Patent Publication Number: US-2021175912-A1

Title: Communication appratus and decoding method

Description:
TECHNICAL FIELD 
     The present disclosure relates to a communication apparatus and a decoding method. 
     BACKGROUND ART 
     There has been a significant research effort made in the area of radio-frequency (RF) transceivers using novel hardware implementations that rely on full digitalization of the RF data path. The motivation for this research is to bring the digital-to-analog interface in an RF transmitter as close as possible to the antenna. This is because designing a digital part using digital CMOS circuits is more cost effective and easily reconfigurable as compared to designing RF and analog parts. State-of-the-art all-digital transmitters typically use baseband DSM (Delta-Sigma Modulator) to digitally upconvert the baseband signals to RF signals. Baseband pulse modulation enables the use of field-programmable gate array (FPGA) devices for implementing a radio-frequency device, providing additional flexibility due to the FPGA inherent reconfigurability. FPGA&#39;s logic capacity, resource diversity, and dedicated high-speed I/O transceivers can be used in the development of agile all-digital transmitters. 
     CITATION LIST 
     Patent Literature 
     
         
         PTL 1: Erwin Janssen, and Derk Reefman, Generating Bit-streams with higher compression gains, US 2007/0018857 A1 
       
    
     Non Patent Literature 
     
         
         NPTL 1: S. R. Norsworthy, R. Schreier, and G. C. Temes, Delta-Sigma Data Converters—Theory, Design and Simulation. IEEE Circuits and Systems Society, 1996. 
         NPTL 2: Ido Tal, and Alexander Vardy, List Decoding of Polar Codes, IEEE Transactions of Information Theory, Volume 61, Issue 5, 2015. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
       FIG. 1  illustrates an example of DSM  10  for an all-digital transmitter. The objective of using DSM is to generate a high-speed 1-bit signal that contains information in the transmit band defined by the targeted standard. One of the potential advantages of a 1-bit coded digital RF signal is the ability to use class-S switched power amplifiers having a very high efficiency.  FIG. 2  depicts output of a typical 1-bit 1 st  order DSM. The comparator  11  for the 1-bit 1 st  order DSM works as: 
     
       
         
           
             
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       FIG. 3  illustrates an example bit sequence of the output of DSM at some n-th baseband sample x(n). 
       FIG. 3  illustrates output of a 1-bit 1 st  order DSM where the quantizer is replaced by addition of error function, e(n). This error function is defined as: 
         e ( n )= p ( n )− u ( n )
 
     The transfer function of a typical DSM in z-domain is given by: 
         P ( z )= STF ( z ) X ( z )+ NTF ( z ) E ( z ) 
     where X(z), P(z) and E(z) are the transfer functions of x(n), p(n) and e(n), respectively. The main asset of the DSM is the possibility of being able to move quantization noise e(n) outside the band of interest, which is called noise shaping. This noise shaping is accomplished by designing appropriate noise shaping function NTF(z). For example, in 1 st  order DSM, NTF(z)=1−z −1 . The performance of a DSM mainly depends on its noise-shaping filter order and its oversampling ratio (OSR), which is the ratio of the sampling frequency to twice the signal bandwidth. For more details on DSM, please refer to NPTL 1. 
     In DSM  10  shown in  FIG. 1 , each bit in the 1-bit coded digital RF signal output from DSM  10  is evaluated based on instantaneous values of u(n). This is visible from the comparator equation as shown below: 
     
       
         
           
             
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     This is a greedy approach whereby the focus is on minimization of quantization error e(n) in n-th baseband sample only. However, this greedy approach doesn&#39;t guarantee the following objective: 
     
       
         
           
             
               
                 
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     where N is the total number of samples of baseband signal x(n). The expression (1) is the summation of all quantization noise across all N samples of baseband signal x(n). The presence of quantization noise leads to a higher noise floor and bad ACLR (Adjacent Channel Leakage Ratio) performance. 
     The DSM mentioned in NPTL 1, as shown in  FIG. 1 , tries to predict the bit sequence that best quantizes the input baseband signal x(n). The DSM uses just the instantaneous input x(n) for this prediction purpose. A correct prediction will result in minimization of the feedback error f(n). A bad prediction will result in accumulation of more and more prediction error. As the input baseband signal x(n) is not known apriori, the output bit stream p(n) may not always be the best possible output. 
     In view of the above, one of the objects to be attained by embodiments disclosed herein is to provide an apparatus and a method that contribute to decrease the quantization noise. It should be noted that this object is merely one of the objects to be attained by the embodiments disclosed herein. Other objects or problems and novel features will be apparent from the following description and the accompanying drawings. 
     Solution to Problem 
     In a first aspect, a communication apparatus includes: a path metric update unit configured to update the path metric of each path at each iteration; a path creator configured to split an existing path into two paths, with one path formed by appending 1 to existing path and, another path formed by appending −1 to the existing path; a path metric sort unit configured to sort the paths in the ascending order of their path metric values; a path pruning unit configured to choose those L paths which have lower path metric values; a select path unit configured to choose a path with the lowest path metric among all available paths at the end of all the baseband samples and the selected path serving as the output bit sequence; a feedback selector configured to select the feedback corresponding to the feedback associated with paths selected in path pruning unit; and a computation unit configured to process the feedback from the feedback selector and the input baseband signal, and to give feedback for next time instant as the output. 
     In a second aspect, a decoding method comprising: updating a path metric of each path at each iteration; splitting an existing path into two paths, with one path being formed by appending 1 to the existing path and, the other path being formed by appending −1 to the existing path; sorting the paths in the ascending order of their path metric values; choosing L (L is an integer more than 1) paths which have lower path metric values; selecting a path with lowest path metric among all available paths at the end of all the baseband samples and the selected path serving as the output bit sequence; selecting the feedback corresponding to the feedback associated with paths selected by path pruning; processing the selected feedback and the input baseband signal to give feedback for next time instant as the output. 
     Advantageous Effects of Invention 
     According to the above-described aspects, it is possible to provide a communication apparatus and a decoding method that contribute to decrease the quantization noise. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram schematically representing a basic configuration of a communication apparatus. 
         FIG. 2  schematically illustrates a timing diagram for a path in 1-bit DSM. 
         FIG. 3  illustrates the mechanism behind a path splitting procedure. 
         FIG. 4  illustrates the mechanism behind the path splitting procedure. 
         FIG. 5  schematically illustrates a configuration of the communication apparatus according to the first exemplary embodiment. 
         FIG. 6  illustrates the timing diagram for the output of the proposed first exemplary embodiment. 
         FIG. 7  schematically illustrates a configuration of the communication apparatus according to the second exemplary embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Exemplary embodiments of present disclosure will be described below with reference to the drawings. In the drawings, the same elements are denoted by the same reference numerals, and thus repeated descriptions are omitted as needed. 
     In order to mitigate the above problem, we incorporate the features of List Decoding, as provided in reference NPTL 2. This will help us to choose the output p(n) that minimizes sum of the all quantization error across all samples of input baseband signal x(n) as stated in Equation (1). Under List decoding, after n-th sample, the system maintains candidates of bit sequences of length n that will closely approximate the complete bit stream that minimizes Equation (1). 
     First Exemplary Embodiment 
     A communication system apparatus according to a first exemplary embodiment will be described.  FIG. 5  is a block diagram schematically illustrating a basic configuration of the communication apparatus  50  according to the first exemplary embodiment. The communication apparatus  50  includes a path creator  52 , a path metric update unit  51 , a path metric sort unit  53 , a path pruning unit  54 , a select path unit  55 , a feedback selector  56 , and a computation unit  57 . 
     Definition of Path: 
     An n-dimensional path l n  is the sequence of output of 1-bit DSM till n-th sample such that 
           n   ={p (0), p (1), . . . , P ( n )} 
     where p(0), p(1), . . . p(n) are the output of the 1-bit DSM as shown in  FIG. 1  at time 0, 1, . . . , n, respectively, when the input baseband samples are x(0), x(1), . . . , x(n), respectively. p(n) is an output of the comparator  11  illustrated in  FIG. 1  and indicates “1” or “−1”. The comparator  11  compares u(n) with a threshold, and output a comparison result as p(n). The input signal x(n) is input to the adder  12 . The adder  12  adds x(n) to f(n−1), and outputs it as u(n). The adder  13  adds u(n) and −p(n), and output it as f(n). For example, in  FIG. 2 , we provide a snapshot of a path in the 1-bit DSM at n=100. The path can be written as follows: 
           100 ={1,−1,−1,1,−1, . . . ,1,1,−1,1}
 
     Path Metric (PM): 
     We define ε(n)=x(n)−p(n). 
     Consider a function PM(   0 ) initialization as follows 
       PM(   0 ) 
       PM(   1 )=|ε(1)| 2  
 
       PM(   n+1 )=PM(   n )+|ε( n+ 1)| 2  
 
     where,    1 ={p(1)} 
           n   ={p (0), p (1), . . . , p ( n )} 
         l   n+1   ={p (0), p (1), . . . , p ( n+ 1)} 
     Note that path    n+1  at time (n+1) is obtained by appending, p(n+1) to the path    n . Thus, PM(⋅) is iteratively updated with value of PM(   n+1 ) obtained by adding square of ε(n+1) to the path metric of the path    n , that is, PM(   n ). 
     Some notations are as follows: 
         n−1 : collection of all paths at the end of processing in (n−1)-th time instance 
         n : collection of all paths at the end of processing in n-th time instance 
     Card(   n ): cardinality of the collection    n    
     L: maximum number of paths that is to be stored at the end of processing in each time instant due to FPGA memory constraint. 
     At n-th instant, the path creator  52  receives as input the list of all paths that were selected after path pruning in previous iteration, i.e,    n−1 , from path pruning unit  54 . For each path    n−1 ϵ   n−1 , the path creator  52  creates two paths    n   α  and    n   β , such that    n   α ={   n−1 ,−1} and    n   β ={   n−1 ,1}. Now,    n   α ,   n   β ϵ   n . Note that Card(   n )=2L. An example of path splitting is given in  FIG. 3  and  FIG. 4  for n=101 and n=102, respectively. Note that    101   1 ={   100 ,1} and    101   2 ={   100 ,−1}. Also,    102   1 ={   101   1 ,1},    102   2 ={   101   1 ,−1},    102   3 ={   101   1 ,1} and    102   4 ={   101   2 ,−1}. 
     At a-th instant, the path metric update unit  51  receives as input the list of p metrics of all paths that were selected after path pruning in previous iteration. i.e.,    n−1 . More specifically, the input to path metric update unit  51  at time n is {PM(   n−1   1 ), PM(   n−1   2 ), . . . , PM(   n−1   Card(       n−1     ) )}. In n-th instant, the path metric update unit  51  updates the path metrics of the paths    n   α  and    n   β  as: 
     
       
         
           
             
               
                 
                   
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     At n-th instar the path metric sort unit  53  sorts the paths in    n  in an ascending order as per the math metric. That is, after sorting, if    n ={   n   1 ,    n   2 , . . . ,  }, then, PM(   n   1 )≤PM(   n   2 )≤ . . . PM( ). The path metric sort unit  53  outputs the result of sort to the path pruning unit  54 . Because of PPG A memory constraint, the path pruning unit  54  selects L paths identified as    n   1 ,    n   2 , . . . ,    n   L , where PM(   n   1 )≤PM(   n   2 )≤ . . . PM(   n   L ) The path pruning unit  54  deletes the rest of the L paths    n   L+1 ,    n   L+2 , . . . ,  . The path metric values of the L selected paths in the n-th time instant, that is, PM(   n   1 ), PM(   n   2 ), . . . , PM(   n   L ), are used in the next time instant (n+1) at the path metric update unit  51 . The path metric values of the delete L paths are PM(   n   L+1 ) to PM( ). 
     At n-th time instant, path pruning unit  54  selects unit L paths out of 2L paths for pruning. This selection of L paths is done using the result of sorting at the path metric sort unit  53 . The path metric sort unit  53  informs the path pruning unit  54  of the L paths that have been of selected. That is, path pruning unit  54  selects the paths identified as    n   1 ,    n   2 , . . . ,    n   L  according to the result of sorting in path metric sort unit  53 . The rest of the paths are deleted. The selected L paths,    n   1 , L n   2 , . . . ,    n   L , are sent hack to the path creator  52  so as to be used in the next time instant (n+1). 
     As described above, the Path pruning unit  54  outputs L (L is an integer more than 1) paths to the path creators  52 . Then, the Path creator  52  creates 2L paths by splitting each of the L paths into two paths, and thus functions as a path splitting unit. The Path Metric updates unit  51  updates the path metrics of the 2L paths. The Path metric sort unit  53  arranges the 2L paths in ascending order of the path metric. The path pruning unit  54  selects new L paths based on the path metric values. That is, the path pruning unit  54  chooses the L paths having the lower path metric values out of 2L paths. The Path pruning unit  54  deletes L paths having the higher path metric values. That is, the path pruning unit  54  retains half of the created paths and deletes the other half of the created paths. 
     The path metric sort unit  53  and the path pruning unit  54  is different from the implementation in PTL 1. In PTL 1, at each time instant, path metrics of all the paths with the same newest L bits are compared. It is obvious that communication apparatus  50  can obtain a multiple groups of paths. In each group, the L newest bits are the same. For path pruning, in each group, the paths with lower path metric are retained and the rest are thrown away. This process gives rise to suboptimal search for the path with the minimum path metric. However, Sort and Pruning procedure described in this embodiment is global in its approach. 
     At n-th instant, the input to the feedback selector  56  are feedback f(n) in each of the paths    n   1,α ,    n   1,β ,    n   2,α ,    n   2,β , . . . ,    α ,    β , where    n   1,α ={   n   1 ,1},    n   1,β ={   n   1 ,−1},    n   2,α ={   n   2 ,1}, l n   2,β ={   n   2 ,−1}, . . . ,    α ={ ,1},    β ={ ,−1}. Using the result of sorting in the path metric sort unit  53 , the feedback selector  56  selects those feedbacks  10 ) corresponding to the paths    n   1 ,    n   2 , . . . ,    n   L . The feedbacks of the selected paths are used in the next time instant (n+1) in the computational unit  57 . 
     At n-th instant, the computation unit  57  receive an input signal x(n) which is the n-th baseband sample of a baseband signal. The computation unit  57  include L sub-units  58  to  510 . Each of the sub-units  58  to  510  includes three adders. For example, the sub-unit  58  includes the adders  58   a  to  58   c . The adder  58   a  adds x(n) to f(n−1), and outputs it to the adders  58   b  and  58   c . The adder  58   b  adds the output from adder  58   a  to “1”. The adder  58   c  adds the output from the adder  58   a  to “−1”. 
     The computational unit  57  is configured red to add the input signal x(n) and the feedback corresponding to the paths    n−1   1 ,    n−1   2 , . . . ,    n−1   L  obtained from the feedback selector  56  in previous time instant n−1. The computational unit  57  has L parallel sub-units with each sub-unit containing three adders. In each sub-unit, the baseband sample is added with the corresponding feedback to get the modified signal. After that, 1 and −1 is subtracted from the modified signal to obtain feedbacks fin) corresponding to the paths    n   1,α ,    n   1,β ,    n   2,α , l n   2,β , . . . ,    α ,    β . The feedback corresponding to the above paths are then sent to feedback selector  56 . 
     After the last sample of baseband signal, x(N) has been quantized at N-th time instant, the select path unit  55  selects the path with the lowest path metric. 
     To accomplish this, it takes as an input all paths obtained alter path splitting in the path creator  52 , that is,    n   1 ,    n   2 , . . . ,  . Using the output of the path metric sort unit  53 , the select path unit  55  selects the path with the lowest path metric value, that is,    n   1 , where PM(   n   1 )≤PM(   n   2 )≤ . . . PM( ) Now, the selected path    n   1  is the output hit stream. 
     In comparison to PLT 1, our implementation of the path metric update unit  51 , the path metric sort unit  53 , the Path creator  52 , the path pruning unit  54  and the associated components are disjoint from the feedback line. In FIG. 4 of PLT 1, the Path Sort and the path metric update is done along the main body. This disjoint nature adds flexibility to the DSM structure. 
       FIG. 6  illustrates the timing diagram of output of the select path unit  55 . The timing diagram shows that there is a latency of N time instants in the output of the proposed list-decoded DSM. This is due to the fact that selection of a path with the lowest path metric is done at the select path unit  55  at the end of each N time instants. 
     Further, the communication apparatus  50  includes a bandpass filter through which the output bitstream (output bit sequence). Then, the communication apparatus  50  modulates the output bitstream with a carrier wave, and then transmit it as RF signal to a receiver. Therefore, it is possible to decrease the quantization noise and thus, effectively improve ACLR of an output bit stream and lower the noise floor. 
     Second Exemplary Embodiment 
     A communication system apparatus according to a second exemplary embodiment will be described.  FIG. 7  is a block diagram schematically illustrating a basic configuration of the communication apparatus  70  according to the second exemplary embodiment. The communication apparatus  70  includes a path creator  72 , a path metric update unit  73 , a path metric sort unit  75 , a path pruning unit  74 , a select path unit  718 , a feedback selector  76 , a computation unit  710 . The communication apparatus  70  includes a computation unit  79 , switch  77 , switch  78 , switch  717  and switch controller  71 . The path creator  72 , the path metric update unit  73 , the path metric sort unit  74 , the path pruning unit  74  and the select path unit  718  correspond to the path creator  52 , the path metric update unit  51 , the path metric sort unit  53 , the path pruning unit  54  and the select path unit  55 , respectively, and the explanation thereof may be omitted. 
     The switch controller  71  chooses Mode 1 when it wants to use the computation unit  710  for computation of feedback (n). The switch controller  71  chooses Mode 2 when it wants to use the computation unit  79  for computation of feedback f(n). Applying list decoding at every time instant is cumbersome. So, an alternative is to define the switch controller  71  that selects the computation unit  710  most of the times. Note that computation unit  710  includes just many parallel units of conventional 1-bit DSM involving comparators. When the switch controller  71  selects the computation unit  710 , the communication apparatus  70  does not execute the list decoding. The computation unit  79  is selected only intermittently. When the switch controller  71  selects the computation unit  79 , the communication apparatus  70  executes the list decoding. 
     Suppose the switch controller  71  is in Mode 1 in n-th time instant. The feedback f(n−1) is sent to the computation unit  710  though a line  726 . The computation unit  710  includes a plurality of sub-units  711  to  713 . Each of the sub-units  711  to  713  includes a comparator  11  and an adder  12  like a structure shown in  FIG. 1 . In each of parallel sub-unit  711  to  713  in the computation unit  710 , the adder  12  adds the input baseband signal x(n) to the feedback f(n−1) of the corresponding path. 
     For example, in computation unit  711  the adder  12  adds the feedback f(n−1)ϵ   n−1   1  in to x(n). Subsequently; the computational unit  711  quantizes the output of the above summation using a comparator  11  that gives 1 or −1 as the output. This quantized output is then sent to the path creator  72  and the path metric update unit  73  via the switch  717 . The feedback is generated by determining the quantization error f(n) which is sent to the switch  78 . 
     Suppose the switch controller  71  is in Mode 2 in n-th time instant. The feedback f(n−1) is sent to the computation unit  79  though a line  724 . The computation unit  79  includes a plurality of sub-units  714  to  716 . Each of the sub-units  714  to  716  includes three adders like the sub-unit  58  as shown in  FIG. 5 . For example, the sub-unit  714  includes the adders  714   a  to  714   c . In each parallel sub-unit  714  to  716  in computation unit  79 , the adder adds the input baseband signal x(n) to the feedback f(n−1) of the corresponding path. 
     For example, in the computational unit  714 , the adder  714   a  adds the feedback f(n−1)ϵ   n−1   1  to x(n). Subsequently, the adders  714   b  and  714   c  add this above summation 1 and −1. Both of the feedbacks from each sub-unit are then sent to the feedback selector  76  so that the feedbacks corresponding to the paths that survived after the path pruning are selected. That is, for sub-unit  714 , the feedbacks f(n)∈   n   1,α  and f(n)∈   n   1,β  are sent to the feedback selector  76 . 
     At n-th instant, the path creator  72  receives as input the list of all paths that were selected after path pruning in the previous iteration, i.e,    n−1 . Also, the path creator  72  receives input from the switch controller  71 . If the switch controller  71  chooses Mode 1, then the path creator  72  makes use of quantized input from the computation unit  710  to extend the paths in    n−1 . Elaborating further, suppose the feedback into the parallel sub-units for path    n−1   1  in the computation unit  710  is f(n). Let the corresponding output after the comparator  11  be p 1 (n). Then the path creator  72  will update path    n−1   1  as    n   1 ={   n−1   1 ,p 1 (n)}. Similarly, the path creator  72  can update other paths    n−1   2 , . . . ,    n−1   L  as    n   2 ={   n−1   2 , p 2 (n)}, . . . ,    n   L ={   n−1   L ,p L (n)}, respectively. 
     As described above, when the switch controller  71  selects Mode 1, the path creator  72  does not perform the path splitting. 
     On the other hand, if the switch controller  71  selects Mode 2, then Path creator  1  performs the path splitting. 
     Elaborating further, for each path    n−1 ϵ   n−1 , the path creator  72  creates two paths    n   α α and    n   β , such that    n   α ={   n−1 ,−1} and    n   β ={   n−1 ,1}. Now,    n   α ,   n   β ϵ   n . Note that Card(   n )=2L. An example of the path splitting is given in  FIG. 3  and  FIG. 4  for n=101 and n=102, respectively. Note that    101   1 ={   100 ,1} and    101   2 ={   100 ,−1}. Also,    102   1 ={   101   1 ,1},    102   2 ={   101   1 ,−1},    102   3 ={l 101   2 ,1}    102   4 ={   101   2 ,−1}. 
     At n-th instant, the path metric update unit  73  receives as input the n-th sample of the input baseband signal x(n). 
     At n-th instant, the path metric update unit  73  receives as input the list of path metrics of all paths that were selected after path pruning in the previous iteration, i.e. {PM(   n−1   1 ), PM(   n−1   2 ), . . . , PM(   n−1   L )}. Elaborating further, if the switch controller  71  selects Mode 1, the path metric update unit  73  also receives the quantized values p 1 (n), p 2 (n), . . . , p L (n). Using these quantized values, the path metric update unit  73  updates the path metrics of each path as follows: 
     
       
         
           
             
               
                 
                   
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     On the other hand, if the switch controller  71  selects Mode 2, then the path metric update  73  updates the path metric as follows. 
     At n-th instant, the path metric update unit  73  receives as input the list of path metrics of all paths that were selected after path pruning in previous iteration, i.e,    n−1 . More specifically, the input to path metric update unit  73  at time n is {PM(   n−1   1 ), PM(   n−1   2 ), . . . , PM( )}, In n-th instant, the path metric update unit  73  updates the path metrics of the paths    n   α  and    n   β  as: 
     
       
         
           
             
               
                 
                   
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     At n-th instant, the path metric sort unit  75  receives as input the updated path metric of the paths in the path creator  72 . 
     More specifically, if the switch controller  71  selects Mode 1, then the input to the path metric sort unit  75  is PM(   n   1 ), PM(   n   2 ), . . . , PM(   n   L )}. In Mode 1, the path metric sort unit  75  just sends the path metric values PM(   n   1 ), PM(   n   2 ), . . . , PM(   n   L ) as a feedback to the path metric update unit  73  so that these path metric values are used in the next time instant (n+1) at path metric update unit  73 . 
     If the switch controller  71  selects Mode 2, then, at n-th instant, the path metric sort unit  75  sorts the paths in    n  in an ascending order as per the path metric. That is, after sorting, if    n ={   n   1 ,    n   2 , . . . ,  }, then PM(   n   1 )≤PM(   n   2 )≤ . . . PM( ). Because of F PGA memory constraint, the path pruning unit  74  selects paths identified as    n   1 ,    n   2 , . . . ,    n   L , where PM(   n   1 )≤PM(   n   2 )≤ . . . M(   n   L ). The path pruning unit  74  deletes the rest of the paths    n   L+1 ,    n   L+2 , . . . ,  . The path metric values of the selected paths in n-th time instant, that is, PM(   n   1 ), PM(   n   2 ), . . . , PM(   n   L ), are used in the next time instant (n+1) at the path metric update unit  73 . 
     The path pruning  74  receives as input all paths from the path creator  72 . At n-th instant, if switch controller  71  selects Mode 1, then the path pruning just send the incoming, paths    n   1 ,    n   2 , . . . , l n   L  back to the path creator  72  for use in next iteration (n+1). 
     When the switch controller  71  selects Mode 2, at n-th time instant, the path pruning unit  74  selects L paths out of 2L paths for the path pruning. This selection of L paths is done using the result of sorting at the path metric sort unit  75 . The path metric sort unit  75  informs the path pruning unit  74  of the L paths that have been of selected. 
     That is, the path pruning unit  74  selects the paths identified as    n   1 ,    n   2 , . . . ,    n   L  according to the result of sorting in path metric sort unit  75 . The rest of the paths are deleted. The selected L paths,    n   1 ,    n   2 , . . . ,    n   L , are sent back to the path creator  72  so as to be used in the next time instant (n+1). 
     At n-th instant, the input to the feedback selector  76  is feedback f(n) in each of the paths    n   1,α ,    n   1,β ,    n   2,α ,    n   2,β , . . . ,    α ,    β , where    n   1,α ={   n   1 ,1},    n   1,β ={   n   1 ,−1},    n   2,α ={   n   2 ,1},    n   2,β ={   n   2 ,−1}, . . . ,    α ={ ,1},    β ={ ,−1}. Using the result of sorting in the path metric sort unit the feedback selector  76  selects those feedbacks tin) corresponding to the paths    n   1 ,    n   2 , . . . ,    n   L . The feedbacks of the selected paths are used in the next time instant (n+1) in the computation unit  710  or the computation unit  79  depending on the mode selected by the switch controller  71  in time instant (n+1). 
     The switch  77  makes its decision at each time instant based on the input from the switch controller  71 . The working of the switch  77  is explained as follows:
         Suppose in n-th step, the switch controller  71  selects Mode 1 and thus the computation unit  710  is used for sending the input baseband signa x(n). In that case, the switch  77  configures to connect port a to port b.   Suppose in n-th step, the switch controller  71  selects Mode 2 and thus the computation unit  79  is used for sending the input baseband signal x(n). In that case, switch  77  configures to connect port a to port c.       

     The switch  78  makes its decision at each time instant based on the input from the switch controller  71 . The working of the switch  78  is explained as follows: 
     Suppose in (n−1)-th step, computation unit  79  is used for computing the feed k f(n−1) and in n-th step, computation unit  710  is to be used for computing the feedback f(n). In that case, for obtaining the feedback f(n−1) for all the paths in    n−1 , the switch  78  configures to connect port a to port d. 
     Suppose in (n−1)-th step, the computation unit  710  is used for computing the feedback f(n−1) and in n-th step, the computation unit  710  is to be used for computing the feedback f(n). In that case, for obtaining the feedback f(n−1) for all the paths in    n−1 , the switch  78  configures to connect port b to port d. 
     Suppose in (n−1)-th step, the computation unit  710  is used for computing the feedback f(n−1) and in n-th step, the computation unit  79  is to be used for computing the feedback f(n). In that case, for obtaining the feedback f(n−1) for all the paths in    n−1 , the switch  78  configures to connect port b to port c. 
     Suppose in (n−1)-th step, computation unit  79  is used for computing the feedback f(n−1) and in n-th step, computation unit  79  is to be used for computing the feedback f(n). In that case, for obtaining the feedback f(n−1) for all the paths in    n−1 , the switch  78  configures to connect port a to port C. 
     After the last sample of baseband signal, x(N) has been quantized at N-th time instant, the block select path unit  718  selects the path with the lowest path metric. 
     To accomplish this, it takes as input all paths obtained after path splitting in path creator  72 , that is,    n   1 ,    n   2 , . . . ,  . Using output of path metric sort  75 , select the path with the lowest path metric value, that is,    n   1 , where PM(   n   1 )≤PM(   n   2 )≤ . . . PM( ). Now, the selected path    n   1  is the output bit sequence. 
     In the exemplary embodiment described above, the phase control device has configured as a disk-like shape device. However, the shape of the phase control device is not limited to this. For example, the phase control device may be configured as a board-like shape device other than the disk-like shape device. 
     Some or all components and units as described in the above embodiments may be composed of hardware circuits or circuitry. Or. some or all components and units as described in the above embodiments may execute the processes by the software The communication apparatus in the above embodiments can execute one or more programs including a set of instructions to cause a computer to perform an algorithm described above with reference to the drawings. These programs may be stored in various types of non-transitory computer readable media and thereby supplied to computers. The non-transitory computer readable media includes various types of tangible storage media. Examples of the non-transitory computer readable media include a magnetic recording medium (such as a flexible disk, a magnetic tape, and a hard disk drive), a magneto-optic recording medium (such as a magneto-optic disk), a Compact Disc Read Only Memory (CD-ROM), CD-R, CD-R/W, and a semiconductor memory (such as a mask ROM, a Programmable ROM (PROM), an Erasable PROM (EPROM), a flash ROM, and a Random Access Memory (RAM)). These programs may be supplied to computers by using various types of transitory computer readable media. Examples of the transitory computer readable media include an electrical signal, an optical signal, and an electromagnetic wave. The transitory computer readable media can be used to supply programs to a computer through a wired communication line (e.g., electric wires and optical fibers) or a wireless communication line. 
     While the present disclosure has been described above with reference to exemplary embodiments, the present disclosure is not limited to the above exemplary embodiments. The configuration and details of the present disclosure can be modified in various ways which can be understood by those skilled in the art within the scope of the disclosure. 
     For example, the whole or part of the embodiments disclosed above can be described as, but not limited to, the following supplementary notes. 
     (Supplemental Note 1) 
     A communication apparatus comprising: 
     a path metric update unit configured to update a path metric of each path at each iteration; 
     a path splitting unit configured to split an existing path into two paths, with one path being formed by appending 1 to the existing path and, the other path being formed by appending −1 to the existing path; 
     a path metric sort unit configured to sort the paths in the ascending order of their path metric values; 
     a path pruning unit configured to choose L (L is an integer more than 1) paths which have lower path metric values; 
     a select path unit configured to select a path with lowest path metric among all available paths at the end of all the baseband samples and the selected path serving as the output bit sequence; 
     a feedback selector configured to select the feedback corresponding to the feedback associated with paths selected by the path pruning unit; 
     a computation unit configured to process the feedback from the feedback selector and the input baseband signal, and to give feedback for next time instant as the output. 
     (Supplemental Note 2) 
     The communication apparatus according to Supplemental note 1, wherein 
     the path splitting unit splits each existing path from previous iteration into two new paths, 
     one of the two new path is created by appending 1 to the existing path, and 
     the other one of the two new path is created by appending −1 to the existing path. 
     (Supplemental Note 3) 
     The communication apparatus according to Supplemental note 1 or 2, wherein 
     the path metric update unit obtains the path metric for each of the two path created by the path splitting unit using the path metric of the existing path and associated quantization noise for each new path. 
     (Supplemental Note 4) 
     The communication apparatus according to any one of Supplemental notes 1 to 3, wherein 
     the path metric sort unit sorts the paths created by the path splitting unit according to path metric values obtained from the path metric update unit in an ascending order, and 
     the path metric sort unit does the sorting in a global fashion. 
     (Supplemental Note 5) 
     The communication apparatus according any one of Supplemental notes 1 to 4, wherein 
     the path pruning unit retains half of the paths created by the path splitting unit based on the results of sorting of the path metric sort unit. 
     (Supplemental Note 6) 
     The communication apparatus according to any one of Supplemental notes 1 to 5, wherein 
     the select path unit selects the path with the lowest path metric at the end of quantization of all samples of input baseband signal. 
     (Supplemental Note 7) 
     The communication apparatus according to any one of Supplemental notes 1 to 6, wherein 
     the feedback selector selects feedback corresponding to paths that are retained by path pruning unit, and 
     the selection of feedbacks is done using result of sorting from the path metric sort unit. 
     (Supplemental Note 8) 
     The communication apparatus according to any one of Supplemental notes 1 to 7, wherein 
     the computation unit takes in feedback of the paths that survived pruning in previous time instant, and adds it to present sample of baseband input signal to obtain feedback of the paths created by the path splitting unit. 
     (Supplemental Note 9) 
     A decoding method of a communication apparatus comprising: 
     updating a path metric of each path at each iteration; 
     splitting an existing path into two paths, with one path being formed by appending 1 to the existing path and, the other path being formed by appending −1 to the existing path; 
     sorting the paths in the ascending order of their path metric values; 
     choosing L (L is an integer more than 1) paths which have lower path metric values; 
     selecting a path with lowest path metric among all available paths at the end of all the baseband samples and the selected path serving as the output bit sequence; 
     selecting the feedback corresponding to the feedback associated with paths selected by path pruning; 
     processing the selected feedback and the input baseband signal, and to give feedback for next time instant as the output. 
     (Supplemental Note 10) 
     The decoding method according to Supplemental note 9, wherein 
     the splitting comprises splitting each existing path from previous iteration into two new paths, 
     one of the two new path is created by appending 1 to the existing path, and 
     the other one of the two new path is created by appending −1 to the existing path. 
     (Supplemental Note 11) 
     The decoding method according to Supplemental note 9 or 10, wherein 
     the updating comprises obtaining the path metric for each of the two path created by the splitting using the path metric of the existing path and associated quantization noise for each new path. 
     (Supplemental Note 12) 
     The decoding method according to any one of Supplemental notes 9 to 11, wherein 
     the sorting comprises sorting the paths created by the path splitting according to path metric values in an ascending order, and 
     the sorting is done in a global fashion. 
     (Supplemental Note 13) 
     The decoding method according to any one of Supplemental notes 9 to 12, wherein 
     the splitting comprises retaining half of the paths created by the path splitting based on the results of sorting. 
     (Supplemental Note 14) 
     The decoding method according to any one of Supplemental notes 9 to 13, wherein 
     the selecting of paths comprises selecting the path with the lowest path metric at the end of quantization of all samples of input baseband signal. 
     (Supplemental Note 15) 
     The decoding method according to any one of Supplemental notes 9 to 14, wherein 
     the selecting of the feedback comprises selecting feedback corresponding to paths that are retained by the path pruning, and 
     the selection of feedbacks is done using result of the sorting. 
     (Supplemental Note 16) 
     The decoding method according to any one of Supplemental notes 9 to 15, wherein 
     the processing comprises taking in the feedback of the paths that survived pruning in previous time instant, and adding it to present sample of baseband input signal to obtain feedback of the paths created by the path splitting. 
     REFERENCE SIGNS LIST 
     
         
           10  DELTA SIGMA MODULATOR 
           11  COMPARATOR 
           12  ADDER 
           13  ADDER 
           50  COMMUNICATION APPARATUS 
           51  PATH METRIC UPDATE UNIT 
           52  PATH CREATOR 
           53  PATH METRIC SORT 
           54  PATH PRUNING 
           55  SELECT PATH UNIT 
           56  FEEDBACK SELECTOR 
           57  COMPUTATION UNIT 
           70  COMMUNICATION APPARATUS 
           72  PATH CREATOR 
           73  PATH METRIC UPDATE UNIT 
           74  PATH PRUNING 
           75  PATH METRIC SORT 
           718  SELECT PATH UNIT 
           76  FEEDBACK SELECTOR 
           79  COMPUTATION UNIT 
           710  COMPUTATION UNIT