunction with the accompanying drawings, in which: 
     FIG. 1 is a conceptual block diagram of a user terminal employing a system and method according to an embodiment of the present invention; 
     FIG. 2 is a flowchart illustrating exemplary processing steps performed in accordance with a puncturing algorithm provided by the system and method employed in the user terminal shown in FIG. 1; and 
     FIG. 3 is a flowchart illustrating exemplary processing steps performed in accordance with another puncturing algorithm provided by the system and method employed in the user terminal shown in FIG.  1 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is a conceptual block diagram illustrating an example of a transmitter  100 , for use in a communications network such as a satellite-based or terrestrial telecommunications network, and which employs a system and method according to an embodiment of the present invention. As illustrated, the transmitter  100  includes a turbo encoder  102  comprising a turbo interleaver  104  and constituent encoders  106  and  108 . 
     A controller  10  for performing a puncturing algorithm according to an embodiment of the present invention applies an appropriate puncturing pattern to the output of the turbo encoder  102  at a puncturing position  112  as will now be described. It is noted that the turbo encoder  102  and controller  110  could be implemented as software in a digital signal processor (DSP) or as logic circuitry in a very large scale integration (VLSI) configuration. It is also possible for the turbo encoder  102  ,for example, to be implemented as circuitry in a VLSI configuration while the controller  110  resides in software in a DSP, or vice-versa. 
     Like conventional convolutional codes, turbo codes are capable of supporting variable channel code rates because the output of the encoder  102  can be punctured by applying simple periodic puncturing patterns. This process is illustrated in FIG. 1 as discussed above, which shows a standard turbo encoder  102  followed by a puncturing function applied at puncturing position  112 . The puncturing function is represented by a binary array governing the puncturing of the coded bits in time. 
     As can be appreciated by one skilled in the art, the output of the turbo encoder is multiplexed in time. That is, if x(k) represents the k-th input bit and y 1 (k) and y 2 (k) represent the corresponding parity bits produced by the two constituent encoders  106  and  108 , then the rate ⅓ turbo code produces the following sequence of coded bits: x( 1 ), y 1 ( 1 ), y 2 ( 1 ); x( 2 ). y 1 ( 2 ), y 2 ( 2 ); . . . x(L), y 1 (L), y 2 (L). A well-known puncturing pattern for producing a rate ½ turbo code from a rate ⅓ turbo encoder is shown in FIG.  1 . As illustrated, the output of the encoder  102  after puncturing at the puncturing component  112  is given by the sequence: 
     x( 1 ),y 1 ( 1 );x( 2 ),y 2 ( 2 );x( 3 ),y 1 ( 3 ); . . . 
     corresponding to the following linear periodic puncturing pattern:  110   101  This coding technique has been extensively investigated in the literature and gives excellent performance. 
     Specifically, in the puncturing array shown at puncturing position  112  ,the value “1” indicates transmission of the corresponding coded bit, and the value “0” indicates that the corresponding coded bit is not transmitted. The pattern is applied periodically to the outputs of the constituent encoders. Accordingly, in the first group of three bits consisting of one systematic data bit and two parity data bits, the parity bit provided by constituent encoder  106  is punctured. However, in the second group of three bits, the parity bit provided by constituent encoder  108  is punctured. 
     The rate matching algorithm according to an embodiment of the present invention that will now be discussed provides optimal or nearly optimal puncturing of turbo coded data when performed after the channel encoding. This algorithm has low implementation complexity yet succeeds in spreading the puncturing in a balanced maimer between constituent encoders. 
     The following variables represent the characteristics of the encoded data: 
     Encoded data (code word): c[ 0 ], c[ 1 ], c[ 2 ], . . . c[Nc−1] 
     Code word length (bits): Nc 
     Available payload (bits): Ni 
     Channel code rate: R 
     It is assumed that Ni&lt;Nc, so that puncturing is required to make encoded data fit the available payload. For illustrative purposes, it is also assumed in this example that input code rate R=⅓ and that the encoded data are presented in the customary fashion for a rate ⅓ turbo code, that is, a systematic bit followed by the corresponding parity bit from the first constituent encoder followed by the corresponding parity bit from the second constituent encoder followed by the next systematic bit, and so on. Thus, the coded bits c[ 3 i] are the systematic bits, the coded bits c[ 3 i+1] are the parity bits produced by the first constituent encoder  106  ,and the coded bits c[ 3 i+2] are the parity bits produced by the second constituent encoder  108 . 
     The following represents a Pseudo-Design Language Description (using C-language conventions) of the algorithm according to an embodiment of the present invention, taking into account the variables defined above: 
     D=Ni−Nc; 
     P=2*Nc/3; 
     d=D/gcd(D,P); 
     p=P/gcd(D,P); 
     s 1 =0; 
     s 2 =((int)(p/2)*d)%p; 
     for(i=0;i&lt;P;i=i+2) 
     {m=3*i/2; 
     s 1 +=d; 
     if(s 1 &gt;=p){Puncture c[m+1]; s 1 −=p;} 
     s 2 +=d; 
     if(s 2 &gt;=p){Puncture c[m+2]; s 2 −=p;}} 
     It is noted that in the above pseudo-code, the integer function gcd (x, y) returns the greatest common divisor of the integers x and y, the term “+=” means to increase the value of the variable on the left side of the term (e.g., s 1 ) by the value of the variable on the right side of the term (e.g., d), the term “−=” means to decrease the value of the variable on the left side of the term (e.g., s 1 ) by the value of the variable on the right side of the term (e.g., p), and the term “%” represents niodulo division. From the pseudo-code description, the following basic design principles are clear: (1) Each parity stream is punctured as uniformly as possible by using a pattern that removes on average d of every p parity bits; (2) The puncturing pattern for the second stream of parity bits (from second constituent encoder) is the same as that of the first but offset from the first by roughly ½ the length of the pattern. 
     These design principles are implemented very simply via a pair of modulo-p accumulators, s 1  and s 2 , one for each parity stream. The accumulators are incremented by d for each encoded information bit and reduced by p when necessary to prevent overflow. Reduction by p triggers the puncturing of the corresponding parity bit from that stream. The puncture patterns for the two constituent encoders are effectively staggered by using different initializations for the two accumulators. 
     The operation of the controller  110  that executes the algorithm specified by the pseudo code described above can be better appreciated in view of the flowchart shown in FIG.  2 . As shown in step  1000  ,the controller  110  initializes the variables discussed above, namely, D, P, d, p, s 1  and s 2 . The processing then continues to step  1010  where it enters the “For” loop shown in the pseudo code. Specifically, the processing determines in step  1010  whether the value of “i”, the loop counting variable, is less than P. If not, this is an indication that all groups of the systematic bits and their associated parity bits (in this example, 3 bit groups), have been processed, and the processing proceeds to step  1020  and ends. 
     However, if the value of i is less than the value of P, the processing proceeds to step  1030  ,where the values of variables “m” and “s 1 ” are changed according to the equations in the pseudo code. It is noted that the value of s 1  is incremented by the value of d. The processing then continues to step  1040  where it is determined whether the new value of s 1  is greater than or equal to the value of p. If so, the processing proceeds to step  1050  where the parity bit output by constituent encoder  106  is punctured. The processing then proceeds to step  1060  where the value of s 1  is decremented by the value of p, and the processing continues to step  1070 .It is noted, however, if it is determined in step  1040  that the new value of s 1  is not greater than or equal to the value of p, the processing proceeds from step  1040  to step  1070 , skipping steps  1050  and  1060 . 
     In step  1070  ,the processing increments the value of s 2  by the value of d. The processing the proceeds to step  1080  where it is determined whether the new value of s 2  is greater than or equal to the value of p. If so, the processing proceeds to step  1090  where the parity bit output by constituent encoder  108  is punctured. The processing then proceeds to step  1100  where the value of s 2  is decremented by the value of p, and the processing returns to step  1010 .It is noted, however, if it is determined in step  1080  that the new value of s 2  is not greater than or equal to the value of p, the processing proceeds from step  1080  to step  1010 , skipping steps  1090  and  1100 . When the processing returns to step  1010  , the value of “i” is incremented in step  1110  as indicated, and the processing repeats as discussed above. 
     The following tables represent examples of the puncturing pattern achieved by the pseudo code and operation of the controller  110  as described above. In these examples the input code rate is R=⅓. Table 1 below illustrates an example of the ideally balanced puncturing pattern for rate ½ as produced by the rate matching algorithm, with d=1 and p=2. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Example of Puncturing Pattern for Rate 1/2 
               
             
          
           
               
                   
                   
                 s1 
                 s2 
                 Puncturing Pattern 
               
             
          
           
               
                 i 
                 m 
                 0 
                 1 
                 c[m] 
                 c[m + 1] 
                 c[m + 2] 
               
               
                   
               
               
                 0 
                 0 
                 1 
                 2 
                 1 
                 1 
                 0 
               
               
                 2 
                 3 
                 2 
                 1 
                 1 
                 0 
                 1 
               
               
                   
               
             
          
         
       
     
     Table 2 below illustrates an example of the ideally balanced puncturing pattern for rate ⅔ as produced by the rate matching algorithm, with d=3 and p=4. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Example of Puncturing Pattern for Rate 2/3 
               
             
          
           
               
                   
                   
                 s1 
                 s2 
                 Puncturing Pattern 
               
             
          
           
               
                 i 
                 m 
                 0 
                 2 
                 c[m] 
                 c[m + 1] 
                 c[m + 2] 
               
               
                   
               
               
                 0 
                 0 
                 3 
                 5 
                 1 
                 1 
                 0 
               
               
                 2 
                 3 
                 6 
                 4 
                 1 
                 0 
                 0 
               
               
                 4 
                 6 
                 5 
                 3 
                 1 
                 0 
                 1 
               
               
                 6 
                 9 
                 4 
                 6 
                 1 
                 0 
                 0 
               
               
                   
               
             
          
         
       
     
     Table 3 below illustrates an example of the ideally balanced puncturing pattern for code rate {fraction (5/12)} as produced by the rate matching algorithm, with d=3 and p=10. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Example of Puncturing Pattern for Rate 5/12 
               
             
          
           
               
                   
                   
                 s1 
                 s2 
                 Puncturing Pattern 
               
             
          
           
               
                 i 
                 m 
                 0 
                 5 
                 c[m] 
                 c[m + 1] 
                 c[m + 2] 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 3 
                 8 
                 1 
                 1 
                 1 
               
               
                 2 
                 3 
                 6 
                 11 
                 1 
                 1 
                 0 
               
               
                 4 
                 6 
                 9 
                 4 
                 1 
                 1 
                 1 
               
               
                 6 
                 9 
                 12 
                 7 
                 1 
                 0 
                 1 
               
               
                 8 
                 12 
                 5 
                 10 
                 1 
                 1 
                 0 
               
               
                 10 
                 15 
                 8 
                 3 
                 1 
                 1 
                 1 
               
               
                 12 
                 18 
                 11 
                 6 
                 1 
                 0 
                 1 
               
               
                 14 
                 21 
                 4 
                 9 
                 1 
                 1 
                 1 
               
               
                 16 
                 24 
                 7 
                 12 
                 1 
                 1 
                 0 
               
               
                 18 
                 27 
                 10 
                 5 
                 1 
                 0 
                 1 
               
               
                   
               
             
          
         
       
     
     For purposes of illustration only, the rate matching algorithm is discussed above in relation to a rate ⅓ turbo code, produced by a turbo encoder  102  comprising two constituent encoders  106  and  108 , each of which produces one parity bit per input information bit. However, as will now be demonstrated, the algorithm is applicable to other code rates. 
     For example, consider a case in which the code rate is R=k/n (every k information bits produces r=n−k parity bits) and the puncturing is to be spread over the r parity streams in a balanced manner. The following modification of the rate matching algorithm is a straightforward adaptation that conforms to the basic concept and meets the balanced puncturing objective. 
     The following represents a pseudo-design language description (using C-language conventions) of the algorithm according to another embodiment of the present invention, taking into account the variables Ni, Nc and R as defined above, and that encoded data (code word) is represented by the terms: c[ 0 ], c[ 1 ], c[ 2 ], . . . c[Nc−1] as discussed above: 
     D=Ni−Nc; 
     P=Nc*(1−R); 
     r=n−k; 
     d=D/gcd(D,P); 
     p=P/gcd(D,P); 
     for(j=0;j&lt;r;++j)s[j]=(j*(int)(p/r)*d)%p; 
     for(i=0;i&lt;P;i=i+r){ 
     m+(n*i)/r; 
     for(j=0;j&lt;r;++j){ 
     s[j]+=d; 
     if(s[j]&gt;=p){ 
     Puncture c[m+j+k]; 
     s[j]−=p; 
     } 
     } 
     } 
     The operation of the controller  1110  executing the pseudo code described above can be better appreciated in view of the flowchart shown in FIG. 3 As shown in step  1200  ,the controller  1110  initializes the variables discussed above, namely, D, P, r , d and p. The processing then continues to step  1210  where it enters the “For” loop shown in the pseudo code to initialize the accumulators s[j] as indicated. Specifically, the processing determines in step  1210  whether the value of “j”, the loop counting variable, is less than r. If so, the processing proceeds to step  1220 , where the values of variable “[j]” is initialized according to the equation in the pseudo code. The processing repeats as long as j is less than r, with j being incremented by “1” each time the processing returns to step  1210  (as represented by the term “++j” in the pseudo code) and before the comparison of j to r is made. 
     Once it is determined in step  1210  that j is not less than r, the processing proceeds to step  1230  where it is determined whether the value of “i”, a loop counter, is less than the value of P. It is noted that the first time this step is reached, the value of i is initialized to zero. If the value of i is less than the value of P, the processing proceeds to step  1240  where the value of “m” is set according to the equation in the pseudo code. 
     The processing then proceeds to step  1250  where it is determined whether the value of j is less than the value of r. It is noted that the first time this step is reached after each time the processing performs step  1240  ,the value of j is initialized to zero. If the value of j is less than the value of r, the processing proceeds to step  1260  where the value of variable s[j] is changed as indicated in the pseudo code. The processing proceeds the step  1270  where it is determined whether the new value of s[j] is greater than or equal to the value of p. If the value of s[j] greater than or equal to the value of p, the bit c[m+j+k] is punctured in step  1280 , as indicated in the pseudo code. The processing then proceeds to step  1290  ,where the value of s[j] is decremented by the value of p, as indicated in the pseudo code. The processing then returns to step  1250  ,and repeats as discussed above. 
     When the processing returns to step  1250  ,the value of j is incremented in step  1295  as indicated in the pseudo code before the comparison of j to r is made. If it is determined in step  1250  that the value of j is not less that or equal to the value of r, the processing returns to step  1230  without performing steps  1260  through  1290  .In returning to step  1230  ,the value of i is incremented in step  1255  as indicated in the pseudo code before the comparison of i to P is made. If the value of i is less than P, the processing proceeds to step  1240  where the value of m is set as discussed above, and then to step  1250  where the processing relating to this step as discussed above is performed. It is noted that as mentioned above when the processing proceeds to step  1250  from step  1240  ,the value of j is initialized to zero. However, if it is determined in step  1230  that the value of i is not less than P, it is determined that the processing has been performed for all groups of bits (i.e., all groups of systematic bits and associated parity bits). The processing thus proceeds to step  1300  and ends. 
     It is noted that the staggering of the pattern could be done differently. For instance, the initialization of the accumulators s[j] could also be done as follows and yield a similar effect: 
     for(j=0;j&lt;r;++j)s[j]=((int)(j*p/r)*d)%p; 
     In fact, it is also possible under certain circumstances (e.g., if the number of punctured bits is divisible by the number of constituent encoders) for the staggers to all be the same since the turbo interleavers effectively randomize the puncturing over time. This would enable a simplified implementation in which one set of variables controls the puncturing of all constituent encoders&#39; outputs. Optimization of the specific choice of staggers could also be done to best match the actual turbo codes and code rates of interest. 
     In another variation of the algorithm, it is noted that it is not necessary to treat all of the parity streams equally. In more complex turbo codes, in which, for example, the constituent encoders produce two or more parity bits per information bit, it may be preferable to puncture certain of the parity streams less than others. This can be accomplished using the above rate matching algorithm by making the values d and p functions of the parity stream j. The algorithm would then increment accumulator s[j] by d[j] modulo p[j], etc. The staggers would again be dependent on the parity stream and again could be non-uniform in this case. 
     As can be appreciated from the above description, the algorithms according to the invention meet the puncturing guidelines with low complexity. When rate matching is performed right after channel encoding, the puncturing pattern provided by the algorithm can be applied directly to the encoded data. When rate matching is performed after channel interleaving, the rate matching algorithm is preferably applied after first inverting the channel interleaving. It is also noted that the above algorithms can be applied to any system using turbo codes in which rate matching is performed apart from the channel encoder. 
     Although only a few exemplary embodiments of the present invention have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the following claims.