Abstract:
The invention relates to a method and an arrangement for decoding a convolutionally encoded signal which comprises code words and the arrangement comprises a neural network which comprises a set of neurons comprising a set of inputs and an output. The received code words are applied to the inputs of the neurons, and the arrangement combines some of the inputs of the neuron in the neuron. In order to enable efficient decoding of the convolutional encoding, some of the output signals of the neural network neurons are fed back to the inputs of the neuron and the neuron multiplies at least some of the inputs of the neuron with one another before combining. The output signal of a predetermined neuron comprises an estimate of a decoded symbol.

Description:
FIELD OF THE INVENTION 
     The invention relates to a method and an arrangement for decoding in a receiver by a feedback neural network a signal that is convolutionally encoded in a transmitter. 
     BACKGROUND OF THE INVENTION 
     In telecommunications the signal path used for transmissions is known to cause interference of the communication. This occurs regardless of the physical form of the transmission path, i.e. whether the path is a radio link, an optical fiber or a copper cable. 
     In order to diminish the effects of interference caused by the transmission path, a digital signal is encoded so as to make the transmission connection more reliable. In that case interference-induced errors in the transmitted signal can be detected and, depending on the encoding method used, even corrected without retransmission. Conventional coding methods used in digital telecommunication include, for example, block coding and convolutional coding. In block coding the bits to be encoded are grouped into blocks and parity bits are added at the end of the blocks so that the correctness of the bits of the preceding block can be checked by means of the parity bits. 
     A typical coding method used in cellular radio applications is convolutional coding which is well suitable for a fading channel. In convolutional coding, the parity bits are placed among the data bits in such a way that the encoding is continuous. The data bits are not grouped into blocks nor are the parity bits connected to immediately preceding data bits, but they are distributed over the area of a bit group of a certain length, the number of bits being called the constraint length of a convolutional code. 
     Convolutional coding can be realized by a shift register. This is illustrated in FIG.  1 . Generally described, the shift register consists of L k-bit stages  100  to  104  and n linear function generators  106  to  112 . It is assumed here that the data to be encoded is binary. Data  114  is shifted into a shift register 116 k-bits at a time. The number of output 118 bits for each k-bit input sequence is n bits. The code rate is defined as R c =k/n. The parameter L is called the constraint length of the convolutional code. 
     The efficiency of convolutional coding depends on the code rate and constraint length used. A large constraint length enables good error correcting capability, but, on the other hand, decoding is then extremely complicated by known methods. 
     Convolutional coding is typically decoded by using a Viterbi algorithm having nearly an optimal performance. It is a drawback of the Viterbi algorithm that its complexity increases exponentially as the constraint length increases. This has set limits to the constraint lengths available for use. 
     Another known decoding method is sequential decoding disclosed in more detail in publication by J. G. Proakis, Digital Communications, 3 rd  edition, pp. 500-503. One of the drawbacks of this algorithm is that the decoding delay does not stay constant but varies. 
     Yet another known decoding method is what is known as a stack algorithm, disclosed in more detail in the above publication by J. G. Proakis, Digital Communications, 3 rd  edition, pp. 503-506. The performance of this algorithm is not as good as that of the Viterbi algorithm. 
     U.S. Pat. No. 5,548,684 discloses a method applying neural networks in the decoding of a convolutional code. The method according to the publication implements the Viterbi algorithm by a neural network. However, the performance of the solution is not adequate enough for practical applications. 
     The known Viterbi algorithm method has the best performance for decoding convolutional coding, but its practical implementation turns out extremely complicated as the constraint length increases. A difficult hardware implementation of the complicated Viterbi algorithm has set limits to the constraint lengths available for use. 
     BRIEF DESCRIPTION OF THE INVENTION 
     An object of the invention is thus to provide a method and an arrangement implementing the method so as to solve the above problems. This is achieved by a method of the invention for decoding a convolutionally encoded signal which comprises code words and in which method decoding is carried out by an artificial neural network which comprises a set of neurons comprising a set of inputs and an output, and that the received set of code words is conducted to the inputs of the neuron by a shift register, and in which neuron, some of the inputs of the neuron are combined. 
     The method of the invention is characterized in that some of the output signals of the neural network neurons are fed back to the inputs of each neuron and at least some of the inputs of the neuron are multiplied with one another before they are combined and that initial values are set for the neurons and the network is allowed to settle into a state of equilibrium, an estimate of the decoded symbol is directed from the output signal of a predetermined neuron to the output of the network after the network has reached the state of equilibrium, the set of code words residing in the shift register are updated, and the above four steps are repeated until the desired number of code words have been decoded. 
     The invention also relates to an arrangement for decoding a convolutionally encoded signal which comprises code words and which arrangement comprises a neural network which comprises a set of neurons comprising a set of inputs and an output, and the received code words are applied to the inputs of the neurons, and which arrangement comprises means for combining some of the inputs of the neuron in the neuron. 
     The arrangement of the invention is characterized in that some of the output signals of the neural network neurons are fed back to the inputs of the neuron and that the neuron comprises means for multiplying at least some of the inputs of the neuron with one another before the combining means and that the output signal of a predetermined neuron comprises an estimate of a decoded symbol. 
     The preferred embodiments of the invention are disclosed in the dependent claims. 
     In the solution of the invention, a convolutional code is decoded by a feedback neural network. The solution of the invention provides many advantages. The solution of the invention provides a performance nearly compatible with the Viterbi algorithm by means of dramatically simpler circuit implementation. In the solution of the invention, equally complicated circuit implementation provides a larger constraint length and thus better error correction than in connection with the Viterbi algorithm. 
     The neural network of the invention can be easily constructed by semiconductor technology, because apart from the couplings of the inputs, the structure of the neural network neurons is very much alike. Consequently, designing and implementing even a large network does not involve great amount of work. The solution can also be advantageously implemented as a VLSI circuit, and therefore it is fast. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the following, the invention will be described in more detail by means of preferred embodiments with reference to the accompanying drawings, in which 
     FIG. 1 shows the above-described example of a convolutional encoder, 
     FIG. 2 illustrates an example of a telecommunication system in which the solution of the invention can be applied, 
     FIG. 3 shows an example of a neuron designed by the method of the invention, 
     FIG. 4 shows an example of the couplings of a neuron in a neural network designed by the method of the invention, 
     FIG. 5 shows a second example of a neuron designed by the method of the invention, 
     FIGS. 6 a  and  6   b  show a second example of the couplings of a neuron in a neural network designed by the method of the invention, 
     FIGS. 7 a  and  7   b  illustrate an example of an implementation of a neural network of the invention, and 
     FIG. 8 illustrates an example of an implementation of a neuron in a neural network of the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The solution of the invention can be applied in any digital data transmission system in which a signal to be transmitted is encoded by convolutional coding. Examples of possible systems include cellular radio systems, radio links, fixed networks or optical networks. 
     FIG. 2 illustrates an example of a telecommunication system of the invention. The figure shows a transmitter  200 , a signal transmission path  202  and a receiver  204 . The receiver implements the operations of the invention. The signal transmission path may be a radio path, a copper cable or an optical fiber, for example. 
     In the transmitter, a data source  206  generates a signal  208  composed of bits. An error correcting code can be added to the signal  208  of the data source by a known forward error correcting (FEC) method, if necessary. This is not shown in the figure. The signal  208  is applied to an encoder  210  carrying out convolutional coding by the desired parameters (constraint length and code rate). The structure of the encoder may be similar to that shown in FIG. 1, for example. The encoded signal may be expressed as code words whose length depends on the code used. The encoded signal is applied to a modulator  212  carrying out the desired modulation. The modulated signal is applied further to output stages  214  and a channel adapter  216  of the transmitter, which are systemependent components. The output stage  214  may be a radio frequency amplifier and a filter, for example. The channel adapter  216  may be an antenna or an electricavoptoconverter, for example. 
     An output signal  218  of the transmitter propagates through the transmission path  202 , i.e. a channel, to the receiver  204 . The receiver comprises a channel adapter  220  and a receiver pre-stage  222 , which are system-dependent components. The prestage  222  may comprise a radio frequency amplifier and a filter, for example. The channel adapter  220  may comprise an antenna or an opto/electrical converter, for example. The signal is applied from the pre-stage  222  further to a demodulator  224  from which a baseband bit stream  226 , which may be complex and comprise separate I- and Q-branch bits, is typically received. Timing information is derived from the received signal in a regenerator  228  by a known method. This timing information is used in demodulation. The receiver further comprises a control unit  230  which can be advantageously implemented by a processor. The control unit  230  controls the operation of the receiver. Information on the timing is also applied to the control unit. 
     In other words, the signal  226  coming from the demodulator  224  comprises the demodulated bits which can be presented as code words. The code words are applied to a decoder  232  which is implemented in the receiver of the invention by a neural network. Convolutional coding is decoded in the decoder and an output signal  324  of the decoder corresponds to the original signal  208 . If an error correcting code was used in the transmitter, the error correcting code is decoded at this stage. This is not shown in the figure. 
     Let us next study the method of the invention for decoding a convolutional code. Generally, the aim of decoding is to find a bit sequence B which minimizes the function                min   B            ∑     s   =   0     T                     r        (     t   +     s                 d                 t       )       -     γ        (     B        (     t   +     s                 d                 t       )       )              2                     =:                       min   B          f        (   B   )                     (   1   )                                
     where r (t+sdt) is a received code word at a time instant t+sdt, dt is a sampling interval, γ is an encoder function and B(t+sdt) is a vector with decoded bits as its components. 
     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)], bε{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, is generated in the signal. Let us indicate a noisy code word received at a time instant s by r(s). Let us assume that white Gaussian noise is involved. 
     Let us study here the generation of a neural network of the invention by way of 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 I can be written as 
     
       
         γ(B(s))=[γ 1 (B(s)), γ 2 (B(s))], 
       
     
     where              γ   i          (     B        (   s   )       )       =       ∏     i   =   1     L              b        (     s   +   1   -   i     )         S     j   ,   i              (     -   1     )            (     -   1     )       R     j   ,   i               ,                          
     and g j,i s are the elements of the G matrix. Now, as in this example L=3, the encoder is thus of the form 
     
       
         γ(B(s))=[−b(s)b(s−2), b(s)b(s−1)b(s−2)] 
       
     
     and the received noisy code word is r(s)=[r 1 (s) r 2 (s))]. 
     When a partial derivative with respect to b(k) is derived from Formula (1), we obtain                        ∂     f        (   B   )           ∂     b        (   k   )           =                      r   1          (   k   )            b        (     k   -   2     )         -         r   2          (   k   )            b        (     k   -   1     )            b        (     k   -   2     )                           -                  r   2          (     k   +   1     )              b        (     k   +   1     )            b        (     k   -   1     )         +         r   1          (     k   +   2     )            b        (     k   +   2     )                         -                  r   2          (     k   +   2     )              b        (     k   +   1     )            b        (     k   +   2     )         +     5          b        (   k   )       .                     (   2   )                                
     When a gradient method is used, b(k) is updated as follows:                b        (   k   )       =       b        (   k   )       -     α            ∂     f        (   B   )           ∂     b        (   k   )           .                 (   3   )                                
     Furthermore, by setting α=⅕ and assuming that b(k) obtains the value −1 or 1, the following equivalence is true for all the values k=0, . . . , T 
     
       
         b(k)=sign(−r 1 (k)b(k−2)+r 2 (k)b(k−1)b(k−2) +r 2 (k+1)b(k+1)b(k−1)−r 1 (k+2)b(k+2) +r 2 (k+2)b(k+1)b(k+2).  (4) 
       
     
     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 (4) and this is repeated until no changes occur in the bits, i.e. the network is stabilized. It should be noted here 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 so that all the neurons k are updated simultaneously. 
     The iteration according to Formula (4) can 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 I l =r(I), where I l =[I l,1 , I l,2 ] are the external inputs coming to the neuron, the state of the k th  neuron can be presented as: 
     
       
         S k =ƒ α (−I k,1 S k−2 +I k,2 S k−1 S k−2 +I k+1,2 S k+1 S k−1 −I k+2,1 S k+2 +I k+2,2 S k+1 S k+2 ),  (5) 
       
     
     where ƒ α  is an activation function, typically a sigmoidal function or a hard limiter. In Formula (4), the signum function ƒ α (x)=sign(x) is used. 
     FIG. 3 illustrates a neuron according to Formula (5). The state S k  of the neuron appears at the output of the neuron. Code words to be decoded are applied to the neuron as an input  300 , the code words being in this example composed of two bits. 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. In accordance with Formula (5), bits I k,1 , I k,2 , I k+1,2  and I k+2,2  are applied to the neuron as an input, Furthermore, feedback outputs of the neurons of the other neural networks, i.e. S k−2 , S k−1 , S k+1 , and S k+2 , are applied to the neuron as an input  302 . The output of each neuron thus comprises one decoded bit. In other words, the two bits I k,1 , I k,2  of the code word to be decoded, the second bits I k+1,2  and I k+2,2  of the following code words and the output values of the two preceding and the two following neurons are applied in accordance with equation 5 to the neuron as an input. 
     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 absence of this feedback in the above derivation of Formula (5) is caused by a coefficient α whose value ⅕ extracts the term 5b(k) from Formula (2). The inputs of the neuron are multiplied with one another in accordance with Formula (5). This is illustrated by dots at the intersection of lines. White dots  304  to  314  denote the multiplication of the inputs and black dots  316  to  318  denote the multiplication of the inputs and the change of the sign of the product. The multiplied signals are summed  320  and applied to an activation function  322  whose output S k    324  is the output value of the neuron. 
     In other words, the activation function can be either a function that generates a hard decision or a soft decision. If the result is a hard function, the outputs of the neuron may thus obtain the value −1 or 1. If the result is a soft decision, the output of the neuron may be a floating point number. Correspondingly, if the demodulator  224  generates soft bit decisions, the input  300  of the neuron comprises floating point numbers, and if the demodulator generates hard bit decisions, the input  300  of the neuron comprises bits. If both of the inputs of the neuron comprise bits, the multiplication between the inputs may be implemented in a simple manner by digital technology. 
     Since the derived neural network is what is called an optimizing neural network, it may be caught in a local minimum. In order to avoid this, noise, whose variance is reduced during stabilization, is added in a preferred embodiment of the invention to an incoming signal in neurons. In that case, Formula (5) is of the form 
     
       
         S k =ƒ α (−I k,1 S k−2 +I k,2 S k−1 S k−2 +I k+1,2 S k+1 S k−1 −I k+2,1 S k+2 +I k+2,2 S k+1 S k+2 +AWGN).  (6) 
       
     
     In decoding, the following steps are generally carried out for each received code word: 
     1. Setting S −1  and S −2  according to previous decisions. The received code words r(t), . . . , r(t+Tdt) are set to inputs I 0 , . . . , I T . 
     2. Initializing S(i), i=0, . . . , T. 
     3. Updating neuron k according to Formula (6) for each k=0, . . . , T. 
     4. Reducing the variance of the added noise. If the required 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. 4 illustrates couplings associated with a single neuron k of a neural network which is designed for decoding code rate ½ and constraint length  3 . Demodulated code words  300  and outputs of neurons  400 ,  402 ,  406  and  408  are applied to the single neuron as an input. The output of the neuron is a value of an activation function  410 , the value being a decoded symbol. The neural network is initialized in a manner such that the previously made bit decisions become the states of neurons −2 and −1. As the states of neurons, 0, . . . T, +1 or −1 is randomly set. Next, the network is allowed to stabilize. The decoded bit is the output of a neuron  404 , i.e. neuron 0, or if more than one bit is decoded at a time, the outputs of neurons 0, . . . , N. 
     Stabilization time of the network can be determined either by allowing the iterations to continue until the bit at the output does not vary or by carrying out a predetermined number of iteration rounds. 
     The following formula can be derived in the above manner for a convolutional code with code rate ½ and constraint length L=9 in order to generate a neural network and neurons: 
     
       
         S k =ƒ α (−I k,1 S k−2 S k−3 S k−5 S k−6 S k−7 S k−8 −I k,2 S k−1 S k−3 S k−4 S k−7 S k−8 + 
       
     
     
       
         I k,3 S k−1 S k−2 S k−5 S k−8 −I k+1,2 S k+1 S k−2 S k−3 S k−6 S k−7 + 
       
     
     
       
         I k+1,3 S k+1 S k−1 S k−4 S k−7 +I k+2,1 S k+2 S k−1 S k−3 S k−4 S k−5 S k−6 + 
       
     
     
       
         I k+2,3 S k+2 S k+1 S k−3 S k−6 +I k+3,1 S k+3 S k+1 S k−2 S k−3 S k−4 S k−5 − 
       
     
     
       
         I k+3,2 S k+3 S k+2 S k−1 S k−4 S k−5 −I k+4,2 S k+4 S k+3 S k+1 S k−3 S k−4 + 
       
     
     
       
         I k+5,1 S k+5 S k+3 S k+2 S k−1 S k−2 S k−3 +I k+5,3 S k+5 S k+4 S k+3 S k−3 + 
       
     
     
       
         I k+6,1 S k+6 S k+4 S k+3 S k+1 S k−1 S k−2 +I k+7,1 S k+7 S k+5 S k+4 S k+2 S k+1 S k−1 − 
       
     
     
       
         I k+7,2 S k+7 S k+6 S k+4 S k+3 S k−1 +I k+8,1 S k+8 S k+6 S k+5 S k+3 S k+2 S k−1 − 
       
     
     
       
         I k+8,2 S k+8 S k+7 S k+5 S k+4 S k−1 +I k+8,3 S k+8 S k+7 S k+6 S k+3 +AWGN.  (7) 
       
     
     The structure of a neuron according to the above formula is illustrated in FIG.  5 . Inputs  500  of the neuron comprise the received code words and inputs  502  comprise the feedbacks from the other neurons of the neural network. Multiplications of the inputs and changes of the signs take place according to Formula (7) and in summing  504  noise is added whose variance is reduced during stabilization. The couplings of a single neuron k of a corresponding neural network are illustrated in FIGS. 6 a  and  6   b , in which each neuron  600  to  632  is similar to that presented in FIG.  5 . 
     Besides, or instead of, the addition of noise, other methods can also be used so as to avoid being caught in a local minimum. The number of iteration rounds to be carried out can be increased. Another alternative is to use several parallel neural networks. When each neural network is stabilized, the best bit decision can be selected from the output of the networks. The selection can be carried out by majority decision, for example, selecting the bit decision which appears most frequently at the output of the parallel neural networks. The decoding result may also be re-decoded and the obtained result may be compared with the received code word, i.e. a solution may be selected which minimizes the function                1     T   b              ∑     s   =   0       T   b                       r        (   s   )       -       r     r                 c            (   s   )              2     .               (   8   )                                
     Decoding can also be accelerated in a manner such that several bit decisions of the adjacent neurons, i.e. neurons S 0 , . . . S N  are simultaneously extracted from the neural network. When the following bits are decoded, the states of neurons S −L+1 , . . . , S −1  have to be initialized into the values obtained above. 
     The decoding method of the invention can also be applied when a code to be decoded is a punctured code. 
     Let us next study the complexity of the solution of the invention mainly from the point of view of implementation. When the constraint length L increases, more neurons are needed in the neural network, whereby stabilizing time increases and hence results in an increase in the number of multiplications, The complexity of a Viterbi decoder is known to increase exponentially as the constraint length L increases. However, an increase in the complexity of a decoder implemented by the neural network of the invention is considerably slower. When the constraint length is L, each neuron of the neural network is coupled to L−1 preceding and L−1 following neurons and L inputs. If it is assumed that the decoding delay is 5L, as it is often the case, the decoder requires 5L neurons and the number of connections is thus 
     
       
         (2(L−1)+Ln)(5L)=10L 2 +5nL 2 −10L, 
       
     
     where n is the number of generators. In the above examples n=2. The number of multiplications to be performed in one neuron depends on the code generator used, but it is ≦O(nL 2 ). The number of multiplications to be carried out during one iteration round, when each neuron is updated once, is 5LnL 2 =O(nL 3 ). This shows how an increase in complexity in the solution of the invention is considerably slower than in connection with the Viterbi algorithm as L increases. 
     Let us next study the structure of a decoder of the invention from the point of view of implementation. The structure of a neural network of the invention is illustrated in FIG. 7 a . The neural network comprises a set of neurons  700  to  710  whose implementation is examined later on. Code words  712  are applied to the neural network as an input and to a shift register  714 . The shift register has the last T+L code words stored therein, where T denotes the decoding delay. Each time a code word has been decoded, the decoded code word is deleted from the register, the code words in the shift register are shifted forward by one and a new code word is included in a last memory location  716  of the register. The shift register is operationally connected to the inputs of the neurons  700  to  710  of the neural network. The neural network further comprises a buffer memory  720  having the outputs of the neurons  700  to  710  as an input and having its buffer memory output operationally connected to inputs  718  of the neurons of the neural network. The number of neurons depends on the properties of the convolutional code to be decoded. 
     The outputs of the neurons of the neural network are thus operationally connected to the buffer memory  720 , from which the outputs are fed back  722  to the inputs  718  of the neurons. The input of the neurons comprises switching means  718  by means of which only the necessary code words and feedbacks are applied according to the derived formula (such as Formulas (6) and (7) presented above) to each neuron on the basis of the convolutional code to be decoded. The switching means  718  can be implemented by a switching matrix or discrete logic circuits. The bit to be each time decoded is derived from the output of a calculation means  724  which calculates the activation function. The calculation means  724  can be implemented by a discrete logic circuits or a processor. 
     A neural network decoder comprises a control unit  726 . A clock signal  728  is applied to the control unit from the regenerator of the timing information of the receiver, as described in connection with FIG.  2 . The control unit handles timing of the decoder, the control of the network stabilizing time and the control unit controls the decoding operation. 
     FIG. 7 b  illustrates another preferred embodiment in which several bit decisions are extracted simultaneously from adjacent neurons, i.e. neurons k . . . k+n, from the neural network. In that case, each time the code words have been decoded, n decoded code words are also deleted from the register, a corresponding n number of code words are shifted forward in the shift register  714  and n new code words are included in the register. 
     FIG. 8 illustrates the structure of a neuron of a neural network of the invention. The output of the neuron comprises the state S k  of the neuron. The code words to be decoded are applied to the neuron as an input  800 , the code words comprising bits. The number of bits in each code word depends on the code rate of the code used. Furthermore, feedback outputs of the other neurons of the neural network are applied to the neuron as an input  802 . 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. However, feedback to itself is also possible if necessary. 
     The inputs of the neuron are multiplied with one another in a matrix  804 . The couplings of the matrix are defined by the convolutional code used, and the formula corresponding to the coupling can be derived as illustrated in the above examples. The change of sign may or may not be involved in the multiplication of the inputs. The multiplied signals are applied to a summer  806  summing the signals. The summed signal is applied further to a calculation means  808  which calculates an activation function and whose output S k    810  is the output value of the neuron. The calculation means  724  can be implemented by a discrete logic circuits or a processor. 
     A function which generates either a hard decision or a soft decision can thus be used as an activation function. If the result is a hard decision, the outputs of the neuron may obtain the value −1 or 1. If the result is a soft decision, the output of the neuron may be a floating point number. Correspondingly, if the demodulator of the receiver generates soft bit decisions, the input  800  of the neuron comprises floating point numbers, and if the demodulator generates hard bit decisions, the input  800  of the neuron comprises bits. If both of the inputs of the neuron comprise bits, the multiplication between the inputs can be implemented in a simple manner by digital technology. 
     In a preferred embodiment of the invention, the neuron comprises a noise generator  812 . Noise generated in the noise generator is applied to the summer  806  in which the noise is added to a sum signal. The variance of the noise to be generated is reduced during stabilization of the neural network, as described above. Gaussian noise or binary noise may be involved, of which binary noise is easier to implement, but a suitable number of Gaussian noise samples can however be stored in a memory element, and this noise can be reused. The generation of noise can be implemented in manners known to those skilled in the art. 
     The decoder of the invention can be constructed in a simple manner by semiconductor technology, because apart from the couplings of the inputs, the structure of the neural network neurons is very much alike. Consequently, designing and implementing even a large network does not involve great amount of work. Testing the complete circuit is also easy to implement. The solution can also be advantageously implemented as a VLSI circuit, and therefore it is fast. It should also be noted that although the structure of the decoder of the invention is simple and easy to implement, it has nearly a theoretically maximum performance. 
     Although the invention is described above with reference to the example according to the accompanying drawings, it is obvious that the invention is not restricted thereto, but it can be modified in many ways within the inventive idea disclosed in the attached claims.