Abstract:
A Viterbi decoder includes a computing device, a memory and a bus. The computing device receives sets of data values and calculates distances for the received sets of data values, accumulates and compares the calculated distances according to a Viterbi algorithm, decides data values and generates control signals dependent on a plurality of decisions associated with a plurality of paths. The memory stores the decided data values and provides at least one output value. The bus connects the computing device and the memory and is configured to convey the control signals to the path memory. The computing device or the memory shifts data strings in the memory according to conditions of the Viterbi algorithm with the control signals associated with the plurality of paths.

Description:
PRIORITY INFORMATION 
     This application claims priority from German application 10 2004 038 754.0 filed Aug. 9, 2004. 
     BACKGROUND OF THE INVENTION 
     The invention relates in general to decoders and in particular to a decoder for executing a Viterbi algorithm. 
     A Viterbi algorithm makes it possible to correct transmission errors in communications systems. The application of a Viterbi algorithm is also known from many other search problems, for example in the field of pattern recognition. The Viterbi algorithm has a disadvantage that the computation is very complex, thereby requiring a relatively large amount of memory resources. As a consequence, a system clock frequency of a decoder for executing a Viterbi algorithm is typically correspondingly high. The system clock frequency at which the individual operations of the Viterbi algorithm are to be executed is generally several times higher than the data rate when the algorithm is employed in communications systems. This requirement is of note particularly in systems having very high data rates, such as digital video broadcasting (“DVB”) systems, because the requisite clock frequencies necessitate the use of relatively expensive technology. 
     The principle of a Viterbi decoder is known, for example, from G. David Forney, Jr., “ The Viterbi Algorithm ,” Proc. IEEE, Vol. 61, No. 3, March 1973, pp. 268-278. Modules used in such a decoder for calculating distances or total distances and for calculating accumulations and comparisons, as well as a generic structure of a logical module for a Viterbi decoder, are employed in decoders according to European Published Patent Application EP 0 769 853 A1. Possibilities for parallelization are known from H. Burckhardt and L. C. Barbosa, “ Contributions to the Application of the Viterbi Algorithm ,” IEEE Trans. on IT, Vol. 31, No. 5, September 1985, pp. 626-634. 
     Prior art Viterbi decoders and Viterbi algorithms typically require a relatively high system clock frequency. 
     One embodiment of a prior art Viterbi decoder  10  having a degree of parallelization p is illustrated in  FIG. 8 . Via a receiver bus  12 , K×N bits of received data r(n, k) are provided to a total-distance module  14 . In the module  14 , total distances are calculated and correspondingly 2 K ×(N+1d(K)) bits are provided on a bus  16  to a computing device  18  having accumulate-and-compare modules  20 . The total distances are stored in a temporary memory  22 . Via a bidirectional distance bus  24 , 2×(N+1d(K)+1)×2 p+1  bits are correspondingly transmitted from the computing device  18  to a distance memory  26  that stores (N+1d(K)+1)×2 L−1  bits. Here L is the length of generator polynomials, of which a set containing a number K is to be considered in the calculation. The received data r(n, k) on the bus  12  are resolved to N bits. The degree of parallelization is p. From the distance memory  26 , a corresponding number of 2×(N+1d(K)+1)×2 p+1  bits are transmitted on the distance bus  24  back to the computing device  18 . 
     The computing device  18  is also connected to a path memory  28  via a bidirectional path bus  30  where 2×T×2 p+1  bits are transmitted from the path memory  28  or a second temporary memory  32  of the computing device  18  to and from the path memory  28  via the path bus  30 . In the path memory  28 , T×2 L− 1 bits are stored. After corresponding calculations, in particular accumulations and comparisons, have been executed in the accumulate-and-compare modules  20 , a search is executed in the computing device  18  and a data bit string c(n, k) determined to be the most desirable is furnished on a line  34  at the output of the Viterbi decoder  10 . 
     In such a Viterbi decoder  10 , a lower system clock frequency can be attained with a plurality of parallel modules, depending on the degree of parallelization (0&lt;p&lt;L−2). In the case where the system clock frequency is equal to the data rate (p=L−2), all 2 L−1  accumulate-and-compare modules  20  are implemented in parallel. The bus then becomes the limiting factor. For available embodiments, it may be that no acceptable compromise can be found between the system clock frequency and the requisite bus widths of the path bus  30  and the distance bus  24 . 
       FIG. 9  illustrates the ratio between the system clock frequency and bus width as functions of the degree of parallelization p for the case of such a Viterbi decoder for DVB systems. Typical parameters are L=7, K=2 and T=64 for data rates up to 50 Mbit/s. If there is no parallelization (p=0) and the bus width is relatively small, a system clock frequency of 1600 MHz is used. If the system clock frequency is to be equal to the data rate (i.e., the degree of parallelization is p=5) a bandwidth of 9000 bits is needed for the bus width. In practice this is not acceptable in light of the realization and the costs arising therefrom. Given an acceptable system clock frequency of up to 100 MHz (p=4), the requisite bus width of 4500 bits is still relatively high for a commercially favorable approach. 
     What is needed is a Viterbi decoder for executing a Viterbi algorithm that allows the system clock frequency to equal the data rate at relatively high bit rates. 
     SUMMARY OF THE INVENTION 
     A Viterbi decoder includes a computing device that receives sets of data values and calculates distances from the received data values and accumulates and compares the distances according to a Viterbi algorithm and decides data values. Also included is a path memory for storing decided-upon data values. A bus connects the computing device and the path memory. The computing device generates control signals dependent on the decisions that are associated with paths. The bus conveys the control signals to the path memory. The computing device and/or the path memory shifts data strings with the control signals associated with the paths in the path memory according to conditions of the Viterbi algorithm. The path memory provides at least one output value. 
     The computing device evaluates the requisite distances, for example all distances required for each set of received values (e.g., in one module), and accumulates and compares the associated distances according to the Viterbi algorithm, where, for example the relatively smallest distances may be selected and stored in a distance memory. 
     The computing device and/or the path memory may delay the data strings in a second part of the path memory using simple shift registers to compensate for the time required for a search among the selected accumulated distances. 
     The computing device and/or the path memory may provide from the path memory, for example, from a shift register in the path memory, the output value that corresponds to the path found by the search having the relatively smallest distance. 
     The computing device may subtract a found distance from all accumulated distances in the next decoder cycle. 
     The path memory may be structured in a row-wise manner to accept row-wise paths from the data strings that have led, upon decision, to a state and that are to be newly shifted in each decoder cycle, for example, to accept paths m(p, t), p=0, 1, . . . , P−1, where P is the number of paths, t=0, 1, . . . , T−1+D, where T is the decoder depth and D is the delay. 
     The path memory may have two parts and executes the shift according to the Viterbi algorithm in the first part, with a specified length T, and a simple shift using shift registers with a further length D in the second part. 
     The computing device and/or the path memory may write, in each decoder cycle, the initial value in each path ({m(p, 0), p=0, 1, . . . , P−1}) according to a fixed pattern that depends on a path number. 
     The computing device and/or the path memory may control the data shift with respect to paths m(p, t) in the first part of the path memory using control signals at the input of the path memory, for example, according to
 
 m ( p, t )= m (2 p+s ( p ),  t− 1), with  p =0, 1 , . . . , P/ 2−1 and
 
 m ( P/ 2 +p, t )= m (2 p+s ( P/ 2 +p ),  t− 1), with  t= 1, 2 , . . . , T− 1,
 
where s(p)ε(0, 1, . . . , S−1), for p=0, 1, . . . , P−1, and S is the number of possible data values.
 
     The computing device and/or the path memory may execute a simple shift in a second part of the path memory, for example, according to
 
 m ( p, t )= m ( p, t− 1), with  p= 0, 1 , . . . , P− 1 , t=T, . . . , T+D− 1,
 
and/or to determine as the output value the selected path (q) having the relatively smallest distance, for example, according to output=m(q, T+D−1).
 
     The decoder may have three modules for evaluating, accumulating and comparing the distances, generating control signals, and executing the search. The decoder may also include a temporary memory for time compensation, a distance memory, and the path memory. A bidirectional bus may be arranged between the distance memory and the computing device for reading the accumulated distance from the next-to-last decoder cycle and storing newly computed accumulated distances. A unidirectional bus may be arranged between the computing device and the path memory for transmitting control signals for the shift in the memory and transmitting an address of the path having the relatively smallest accumulated distance. 
     The decoder may have a system clock frequency equal to the decoder cycle frequency or the data rate. As such, the number of accumulate-and-compare modules of the computing device are equal to the number of states, for example, paths. The bus width of the bus to the distance memory may be sized for reading and storing the distances for all paths at the same time, with the bus to the path memory carrying all the control signals at the same time. 
     The decoder may have a system frequency as a multiple X of a data rate or a decoder cycle frequency. As such, the number of accumulate-and-compare modules in the computing device are P/X, with P being the number of paths or states, the bus to the distance memory reading and storing P/X distances, and the bus to the path memory carrying P/X control signals, for example, at the same time. 
     The decoder may process data as binary data for encoding (S=2) and may process data values, for example, bit strings, encoded with a convolutional encoder of a length (L bits) and an encoding rate (1/K). The reception range is resolved to N bits on a range of whole numbers from 0 to 2N−2, the number of possible states or paths is 2L−1, and the ratio between the system frequency and the data rate is a power of two (X=2x, x=0, 1, . . . , L−2). Further, the bus width to the distance memory may be of a size for reading and storing a total of 2(N+1d(K)+2)2x+1 bits at the same time, and the bus width to the path memory may be 2x+1 bits for control signals and L−1 bits for the address of the path having the relatively smallest accumulated distance. 
     The decoder of the invention makes it possible to fabricate commercially favorable IC (integrated circuit) solutions. The proposed decoder architecture includes the computing devices adapted for the Viterbi algorithm and a relatively efficient approach to a memory structure that can replace its contents in accordance with the Viterbi algorithm within, for example, a single system clock cycle. 
     These and other objects, features and advantages of the present invention will become more apparent in light of the following detailed description of preferred embodiments thereof, as illustrated in the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustration of a memory portion of a Viterbi decoder; 
         FIG. 2  is a block diagram of an accumulate-and-compare module within a Viterbi decoder; 
         FIG. 3  is a block diagram of various components of a Viterbi decoder having the memory portion of  FIG. 1 ; 
         FIG. 4  is a graph illustrating the relationship of the system clock frequency and bus width as functions of the degree of parallelization for the Viterbi decoder of  FIGS. 1-3 ; 
         FIG. 5  is a block diagram of a prior art distance-calculating module; 
         FIG. 6  is a block diagram of a prior art module for accumulating and comparing distances; 
         FIG. 7  is a block diagram of a prior art Viterbi decoder; 
         FIG. 8  is a block diagram of various components of a prior art Viterbi decoder; 
         FIG. 9  is a graph illustrating the relationship of the system clock frequency and bus width as functions of the degree of parallelization of the prior art Viterbi decoder of  FIG. 8 ; 
         FIG. 10  is a diagram illustrating the principle of convolutional encoding; and 
         FIG. 11  is a state diagram of a convolutional encoder for the convolutional encoding principle illustrated in  FIG. 10 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , a two-part structure of a memory device  40  as a part of a Viterbi decoder may be used in conjunction with a Viterbi algorithm at relatively high data rates. A relatively simple construction of the memory  40  is possible using simple technology due to the structure of a path memory as the memory  40  is adapted according to the Viterbi algorithm. Here the dependence between the system clock frequency and the bus width is separated for every degree of parallelization. 
     A Viterbi algorithm is executed in a Viterbi decoder in a known manner. In a communications system, for example, the Viterbi decoder is situated in a receiver-side device and is part of relatively extensive signal processing comprising, for example, demodulation, equalization, etc. 
     A Viterbi decoder  42  having the memory  40  of  FIG. 1  is illustrated in  FIG. 3 . In comparison to the prior art Viterbi decoder  10  of  FIG. 8 , the Viterbi decoder  42  of  FIG. 3  differs in particular in how a computing device  44 , which comprises accumulate-and-compare modules  46 ,  48  for accumulating and comparing distances, is connected to the memory device  40  described of  FIG. 1 . The connection comprises a unidirectional control bus  50  for transmitting, for example, 1×2 p+1  bits from the computing device  44  to the memory device  40 . 
     The memory device  40  includes a path memory  52  having a memory capacity of T×2 L−1  bits, and a demultiplexer  54 . The computing device  44  includes an output on a line  56  from which the address of the state having the determined relatively smallest or “minimal” distance q is provided to the demultiplexer  54 . The address comprises L−1 bits. From the demultiplexer  54  or the memory device  40 , the corresponding data bit string c(n, k) is conveyed on a line  118  at an output of the Viterbi decoder  42 . 
     A received value r(n, k) is associated with each encoded bit c(n, k) of the output data on the line  118 . From the received values r(n, k), the Viterbi algorithm reconstructs, with as few errors as possible, a data bit string {b(n)} sent by a transmitting device. The following prerequisites govern the usage of the Viterbi algorithm. 
     The received value range extends between two nominal values that correspond to the two possible values {W 0  and W 1 } of an encoded bit (0 or 1). In the extreme case referred to as “hard decision,” the received value range includes only the two nominal values. The efficiency of the decoder improves if the received value range is more highly resolved, a situation referred to as “soft decision.” 
     As a second prerequisite, a distance metric is defined in terms of the distance between received values and nominal values according to equation 1:
 
 d   0 ( r )=distance{ r, W   0 } and  d   1 ( r )=distance{ r, W   1 },  (1)
 
where d 0  and d 1  describe deviation values or distances and the assumption is made that a smaller distance from a nominal value W indicates a higher probability for this value. The maximal distance d 0 (W 1 )=d 1 (W 0 )=d max  defines a symmetrical received value range. The metric may be further defined such that the sum of two distances always remains constant for each received value r(n, k), so that d 0 (r)+d 1 (r)=d max .
 
     A third prerequisite is assumed with respect to a received value range. The received value range and the metric applied are to guarantee the existence of a neutral value W n  such that d 0 (W n )=d 1 (W n )=d max /2. This neutral value is needed to replace missing received values r(n, k) that correspond to encoded bits c(n, k) omitted as a result of puncturing. 
     A fourth prerequisite commonly relates to a structure for the application of the Viterbi algorithm. For each of the 2 L−1  possible states, this structure includes a distance accumulator {A q (n), q=0, . . . , 2 L−1 } and a path memory  52  with {M q (n)={m q (n, 0), . . . , m q (n, T−1)}, q=0, . . . , 2 L−1 −1} of length T bits in which are stored all decided-upon bits b up to time n that have led to the state. Parameter T defines a decoding depth, which directly determines the efficiency of the Viterbi decoder  42 . 
     The Viterbi algorithm includes a plurality of steps for each new input of K received values {r(n, 0), . . . , r(n, K−1)}. 
     In a first step, a total distance is calculated. Because a set of K bits corresponds to one bit from the data bit string, a total distance for the entire set of bits is used according to equation 2: 
                       d       c   ⁡     (   0   )       ,     c   ⁡     (   0   )       ,   …   ⁢           ,     c   ⁡     (     K   -   1     )           ⁢     {         r   ⁡     (     n   ,   0     )       ⁢     r   ⁡     (     n   ,   1     )         ,   …   ⁢           ,     r   ⁡     (     n   ,     K   -   1       )         }       =       ∑     k   =   0       K   -   1       ⁢         d     c   ⁡     (   K   )         ⁡     (     r   ⁡     (     n   ,   k     )       )       .               (   2   )               
With K bits {c( 0 ), c( 1 ), . . . , c(K−1)}, the number of distinct total distances that are calculated for a set of K received values is 2 K .
 
     In a second step, two competing values for each state are calculated and compared for the distance accumulator. This is also referred to as an accumulate and compare operation as given by equation 3: 
                             A     new   /   0       =       A       old   /   b     =   0       +     d       c   /   b     =   0                       A     new   /   1       =       A       old   /   b     =   1       +     d       c   /   b     =   1                 ,     s   =         0           A     new   /   0       &lt;     A             ⁢     new   /   1                   1           A     new   /   0       ≥     A             ⁢     new   /   1                   ,           (   3   )               
where, according to a conventional state diagram, which is illustrated in  FIG. 11 , the values A old/b  from the distance accumulators arise from two possible prior states and the values d c/b  as total distances correspond to the K encoded bits.
 
     In a third step, the following values are associated and shifted according to the comparison result s, specifically the distance accumulator A new =A new/s , the path memory M new : m new (n, 0)=b; m new (n, t)=m old/s (n, t−1), t=1, . . . , T, and the candidate bit for output b new =m old/s (n, T−1)(4), the candidate bit b following a fixed specified pattern according to the state diagram, in which the first half of the states are assigned a 0 and the remainder of the states are assigned a 1. 
     In a fourth step, the state having the minimal distance accumulator q determines the newly decided-upon bit b at the output according to equation 4: 
                     A   min     =         A   q     ⁡     (   n   )       =           min       x   =   0     ,   …   ⁢           ,       2     L   -   1       -   1         ⁢     {     Ax   ⁡     (   n   )       }       ⇒     b   ⁡     (   n   )         =       b     new   /   q       .                 (   4   )               
This bit is typically from the sent data bit string b(n−T). The delay of T is due to the decoding process.
 
     In a fifth step, the values in the distance accumulators thus remain limited, the minimum A q (n) of all the newly obtained values in the distance accumulators being subtracted for this purpose according to A new (n)=A new (n)−A q (n). 
     In a sixth step, these values are employed as old values in the next pass or employed as values that are to be used in the next cycle, so that according to equation 5:
 
 A   old ( n+ 1)= A   new ( n ) and  M   old ( n+ 1)= M   new ( n ).  (5)
 
     By way of illustration, a frequently applied method is represented for an exemplary convolutional code. If the received values are resolved to N bits, the reception range will include values {0, 1, . . . , 2 N −2}, with W 0 =0, W 1 =2 N −2 and W n =2 N−1 −1. For this purpose, a simple metric is adapted as per equation 6:
 
 d   0 ( r )= r  and  d   1 ( r )=2 N −2− r  for  rε{ 0, . . . , 2 N −2}
 
             d   max =2 N −2 and 0 ≦d   0 ( r ),  d   1 ( r )≦2 N −2.  (6)

     The value range of the total distances, that is, a total of 2 K  values according to equation (2), is then limited to 1d(K)+N and the value range of the distance accumulators is one bit larger. 
     The Viterbi decoder  42  of  FIG. 3  and the prior art Viterbi decoder  10  of  FIG. 8  each include some components that are the same, for example, the receiver bus  12 , the distance-calculating module  14 , the distance bus  24 , and the distance memory  26 . The distances or total distances may be determined, for example, in accordance with at least equation (2). The total distance module  14  is used to calculate the distances. According to  FIG. 5 , a known distance-calculating module  14  comprises two inputs for the input of received data values r(n, 0) and r(n, 1) on lines  58 ,  60 , which have been subjected to appropriate preliminary processing. Each of these data values r(n, 0), r(n, 1) is fed to a corresponding first and third adder  62 ,  64 , respectively. The other one of these two data values r(n, 1) or r(n, 0) is fed to the first and third adders  62 ,  64 , respectively. Also, data values d 00  and d 10  are output on lines  66 ,  68  from the adders  62 ,  64 , respectively. Further, received data values r(n, 0), r(n, 1) are each fed to an associated subtraction element  70 ,  72  that subtracts 2 N −2. The subtraction results on lines  74 ,  76  are each fed to a second and a fourth adder  78 ,  80 , respectively. The subtraction results on the lines  74 ,  76  are also cross-fed to these adders  78 ,  80 . The results from these adders  78 ,  80  are output on lines  82 ,  84  as further data values d 11  and d 01  respectively. 
     Steps  2  and  3  of the Viterbi algorithm represent the actual base operation for the Viterbi decoder  42  and are the accumulate and compare operations. These steps are executed in one or, according to the invention, a plurality of parallel accumulate-and-compare modules  46 ,  48  ( FIG. 3 ) for accumulating and comparing the distances. 
       FIG. 7  illustrates a generic structure of a known Viterbi decoder  86  for implementing equation (5). The decoder  86  exhibits symmetry that makes the various kinds of parallelization possible. For every number of states, it is possible to identify a smallest processing step in which two states are to be handled in one step. The unlike sequences of input and output states, however, prohibit overwriting of old values as soon as new ones are calculated. 
     “In-place” calculation is consequently not possible, so that a temporary memory is used which holds the newly calculated values A new , M new  until the correct moment for overwriting. In terms of realization, the size of this temporary memory for all states lies between values of ¼ and 1. 
     Given a degree of parallelization p, the structure of the Viterbi decoder  86  requires 2×2 p  accumulate-and-compare modules in a parallel implementation, and the entire six-step procedure is executed 2 L−3−p  times for each output bit. The ratio of system clock frequency and data rate can be thus determined. If L=7, for example, there are two extrema. With 64 accumulate-and-compare modules, p=5, and the system clock frequency is equal to the data rate. With just two accumulate-and-compare modules, p=0, and the system clock frequency is a factor of 32 higher than the data rate. 
     The known generic structure of the Viterbi decoder according to the foregoing preferred exemplary embodiment can be generalized without substantial structural differences. If the original data string, instead of binary elements or bits, contains symbols from a polyvalent alphabet having N s  symbols, a polyvalent arithmetic being applied in the convolutional encoder and in the calculation of distances, there are N s   L−1  possible states and a plurality N s  of paths leading to each state upon a transition in the state diagram. This requires a comparison of N s  distances in the accumulate-and-compare module. Bits are also replaced with symbols in the Viterbi decoder  42  of the present invention. The structure of the decoder of  FIGS. 5-7  and procedural steps  1 - 6  of the Viterbi decoder remain largely unchanged. 
       FIG. 1  illustrates a memory device  40  having a two-part construction. The first part is a controlled memory portion  88  under the control of additional control signals s. The second part comprises a shift register  90 . 
     The structure of the memory device  40  introduces the additional control signals {s(k), k=0, . . . , 2 L−1 } in the path memory  52 , organized in matrix fashion, for the individual data elements {m(k, t), k=0, . . . , 2 L−1 , t=0, . . . , T−1}, which, according to the state diagram and according to the comparison result, make possible all requisite shifts between the individual paths directly in the memory. In this way, the corresponding path bus of the prior art is replaced by the substantially narrower control bus  50  as a control bus for transmitting 2 L−1  bits. 
     In the first part  88  of the memory  40 , a shift of each bit between the individual paths by a demultiplexer controlled by the control signals s(k) is possible. Only the first bits are specified in all paths, zeroes being specified in the first half and ones in the second half. Before all other bits there is a demultiplexer according to the transition rules of equation (5). The upper transition is selected if s=0 and the lower transition if s=1. 
     The second part  90  of the memory device  40  comprises simple shift registers which serve to compensate for the processing delays. The length of the shift register  90  may match the number of delay cycles in the accumulate-and-compare modules and in the minimum search. 
     This memory structure makes it possible to use a simplified accumulate-and-compare module  46  according to  FIG. 2 . Via two inputs, corresponding values A old/b=0  and A old/b=1  are applied on the lines  92 ,  94  to this module  46 . The inputs on the lines  92 ,  94  are each conveyed to an input of a corresponding adder  96 ,  98 . A distance value d c/b=0  on a line  100  is applied to the first adder  96  for addition to the corresponding first input value. A corresponding distance value d c/b=1  on a line  102  is applied to the second adder  98  for addition to the second input value on the line  94 . The output values of the two adders  96 ,  98  are fed to a comparator  104 . A control signal s is provided at an output of the comparator  104 , which is fed to an output of the accumulate-and-compare module  46  and is also fed to a module  106  for selection of the smaller of the distances. Also, the added values on the lines  108 ,  110  of the two adders  96 ,  98  are fed to the module  106  for selection of the smaller distance. The calculation of the new value, that is, the selection of the found minimal distance A new , takes place in the module  106  for selection of the smaller distance. Thus the accumulate-and-compare module  46  has two inputs for distances and two outputs, one for the found minimal distance A new  on a line  112  and the other for control signal s on a line  114 . Here s=0 if A old/b=0 &lt;A old/b=1 , and s=1 otherwise. 
     The structure of the memory device  40  of  FIG. 1  also makes possible a simplified realization of the entire Viterbi decoder  42 , as illustrated in  FIG. 3 . 
     The arrangement and manner of functioning of the individual components of the decoder  42  of  FIG. 3  is somewhat similar to the prior art decoder  10  of  FIG. 8 . The bidirectional path bus  30  of  FIG. 8  is replaced with a unidirectional control bus  50  in  FIG. 3  from the computing device  44  having the accumulate-and-compare modules  46 ,  48  for the transmission of 1×2 p+1  bits to the memory  40 . 
     As discussed above, the memory  40  comprises the path memory  52  and the demultiplexer  54 . The path memory  52  stores T×2 L−1  bits. Further, the address line  56  leads to the memory  40  from the computing device  44 , in particular from an output of a minimum-search module  116 . The address line  56  serves to transmit an address of the state having the minimal distance q, with a data volume of L−1 bits, to feed the address to the demultiplexer  54 . From the memory  40 , or under control of the demultiplexer  54 , the ultimately determined data bit string c(n, k) is provided on a line  118  to the output of the Viterbi decoder  42 . 
     The wide path bus  30  according to the prior art decoder  10  of  FIG. 8  is in this way replaced by the narrow control bus  50  ( FIG. 3 ). The relatively large temporary memory  22 ,  32  for paths in the computing device  10  according to the prior art is replaced by relatively smaller temporary memories  120 ,  122 . To this end there are other L−1 bits to be transmitted as the address q of the selected path. The demultiplexer  54  selects, for the reconstructed output bit c(n, k), the last bit in the path that corresponds to the minimal distance. A delay of the system clock frequency in the accumulate-and-compare module  46 ,  48  is obligatory so that the old distances in the distance memory can be overwritten with the newly calculated distances at the proper time. The minimum search involves an additional delay of D system clock cycles, so that the shift registers at the end of each path in the path memory  52  are formed as D+1 system clock cycles long in order for the corresponding output bit to be correctly associated with the minimum found. These delays also require a slight expansion, by one bit, of the value range for distance accumulators. 
     The Viterbi decoder  42  offers a relaxed dependence between the system clock frequency and the bus widths, as illustrated in  FIG. 4  for various degrees of parallelization p. For ease of comparison with  FIG. 9 , the same parameters have been used in  FIG. 4  as in  FIG. 9 . 
     The Viterbi decoder  42  offers a relatively small bus width of 900 bits, which can be realized economically, even when the system clock frequency is equal to the data rate, which corresponds to a degree of parallelization p=5. In the DVB example, the system clock frequency is then 50 MHz. Given a system clock frequency of 100 MHz (i.e., a degree of parallelization p=4) the requisite bus width drops to 450 bits, which is a factor of 10 narrower than the requisite bus width according to standard memory structures. 
     Applied at the input of the Viterbi decoder  42  are data or data values r(n, k) on the line  12 , which have been transmitted via a usually wireless interface of a communications system. The actual data to be sent, which on the receiver side for example are to be reconstructed using the Viterbi algorithm, are processed by error-protection encoding on the transmitter side. What follows is an explanation of the transmitter-side convolutional encoding of a bit string to be transmitted. 
     A data bit string { . . . , b(n), b(n+1), . . . } is to be transmitted. For the employment of the Viterbi algorithm on the receiver side, this data bit string is encoded in the following way on the transmitter side: 
     In a first step, the data of the data bit string are pushed into a shift buffer. At each step, the shift buffer of length L bits {B( 0 ), B( 1 ), . . . , B(L−1)} is shifted to the right {B(m)=B(m−1), m=2, 3, . . . , L−1} and filled with a new input bit {B( 0 )=b(n)}. The length L defines a parameter of the encoding, the “constraint length.” 
     In a second step, K output bits {c(n, k), k=0, 1, . . . , K−1} are calculated according to the buffer state at the output. The calculation is uniquely determined with a set of K generator polynomials of length L {G(k, m), k=0, 1, . . . , K−1, m=0, 1, . . . , L−1} with binary coefficients 0 or 1, according to equation 7: 
                       c   ⁡     (     n   ,   k     )       =         ∑     m   =   0       L   -   1       ⁢       G   ⁡     (     k   ,   m     )       ·     B   ⁡     (   m   )           =       ∑     m   =   0       L   -   1       ⁢       G   ⁡     (     k   ,   m     )       ·     b   ⁡     (     n   -   m     )               ,           (   7   )               
the additions in the sum being understood in the sense of modulo 2 addition (EXOR). The ratio between the number of useful bits at the input and the number of bits for transmission at the output is defined as a second parameter, namely the “code rate” R. In this case, R=1/K.
 
     Third, to obtain different code rates R, the encoding described above is followed by the application of “puncturing” as a post-processing operation. In this process, from P successive sets of K bits, certain bits are dropped in accordance with a previously specified binary P-matrix {P(a, b), a=0, 1, . . . , K−1, b=0, 1, . . . , P−1}; these bits are marked with P(a, b)=0. With the number of ones in the matrix P 1 , the code rate can be determined as R=P/P 1  lying between 1/K and 1, at most all the PK matrix coefficients being 1 and at least one 1 appearing in each P-column. 
       FIG. 10  illustrates a prior art example in which the code word of a convolutional code can be infinitely long. A description of the encoding with a state diagram is helpful for analysis of the Viterbi algorithm. The state of the encoder is uniquely determined with the last L−1 bits of the buffer Z B(1), . . . , B(L−1) . In the binary case there are 2 L−1  distinct states, and from each of them there are two possible transitions into a next state in dependence on the new bit at the input b=b(n). Upon each transition, K encoded bits c={c( 0 ), . . . , c(K−1)} are generated at the output. The generator polynomials are always selected such that all K bits in the two competing bit sets are distinct. 
       FIG. 11  is a state diagram of the convolutional encoder for the example of  FIG. 10 . From the state diagram it follows that only certain transitions are possible, for example from the states {Z 00 , Z 01 } only to the states {Z 00 , Z 10 } and from {Z 10 , Z 10 } to the states {Z 01 , Z 11 }. This analysis can be generalized. Let all states be numbered with {Z k , k=0, . . . , 2 L−1 }. The transition rule is then as follows:
 Z K  with b=0, the code being=c {Z 2K , Z 2K+1 }            k=0, . . . , 2 L−2   Z 2   L−2   +k  with b=1, the code being=  c , 
where  c  denotes the inverted code word.

     Next, the encoded data {p(m)} are transmitted using a modulation, for example quadrature amplitude modulation (“QAM”) or phase shift keying (“PSK”), over a channel, for example, a channel of a wireless interface of a communications system. As a result of the transmission, the data becomes distorted and noise and other interference signals are superimposed on the data. The original data are reconstructed with the Viterbi algorithm. 
     Although the present invention has been shown and described with respect to several preferred embodiments thereof, various changes, omissions and additions to the form and detail thereof, may be made therein, without departing from the spirit and scope of the invention.