Abstract:
The invention relates to a method and arrangement for advantageously decoding and channel correcting a convolutionally encoded signal received over a transmission path. The signal comprises code words and the arrangement comprises a neural network comprising a set of neurons which comprise a set of inputs and an output. The received code words ( 400 ) and at least some of the output signals ( 402 ) of the neural network neurons are connected to the inputs of the neurons, and the neurons comprise means ( 404 ) for multiplying at least some of the neuron inputs prior to combining means ( 406 ). The arrangement also comprises means ( 123 ) for estimating the transmission channel. Further, estimated channel data ( 400 ) is connected to the inputs of the neurons and a predetermined neuron is arranged to give an estimate of the channel-corrected and decoded symbol in its output signal.

Description:
FIELD OF THE INVENTION 
     The invention relates to a method and an arrangement for decoding and channel correcting a convolutionally encoded signal in a receiver, by means of a feedback neural network, said signal being received over a transmission path. 
     BACKGROUND OF THE INVENTION 
     In telecommunication connections, the transmission path used for transmitting signals is known to cause interference to telecommunication. This occurs regardless of the physical form of the transmission path, i.e. whether the transmission path is a radio link, an optical fibre or a copper cable. Particularly in telecommunications over a radio path there are frequently situations where the quality of the transmission path varies from one occasion to another and also during a connection. 
     Radio path fading is a typical phenomenon that causes changes in a transmission channel. Other simultaneous connections may also cause interferences and they can vary as a function of time and place. 
     In a typical radio telecommunication environment the signals between a transmitter and a receiver propagate on a plurality of routes. This multipath propagation mainly results from signal reflections from surrounding surfaces. The signals that propagated via different routes reach the receiver at different times due to different transit delays. Various methods have been developed in order to compensate the interference caused by this multipath propagation. 
     In order to reduce the effects of interference caused by the transmission path, a digital signal is encoded so as to make the transmission connection more reliable. Thus the errors caused by the interference in the transmitted signal can be detected and, depending on the encoding method used, also corrected without retransmission. Conventional encoding methods used in digital telecommunication include, for instance, block coding and convolutional coding. In block coding the bits to be encoded are grouped into blocks at the end of which are added parity bits, by means of which the correctness of the bits of the preceding block can be checked. 
     In the receiver, the errors caused by multipath propagation are typically first corrected, for instance, by a linear transversal corrector and thereafter the convolutional code is decoded. 
     The efficiency of convolutional coding depends on the code rate and constraint length used. A large constraint length enables good error correction capability, but on the other hand, decoding by known methods is then very complicated. 
     In general, convolutional coding is decoded by using a Viterbi algorithm that has nearly optimal performance. However, the Viterbi algorithm has a drawback that its complexity increases exponentially as the constraint length increases. This restricts the constraint lengths available. 
     Another known decoding method is sequential decoding that is described in greater detail in  Digital Communications , J. G. Proakis, 3rd edition, pp. 500-503. One drawback of this algorithm is that the decoding delay does not remain constant but varies. 
     Yet another known decoding method is a so-called stack algorithm that is described in greater detail in the above-mentioned publication  Digital Communications , J. G. Proakis, 3rd edition, pp. 503-506. The performance of this algorithm is not so good as that of the Viterbi algorithm. 
     Of the known methods, the Viterbi algorithm has the best performance for decoding the convolutional code, but its implementation has turned out to be extremely difficult in practice as the constraint length increases. The difficult implementation of the complicated Viterbi algorithm by circuitry has restricted the constraint lengths available for use. 
     A separate channel corrector and decoder are a suboptimal solution. Use of channel data, in particular within the Viterbi algorithm when computing the metrics, leads to increased complexity and the implementation of practical applications is impossible. 
     BRIEF DESCRIPTION OF THE INVENTION 
     The object of the invention is to provide a method and an arrangement implementing the method such that the above-mentioned drawbacks can be solved. This is achieved by a method of the invention for decoding a convolutionally encoded signal received over a transmission path, which signal comprises code words and in which method a transmission channel is estimated, decoding is carried out by means of an artificial neural network, the neural network comprising a set of neurons which comprise a set of inputs and an output, the received code word set is conducted to the inputs of the neuron, at least some of the inputs of the neuron are multiplied, after multiplication some of the inputs of the neuron are combined, some of the output signals of the neural network neurons are fed back to the inputs of each neuron, initial values of the neurons are set and the network is allowed to stabilize. 
     Further, in the method of the invention the multiplication of the neuron inputs depends on the convolutional code used in signal encoding and on the estimated channel and on the fact that an estimate of the decoded and channel-corrected symbol is conducted from the output signal of a predetermined neuron to the output of the network after the network has reached a stabilized state, the set of code words in the shift register is updated and the above-described four last steps are repeated until the desired number of code words are decoded. 
     The invention also relates to an arrangement for decoding and channel correcting a convolutionally encoded signal received over a transmission path, the signal comprising code words and the arrangement comprising a neural network which comprises a set of neurons which comprise a set of inputs and an output, the received code words being applied to the inputs of said neurons and to at least some of the output signals of the neural network neurons, the neurons comprising means for multiplying at least some of the inputs of the neuron prior to combining means, the arrangement comprising means for estimating the transmission channel. Further in the arrangement of the invention, estimated channel data is applied to the inputs of the neurons, and a predetermined neuron is arranged to give an estimate of the channel-corrected and decoded symbol in its output signal. 
     The preferred embodiments of the invention are disclosed in the dependent claims. 
     In the solution of the invention, convolutional code decoding and channel correction are performed by means of a feedback neural network. Several advantages are achieved with the solution of the invention. Performance that is close to that of the Viterbi algorithm is achieved with the solution of the invention by means of considerably simpler circuitry. In the solution of the invention, equally complicated circuitry permits a larger constraint length and thus improved error correction over the Viterbi algorithm. 
     The neural network of the invention can be readily constructed by semiconductor technology, since the neurons of the neural network are very similar to one another in structure, only the input couplings vary. Consequently, to design and implement even a large network does not involve a great amount of work. The solution can also be advantageously implemented as a VLSI circuit, which makes it fast. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the following the invention will be described in greater detail in connection with preferred embodiments with reference to the accompanying drawings, wherein 
     FIG. 1 illustrates an example of a telecommunications system where the solution of the invention can be applied, 
     FIG. 2 shows an example of a neuron designed by means of the method of the invention, 
     FIG. 3 shows an example of couplings of the neural network neuron designed by means of the method of the invention, 
     FIG. 4 illustrates an example of the implementation of the neural network neuron of the invention, 
     FIGS. 5 a  and  5   b  illustrate an implementation example of a neural network of the invention, 
     FIG. 6 illustrates an example where decoding is performed by means of a plurality of parallel neural networks. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The solution of the invention can be applied in any digital data transmission system where a signal to be transmitted is encoded by convolutional coding. Examples of possible systems include cellular radio systems, radio links, wired networks or optical networks. 
     FIG. 1 illustrates an example of a telecommunications system according to the invention. The figure shows a transmitter  100 , a signal transmission path  102  and a receiver  104 . The operations of the invention are implemented in the receiver. The signal transmission path can be a radio path, a copper cable or an optical fibre, for instance. 
     In the transmitter, a data source  106  generates a signal  108  composed of bits. An error correcting code can be added to the data source signal  108  by a known FEC (Forward Error Correcting) method, if necessary. This is not shown in the figure. The signal  108  is applied to an encoder  110  where convolutional coding is effected with desired parameters (constraint length and code rate). The encoder can have a prior art structure. The encoded signal can be understood as code words whose length depends on the code used. The encoded signal is applied to a modulator  112  where the desired modulation is performed. The modulated signal is further applied to output stages  114  and a channel adapter  116  of the transmitter which are system-dependent components. The output stage  114  can be a radio frequency amplifier and a filter, for instance. The channel adapter  116  can be an antenna or an electrical/opto-converter, for instance. 
     A transmitter output signal  118  propagates through the transmission path  102 , i.e. the channel, to the receiver  104 . The receiver comprises a channel adapter  120  and a receiver pre-stage  122  which are system-dependent components. The output stage  122  can comprise a radio frequency amplifier and a filter, for instance. The channel adapter  120  can comprise an antenna or an opto/electrical converter, for instance. The signal is applied from the pre-stage  122  further to a channel estimator  123  where channel estimation is performed by using known methods. From the channel estimator, the signal is applied to a demodulator  124  from which is typically received a baseband bit stream  126  which can be complex and comprise separate I- and Q-branch bits. Timing information is derived from the received signal in a regenerator  128  by a known method. This timing information is used in demodulation. The receiver further comprises a control unit  130  which can be advantageously implemented by a processor. The control unit  130  controls the operation of the receiver. Information on the timing is also applied to the control unit. 
     The signal  126  coming from the demodulator  124  thus comprises the demodulated bits which can be presented as code words. The code words are applied to a decoder  132  which is implemented by a neural network in the receiver of the invention. Convolutional coding is decoded in the decoder and the decoder output signal  134  corresponds to the original signal  108 . In connection with convolutional coding, the channel data obtained from the channel estimator  123  is taken into account, i.e. channel correction is performed. If an error correcting code was used in the transmitter, it is decoded at this stage. This is not shown in the figure. 
     The method for decoding the convolutional code and performing the channel correction in accordance with the invention is studied next in greater detail. It is assumed in this example that 4 QAM modulation is used. Generally, the aim of the decoding is to find a bit sequence B that minimizes the function                min   B            ∑     s   =   0     T                                r        (     t   +   sdt     )       -     h                     γ   c          (     B        (     t   +   sdt     )       )                2                     =          :                       min   B          f        (   B   )                     (   1   )                                
     where r(t+sdt) is a received code word at a time instant t+sdt, 
     dt is a symbol interval, 
     h=[h 1 , h 2 ] are channel coefficients of a two-path channel, 
     γ c  (B(t+sdt))=[γ(B(t+sdt)), γ(B(t+(s−1)dt)) a vector with a current code word and a preceding code word as components. When 4 QAM modulation is used, these are complex values. 
     For the sake of clarity, r(s)=r(t+sdt) and B(s)=B(t+sdt) are used. Furthermore, instead of bit values 0 and 1, values −1 and 1 are used. In Formula (1) 
     
       
           B ( s )=[ b ( s - L +1), . . . ,  b ( s )],  b ε{1-,1}, 
       
     
     b(−L+1), . . . , b(0) are fixed, L is the constraint length and T is the decoding delay. The encoder function γ corresponds to the generation matrix G of a convolutional encoder. On the transmission path, interference, such as noise, appears in the signal. A noisy code word received at a time instant s is indicated by r(s). It is assumed that the noise is white Gaussian noise. 
     Let us study here the generation of a neural network of the invention by means of an example employing a convolutional code with code rate ½ and constraint length L=3. The generation matrix G for such a code is        G   =       [         1       0       1           1       1       1         ]     .                            
     The encoder for the convolutional code with code rate ½ and constraint length L can be written as a complex function 
     
       
         γ( B ( s ))=γ 1 ( B ( s ))+iγ 2 ( B ( s )), 
       
     
     where              γ   j          (     B        (   s   )       )       =       ∏     i   =   1     L                         (     b        (     s   +   1   -   i     )       )       g   ij            (     -   1     )            (     -   1     )       g   js             ,                          
     and g j,i s are the elements of the matrix G. Now, as in this example L=3, the encoder is of the form 
     
       
         γ( B ( s ))=− b ( s ) b ( s− 2)+ ib ( s ) b ( s− 1) b ( s− 2) 
       
     
     and the received noisy complex code word is r(s)=r 1 (s)+ir 2 (s). 
     Equation (1) is written out as:                             ∑   s                              r        (   s   )       -     h                     γ   c          (     B        (   s   )       )                2       =                  ∑   s                     (         1   2          [         re        (     r        (   s   )       )       2     +       im        (     r        (   s   )       )       2       ]       +                                  [         re        (       r        (   s   )            h   1   c       )            b        (   s   )            b        (     s   -   2     )         -                                    im        (       r        (   s   )            h   1   c       )            b        (   s   )            b        (     s   -   1     )            b        (     s   -   2     )         ]     +                            [         re        (       r        (   s   )            h   2   c       )            b        (     s   -   1     )            b        (     s   -   3     )         -                                    im        (       r        (   s   )            h   2   c       )            b        (     s   -   1     )            b        (     s   -   2     )            b        (     s   -   3     )         ]     +                              1   2                     h   1   c            h   1     [           b        (   s   )       2            b        (     s   -   2     )       2       +                                          b        (   s   )       2            b        (     s   -   1     )       2            b        (     s   -   2     )       2       ]       +                              1   2                     h   2   c            h   2     [           b        (     s   -   1     )       2            b        (     s   -   3     )       2       +                                          b        (     s   -   1     )       2            b        (     s   -   2     )       2            b        (     s   -   3     )       2       ]       +                              re        (       h   1   c          h   2       )            b        (   s   )            b        (     s   -   1     )            b        (     s   -   2     )                                    b        (     s   -   3     )       -       im        (       h   1   c          h   2       )            b        (   s   )            b        (     s   -   1     )                                        b        (     s   -   2     )            b        (     s   -   3     )         +       im        (       h   1   c          h   2       )            b        (   s   )                                        b        (     s   -   1     )              b        (     s   -   2     )       2          b        (     s   -   3     )         +     re        (       h   1   c          h   2       )                                      b        (   s   )              b        (     s   -   1     )       2        b          (     s   -   2     )     2          b        (     s   -   3     )         )     .                 (   2   )                                  
     In the above, the superscript c refers to a complex conjugate. As b(s−1) 2 =1 and b(s−2) 2 =1, the minima of the above function (2) and the function                             f   ^          (   B   )       :=     =                  ∑   s                     (         1   2          [         re        (     r        (   s   )       )       2     +       im        (     r        (   s   )       )       2       ]       +                                    [         re        (       r        (   s   )            h   1   c       )            b        (   s   )            b        (     s   -   2     )         -     im        (       r        (   s   )            h   1   c       )          b        (   s   )            b        (     s   -   1     )                                          b        (     s   -   2     )       ]       +     [         re        (       r        (   s   )            h   2   c       )            b        (     s   -   1     )            b        (     s   -   3     )         -     im        (       r        (   s   )            h   2   c       )                                          b        (     s   -   1     )            b        (     s   -   2     )            b        (     s   -   3     )         ]     +       1   2                     h   1   c            h   1     [           b        (   s   )       2            b        (     s   -   2     )       2       +                                            b        (   s   )       2            b        (     s   -   1     )       2            b        (     s   -   2     )       2       ]       +       1   2                     h   2   c            h   2     [           b        (     s   -   1     )       2            b        (     s   -   3     )       2       +                                          b        (     s   -   1     )       2            b        (     s   -   2     )       2            b        (     s   -   3     )       2       ]       +       re        (       h   1   c          h   2       )            b        (   s   )                                      b        (     s   -   1     )            b        (     s   -   2     )            b        (     s   -   3     )         -       im        (       h   1   c          h   2       )            b        (   s   )            b        (     s   -   1     )                                        b        (     s   -   2     )            b        (     s   -   3     )         +       im        (       h   1   c          h   2       )            b        (   s   )            b        (     s   -   1     )            b        (     s   -   3     )         +                                re        (       h   1   c          h   2       )          b        (   s   )            b        (     s   -   3     )         )     .                 (   3   )                                  
     are the same. The differences between the functions are in the two last terms. To eliminate complicated feedbacks, the function (3) will be employed. 
     (3) is differentiated with respect to b(k). Then we obtain a partial derivative which is of the form                             ∂       f   ^          (   B   )           ∂     b        (   k   )           =                    re        (       r        (   k   )            h   1   c       )            b        (     k   -   2     )         -       im        (       r        (   k   )            h   1   c       )            b        (     k   -   1     )            b        (     k   -   2     )         -                                  im        (       r        (     k   +   1     )            h   1   c       )            b        (     k   +   1     )            b        (     k   -   1     )         +                                  re        (       r        (     k   +   1     )            h   2   c       )            b        (     k   -   2     )         -                                im        (       r        (     k   +   1     )            h   2   c       )          b        (     k   -   1     )            b        (     k   -   2     )         +                                  re        (       r        (     k   +   2     )            h   1   c       )            b        (     k   +   2     )         -                                im        (       r        (     k   +   2     )            h   1   c       )          b        (     k   +   2     )            b        (     k   +   1     )         -                                  im        (       r        (     k   +   2     )            h   2   c       )            b        (     k   +   1     )            b        (     k   -   1     )         +                                  re        (       r        (     k   +   3     )            h   2   c       )            b        (     k   +   2     )         -                                  im        (       r        (     k   +   3     )            h   2   c       )            b        (     k   +   2     )            b        (     k   +   1     )         +       re        (       h   1   c          h   2       )            b        (     k   -   3     )         +                                  re        (       h   1   c          h   2       )            b        (     k   -   2     )            b        (     k   -   1     )            b        (     k   -   3     )         -                                  im        (       h   1   c          h   2       )            b        (     k   -   2     )            b        (     k   -   3     )         +       im        (       h   1   c          h   2       )            b        (     k   -   1     )                                      b        (     k   -   3     )       +       re        (       h   1   c          h   2       )            b        (     k   +   1     )            b        (     k   -   1     )            b        (     k   -   2     )         +                                  im        (       h   1   c          h   2       )            b        (     k   +   1     )            b        (     k   -   2     )         +                                  re        (       h   1   c          h   2       )            b        (     k   +   2     )            b        (     k   +   1     )            b        (     k   -   1     )         -                                  im        (       h   1   c          h   2       )            b        (     k   +   2     )            b        (     k   -   1     )         +                                  re        (       h   1   c          h   2       )            b        (     k   +   3     )            b        (     k   +   2     )            b        (     k   +   1     )         -                                  im        (       h   1   c          h   2       )            b        (     k   +   3     )            b        (     k   +   1     )         +       im        (       h   1   c          h   2       )            b        (     k   +   3     )                                      b        (     k   +   2     )       +       re        (       h   1   c          h   2       )            b        (     k   +   3     )         +     5        (         h   1   c          h   1       +       h   2   c          h   2         )            b        (   k   )       .                       (   4   )                                  
     Now we use a gradient method          b        (   k   )       =       b        (   k   )       -     α                       ∂       f   ^          (   B   )           ∂     b        (   k   )           .                                
     By selecting        α   =     1     5        (         h   1   c          h   1       +       h   2   c          h   2         )                                
     it is possible to eliminate the feedbacks appearing in the last term of Formula (4). Further by assuming that b(k) obtains values −1 or 1, the following equivalence is true for all the values k=0, . . . , T 
     
       
           b ( k )=sign( 
       
     
     
       
         − re ( r ( k ) h   1   c ) b ( k −2)+ im ( r ( k ) h   1   c ) b ( k −1) b ( k −2) 
       
     
     
       
         + im ( r ( k +1) h   1   c ) b ( k +1) b ( k −1)− re ( r ( k +1) h   2   c ) b ( k −2) 
       
     
     
       
         + im ( r ( k +1) h   2   c ) b ( k −1) b ( k −2)− re ( r ( k +2) h   1   c ) b ( k +2) 
       
     
     
       
         + im ( r ( k +2) h   1   c ) b ( k +2) b ( k +1)+ im ( r ( k +2) h   2   c ) b ( k +1) b ( k −1) 
       
     
     
       
         − re ( r ( k +3) h   2   c ) b ( k +2)+ im ( r ( k +3) h   2   c ) b ( k +2) b ( k +1)− re ( h   1   c   h   2 ) b ( k− 3) 
       
     
     
       
         − re ( h   1   c   h   2 ) b ( k −2) b ( k −1) b ( k −3)+ im ( h   1   c   h   2 ) b ( k −2) b ( k −3) 
       
     
     
       
         − im ( h   1   c   h   2 ) b ( k −1) b ( k −3)− re ( h   1   c   h   2 ) b ( k +1) b ( k −1) b ( k −2) 
       
     
     
       
         − im (h 1   c   h   2 ) b ( k +1) b ( k −2)− re ( h   1   c   h   2 ) b ( k +2) b ( k +1) b ( k −1) 
       
     
     
       
         + im ( h   1   c   h   2 ) b ( k +2) b ( k −1)− re ( h   1   c   h   2 ) b ( k +3) b ( k +2) b ( k +1) 
       
     
     
       
         + im ( h   1   c   h   2 ) b ( k +3) b ( k +1)− im ( h   1   c   h   2 ) b ( k +3) b ( k +2)= re ( h   1   c   h   2 ) b ( k +3)).  (5) 
       
     
     From the above the following updating rule is obtained: one k at a time is selected and a corresponding bit is updated by using Formula (5) and this is repeated until no changes occur in the bits, i.e. the network is stabilized. It should be noted that if k=T−1, or k=T, then b(T+1)=0 and b(T+2)=0 are set. In the actual implementation, the operation may take place in parallel such that all neurons k are updated simultaneously. 
     The iteration according to Formula (5) can thus be presented as an artificial neuron of the neural network. By setting S k =b(k), where S k  is the state of the k th  neuron and when re and im are the real and imaginary parts of the external inputs coming to the neuron, the state of the k th  neuron can be presented as: 
     
       
           S   k   =f   a (− re ( r ( k ) h   1   c ) S   k−2   +im ( r ( k ) h   1   c ) S   k−1   S   k−2   
       
     
     
       
         + im ( r ( k +1) h   2   c )S k−1   S   k−2   −re ( r ( k +2) h   1   c )S k+2   
       
     
     
       
         + im ( r ( k +1)h 2   c )S k−1   S   k−2   −re ( r ( k +2) h   1   c )S k+2   
       
     
     
       
         + im ( r ( k +2) h   1   c ) S   k+2   S   k+1   +im ( r ( k +2)h 2   c )S k+1   S   k−1   S   k−1   
       
     
     
       
         − re ( r ( k +3) h   2   c )S k+2   +im ( r ( k +3) h   2   c )S k+2   S   k+1   −re (h 1   c   h   2 )S k−3   
       
     
     
       
         − re ( h   1   c   h   2 ) S   k−2   S   k−1   S   k−3   +im ( h   1   c   h   2 ) S   k−2   S   k−3   
       
     
     
       
         − im ( h   1   c   h   2 ) S   k−1   S   k−3   −re ( h   1   c   h   2 ) S   k+1   S   k−1   S   k−2   
       
     
     
       
         − im (h 1   c   h   2 ) S   k+1   S   k−2   −re ( h   1   c   h   2 ) S   k+2   S   k+1   S   k−1   
       
     
     
       
         + im ( h   1   c   h   2 ) S   k+2   S   k−1   −re ( h   1   c   h   2 ) S   k+3   S   k+2   S   k+1   
       
     
     
       
         + im ( h   1   c   h   2 ) S   k+3   S   k+1   −im ( h   1   c   h   2 ) S   k+3   S   k+2   −re ( h   1   c   h   2 )S k+3 ),  (6) 
       
     
     where f a  is an activation function, typically a sigmoidal function or a hard limiter. In Formula (5) a signum function f a (x)=sign(x) is used. 
     FIG. 2 illustrates a neuron according to Formula (6). The state S k  of the neuron appears at the neuron output. According to Formula (6), real and imaginary parts of the products of the received corrupted code words r(t) and channel coefficients h 1  and h 2  (or their conjugates) as well as real and imaginary parts of the products of channel coefficients h 1  and h 2  (or their conjugates) are applied to the neuron as an input  200 . Since the code rate of the code used was ½, one bit to be encoded results in two bits when encoded. Correspondingly, in decoding one decoded bit represents two bits of the code word. Furthermore, feedback outputs of other neural network neurons, i.e. S k−3 , S k−2 , S k−1 , S k+1 , S k+2 , and S k+3 , are applied to the neuron as an input  202 . The output of each neuron thus comprises one decoded bit. 
     In a preferred embodiment of the invention, the neuron is not fed back to itself, i.e. the value S k  is not applied to the neuron as an input. The inputs of the neuron are multiplied according to Formula (6). This is illustrated by dots at the intersection of the lines. White dots denote the multiplication of the inputs and black dots denote the multiplication of the inputs and the change of the sign of the product. The multiplied signals are summed  204  and applied to an activation function  206  whose output S k    208  is the output value of the neuron. 
     The activation function employed can be either a hard-decision or a soft-decision function or a step function. If the result is a hard decision, the neuron outputs can have values −1 or 1. If the result is a soft decision, the neuron output can be a floating point number. Correspondingly, if the demodulator  124  produces soft bit decisions, neuron input  200  comprises floating point numbers, and if the demodulator produces hard bit decisions, the neuron input  200  comprises bits. If both of the neuron inputs comprise bits, the multiplication between the inputs can be implemented in a simple manner by digital technology. 
     Since the derived neural network is a so-called optimizing neural network, it may be caught in a local minimum. To avoid this, in one preferred embodiment of the invention, noise (AWGN) whose variance reduces during the stabilization stage is added to the incoming signal in the neurons. In that case, Formula (6) is of the form 
     
       
           S   k   =f   a (− re ( r ( k ) h   1   c )  S   k−2   +im ( r ( k ) 1   c ) S   k−1   S   k−2   
       
     
     
       
         + im ( r ( k +1)h 1   c ) S   k+1   S   k−1   −re ( r ( k +1) h   2   c ) S   k−2   
       
     
     
       
         + im ( r ( k +1) h   2   c ) S   k−1   S   k−2   −re ( r ( k +2) h   1   c ) S   k+2   
       
     
     
       
         + im ( r ( k +2) h   1   c ) S   k+2   S   k+   +im ( r ( k +2) h   2   c ) S   k+1   S   k−1   
       
     
     
       
         − re ( r ( k   +3)   h   2   c ) S   k+2   +im ( r ( k +3) h   2   c ) S   k+2   S   k+1   −re ( h   1   c   h   2 ) S   k−3   
       
     
     
       
         − re ( h   1   c   h   2 ) S   k−2   S   k−1   S   k−3   +im ( h   1   c   h   2 ) S   k−2   S   k−3   
       
     
     
       
         − im ( h   1   c   h   2 ) S   k−1   S   k−3   −re ( h   1   c   h   2 ) S   k+1   S   k−1   S   k−2   
       
     
     
       
         − im ( h   1   c   h   2 ) S   k+1   S   k−2   −re ( h   1   c   h   2 ) S   k+2   S   k+1   S   k−1   
       
     
     
       
         + im ( h   1   c   h   2 ) S   k+2   S   k−1   −re ( h   1   c   h   2 ) S   k+3   S   k+2   S   k+1   
       
     
     
       
         + im ( h   1   c   h   2 ) S   k+3   S   k+1   −im ( h   1   c   h   2 ) S   k+3   S   k+2   −re ( h   1   c   h   2 ) S   k+3   +AWGN).   (7) 
       
     
     In decoding, the following steps are generally carried out for each received code word: 
     1. Setting S −1 , S −2  and S −3  according to previous decisions. The products of the real and imaginary parts of the products of the received code words r(t), . . . , r(t+Tdt) and the channel coefficients are applied to the neuron inputs  200 . 
     2. Initializing S(i), i=0, . . . , T. 
     3. Updating the neuron k for each k=0, . . . , T according to Formula (7). 
     4. Reducing the variance of the added noise. If the necessary number of iteration rounds have been carried out, the procedure is terminated, otherwise the procedure returns to step  3 . 
     After this, the bit to be decoded is at the output of neuron 0. 
     FIG. 3 illustrates couplings of the neural network designed for decoding code rate ½ and constraint length  3 . The demodulated code words  322  and the channel data  324  received from the channel estimation means are applied to a single neuron  306  as an input. The code words and the channel data are multiplied according to Formula (6) in a multiplier  326 . Further, outputs  328 ,  330  from the adjacent neurons  300  to  304 ,  308  to  320  are applied to the neuron  306  as an input. The neuron output is the value of the activation function  326 , the value being a decoded symbol. The neural network is initialized such that the previously made bit decisions become the states of the neurons −3, −2 and −1, i.e.  300  to  304 . As the states of the neurons 0, . . . , T, i.e.  306  to  320 , +1 or −1 are set randomly. Thereafter, the network is allowed to stabilize. The decoded bit is the output of the neuron  306 , i.e. neuron 0, or if more than one bit is decoded at a time, the outputs of the neurons 0, . . . , N. 
     Duration of the network stabilization can be determined either by allowing the iterations to continue until the bit at the output does not vary or by performing a predetermined number of iteration rounds. 
     In order to avoid being caught in a local minimum, other methods together with or instead of noise addition can also be used. The number of iteration rounds to be performed can be increased. Another option is to use several parallel neural networks. When each neural network is stabilized, the best bit decision can be selected from the outputs of the networks. The selection can be made by a majority decision, for instance, selecting the bit decision that occurs most frequently at the outputs of the parallel neural networks. It is also possible to re-encode the decoding result and compare the obtained result with the received code word, i.e. to select a result that minimizes the function                1     T   b              ∑     s   =   0       T   b                                  r        (   s   )       -       r   re          (   s   )              2     .               (   8   )                                
     Decoding can also be accelerated such that several bit decisions of the adjacent neurons, i.e. neurons S 0 , . . . , S N , are extracted simultaneously from the neural network. When decoding the subsequent bits, the states of the neurons S −L+1 , . . . , S −1  have to be initialized to have the preceding values. 
     The method of the invention can also be applied when the code to be decoded is a punctured code. 
     The solution of the invention can also be advantageously applied such that fast channel estimates are utilized. Each symbol can be expressed using symbol-specific channel data, even though the convolutional code extends over a plurality of symbols. 
     Let us study next the complexity of the solution of the invention mainly from the viewpoint of implementation. When the constraint length L increases, more neurons are needed in the neural network and the duration of stabilization increases, and consequently the number of multiplications increases. It is known that the complexity of a Viterbi decoder increases exponentially as the constraint length L increases. However, the complexity of the decoder implemented by means of the neural network of the invention increases much more slowly. When the constraint length is L and the number of channel taps is H, each neuron of the neural network is coupled to L+H−2 preceding and L+H−2 subsequent neurons and to L inputs. If it is assumed that the decoding delay is 5L, as it generally is, the decoder requires 5L neurons and thus the maximum number of connections is in the order of O (H 2 L 2 n), where n is the number of generators. 
     The number of multiplications to be performed in one neuron depends on the code generator used, but it is ≦O(nH 3 +nH 2 L+nHL 2 ). Thus, during one iteration round, when each neuron is updated once, the number of multiplications to be performed is O(nLH 3 +nH 2 L 2 +nHL 3 ). This shows how the complexity in the solution of the invention increases considerably more slowly than in connection with the Viterbi algorithm as L increases. 
     FIG. 4 illustrates the implementation of the neuron of the neural network according to the invention. The neuron state at the neuron output is S k . Interfered code words to be decoded, typically composed of bits, and channel data are applied to the neuron as an input  400 . The number of bits in each code word depends on the code rate of the code used. Further, feedback outputs of other neural network neurons are applied to the neuron as an input  402 . In a preferred embodiment of the invention, the neuron does not comprise feedback to itself, i.e. the value S k  is not applied to the neuron as an input, but feedback to itself is possible if necessary. 
     The inputs of the neuron are multiplied in a matrix  404 . The matrix couplings are defined by the convolutional code and channel model used, and the formula corresponding to the couplings can be derived as illustrated in the above examples. The inputs can be multiplied with or without a change of sign. The multiplied signals are applied to a summer  406  where they are summed and the summed signal is further applied to a calculation means  408  which calculates the activation function and whose output S k    410  is the output value of the neuron. The calculation means  408  can be implemented by a gate array or a processor and software. 
     The function producing either a hard or a soft decision can thus be used as the activation function. If the result is a hard decision, the neuron outputs can have values −1 or 1. If the result is a soft decision, the neuron output can be a floating point number. Correspondingly, if the demodulator of the receiver produces soft bit decisions, floating point numbers are at the neuron input  400 , and if the demodulator produces hard bit decisions, bits are at the neuron input  400 . If both of the neuron inputs comprise bits, the multiplication between the inputs can be implemented in a simple manner by digital technology. 
     In one preferred embodiment of the invention, the neuron comprises a noise generator  412  and the generated noise is applied to a summer  406  where it is added to a sum signal. Variance of the noise to be generated reduces during the stabilization of the neural network, as described above. The noise can be Gaussian noise or binary noise. The binary noise is easier to implement, but on the other hand, a suitable number of Gaussian noise samples can be stored in a memory element and this noise can be reused. Noise generation can be implemented in manners know to the person skilled in the art. 
     The structure of the decoder of the invention is studied next from the viewpoint of implementation. FIG. 5 a  illustrates the structure of the neural network of the invention. The neural network comprises a set of neurons  500  to  510 , the implementation of which is described above. Code words  512  that are applied to a shift register  514  are applied to the neural network as an input. The latest T+L code words, where T is the decoding delay, are stored in the shift register. Upon completing the decoding of a code word, the decoded code word is deleted from the register, the code words in the register are shifted one step forward and a new code word is adopted in the last storage location  516  of the register. Operationally, the shift register is connected to the inputs of the neural network neurons  500  to  510 . Channel data  517  from the channel estimation means is further applied to the neural network as an input. The channel data is applied to a buffer memory  518 . The neural network further comprises a buffer memory  520  whose input comprises the outputs of the neurons  500  to  510  and whose buffer memory output is operationally connected to the inputs  724  of the neural network neurons. The number of the neurons depends on the characteristics of the convolutional code to be decoded. 
     The outputs of the neural network neurons are thus operationally connected to the buffer memory  520 , from which the outputs are fed back  522  to the inputs  524  of the neurons. The neuron inputs comprise switching means  524  by which only the necessary code words and feedbacks are applied to each neuron, in accordance with a formula (as Formula (7) above) derived on the basis of the convolutional code to be decoded and the channel data. The switching means  524  can be implemented by means of a switching matrix or a discrete logic circuit. The bit to be decoded is obtained from the output of the calculation means  526  calculating the activation function. The calculation means  526  can be implemented by separate logic circuits or a processor and software. 
     The neural network decoder comprises a control unit  528 , to which is applied a clock signal  530  as an input from the timing information regenerator of the receiver, as is described in connection with FIG.  1 . The control unit takes care of the decoder timing, the control of the network stabilization time and controls the operation of decoding. 
     FIG. 5 b  illustrates a second preferred embodiment, in which several bit decisions of the adjacent neurons, i.e. neurons k . . . k+n, are extracted simultaneously from the neural network. In that case, the equipment comprises a plurality of calculation means  526   a ,  526   b . Also in that case, upon completing the decoding of the code words, n decoded code words are deleted from the register, the code words in the shift register  514  are shifted a corresponding number n of steps forward and n new code words are adopted in the register. 
     FIG. 6 illustrates yet another embodiment of the invention, in which decoding is performed by means of a plurality of parallel neural networks. In that case the code words and the channel data  600  are applied to two or more neural networks  602 ,  604  arranged in parallel. The outputs of the calculation means  606 ,  608  of the neural networks are applied to a decision unit  610  where the best estimate for a decoded bit is selected from the outputs of the parallel neural networks. The decision unit can be advantageously implemented by means of separate logic circuits or a processor and software. The decision on the best estimate can be implemented in a variety of ways. For instance, from the outputs of the parallel neural networks, it is possible to select the value that occurs at most outputs to be a decoded bit. The decoded bit can also be re-encoded and from the outputs of the parallel neural networks the value that is found correct by re-encoding is selected to be the decoded bit. For the sake of clarity, re-encoding is not shown in the figure but it can be implemented in manners known to the person skilled in the art. 
     The decoder of the invention can be readily constructed by semiconductor technology, since the neurons of the neural network are very similar to one another in structure, only the input couplings vary. Consequently, to design and implement even a large network does not involve a great amount of work. Testing of the completed circuit is also simple to implement. The solution can also be advantageously implemented as a VLSI circuit, which makes it fast. It should also be noted that even though the structure of the decoder of the invention is simple and easy to implement, its performance is close to the theoretical maximum. 
     Even though the invention is described above with reference to the example of the accompanying drawings, it is obvious that the invention is not restricted thereto, but it can be modified in variety of ways within the scope of the inventive idea disclosed in the attached claims.