Abstract:
A method and apparatus for 45° phase ambiguity resolution for one coded bit per symbol 8PSK modulation resolves phase ambiguity by selection of pre-differential encoders. A trellis encoder for 8PSK modulation of the type in which input data bits are encoded to a three-bit symbols includes a differential encoder, a convolutional encoder and first and second encoding assemblies. A decoder for decoding trellis coded data of 8PSK modulation includes a Viterbi decoder, a differential decoder, a convolutional decoder and first and second decoder assemblies. Each of the encoding and decoding assemblies includes multiplexing logic for selecting from among possible data paths according to a phase invariant scheme.

Description:
RELATED APPLICATION 
     This application claims priority to U.S. Provisional Application Ser. No. 60/082,200 filed Apr. 17, 1998, the entire teachings of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Trellis-coded modulation (TCM) combines channel coding and modulation at a transmitter. Information bits are sent into a TCM encoder in parallel. The least-significant bits (LSBs) are convolutionally encoded. The most-significant bits (MSBs) are usually left uncoded and combined with the output of the convolutional coder to form a symbol on a signal constellation through a signal mapper. One advantage of TCM is that although no error control coding is performed on any bit other than the LSB of the input information data, the decoder is able to provide error correction on all bits. Therefore, significant coding gain over uncoded modulation can be achieved. 
     In eight-state phase shift keying (8PSK) modulation, a modulated carrier signal is transmitted with symbols that each represent three data bits. A difficulty with PSK transmission is that the modulated carrier as transmitted can be affected by undesirable phase rotation. At the receiver, such phase rotation corresponds to a rotation of the received signal constellation such that decoded symbols do not match those which were transmitted. 
     It is known to provide resolution of the phase ambiguities for 2/3, 5/6 and 8/9 trellis coded 8PSK modulation schemes in which the modulation is based on two coded bits per symbol. Such known approaches enable 90°, 180° and 270° phase ambiguities to be resolved. 
     SUMMARY OF THE INVENTION 
     The present invention provides a method and apparatus for 45° phase ambiguity resolution for one coded bit per symbol 8PSK modulation. The phase ambiguity is resolved by novel selection of a pre-differential encoder. 
     According to the present invention, a trellis encoder for 8PSK modulation of the type wherein a set of input data bits are encoded to three-bit symbols includes a first differential encoder, a convolutional encoder and first and second encoding assemblies. The first differential encoder has an input for receiving a first data bit of the set of input data bits. The convolutional encoder has an input connected to an output of the first differential encoder, and first and second convolutional encoder outputs. Each of the first and second encoding assemblies includes first and second multiplexers, and second and third differential encoders. The first multiplexer has a data input for receiving a pair of data bits of the set of input data bits with one of the pair of data bits preceding another of the pair of data bits in time, first and second select inputs respectively connected to the first and second convolutional encoder outputs, and a pair of outputs. The second differential encoder has an input connected to one of the first multiplexer outputs and the third differential encoder has an input connected to another one of the first multiplexer outputs. The second multiplexer has a pair of data inputs each respectively connected to a different one of the second and third differential encoder outputs, first and second select inputs respectively connected to the first and second convolutional encoder outputs, and an output. 
     According to an aspect of the invention, the multiplexers of the first encoding assembly are responsive to connect certain input data bits for coding by one of the second and third differential encoders based on the binary levels of the first and second convolutional encoder outputs. 
     According to another aspect of the invention, the multiplexers of the second encoding assembly are responsive to connect certain other input data bits for coding by one of the second and third differential encoders based on the binary levels of the first and second convolutional encoder outputs and the second multiplexer output of the first encoding assembly. 
     Further in accordance with the invention, a decoder for decoding trellis coded data of the type wherein input data bits are encoded to three-bit symbols in 8PSK modulation includes a Viterbi decoder, a first differential decoder, a convolutional encoder and first and second decoder assemblies. The Viterbi decoder provides an estimate of a first coded bit from a received phase point signal. The first differential decoder has an input for receiving the first coded bit estimate. The convolutional encoder has an input for receiving the first coded bit estimate, and first and second convolutional encoder outputs. Each of the first and second decoding assemblies includes first and second multiplexers, and second and third differential decoders. The first multiplexer has a data input for receiving a pair of second bit estimates, first and second select inputs respectively connected to the first and second convolutional encoder outputs, and a pair of outputs. The second differential decoder has an input connected to one of the first multiplexer outputs. The third differential decoder has an input connected to another of the first multiplexer outputs. The second multiplexer has a pair of data inputs each respectively connected to a different one of the second and third differential encoder outputs, first and second select inputs respectively connected to the first and second convolutional encoder outputs, and an output. 
     An advantage of the phase ambiguity resolution approach of the present invention is that less time is needed to acquire signal synchronization since sector rotation is avoided. This approach balances better phase resolution performance with fewer coded bits per symbol and has application to punctured and unpunctured trellis coded modulation. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of preferred embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. 
     FIG. 1 shows a signal constellation for 8PSK modulation. 
     FIG. 2 shows a block diagram of a rotationally invariant encoder for 8PSK modulation in accordance with the present invention. 
     FIG. 3 shows a circuit block diagram of a differential encoder for use in the encoder of FIG. 2. 
     FIG. 4 shows a block diagram of a rotationally invariant decoder for 8PSK modulation in accordance with the present invention. 
     FIG. 5 shows a circuit block diagram of a differential decoder for use in the decoder of FIG. 4. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The principles of the present invention are now described with reference to FIGS. 1 to 5. FIG. 1 illustrates a particular signal constellation for 8PSK in which the symbol mapping is arranged for one coded bit per symbol. In particular, a three-bit symbol (v u c) mapping that defines the 8 PSK one coded bit per symbol is shown. The notation (v&#39;u&#39;c&#39;) is used further herein to indicate a symbol succeeding symbol (vuc), where it can be seen that v and v&#39; represent the most significant bits and c and c&#39; represent the least significant bits. Each of the three-bit symbols corresponds to a particular carrier phase shift as shown in Table 1 below: 
     
                       TABLE 1______________________________________Bits    000    001    010  011   100  101  110  111Phase Shift   0°          45°                 90°                      135°                            180°                                 225°                                      270°                                           315°______________________________________ 
    
     It is apparent from FIG. 1 that a 45° phase rotation leads to the following transformation as indicated in Table 2 below: 
     
                       TABLE 2______________________________________       45° rotation transformation______________________________________c = 0         vuc → vu (c⊕1)c = 1         vuc → v (u⊕1)(c⊕1) if u = 0         vuc → (v⊕1)(u⊕1)(c⊕1) if u______________________________________         = 1 
    
     The same transformations hold for the primed symbol (v&#39;u&#39;c&#39;). The transformations in Table 2 can be written as follows: 
     
         for c=1, U=(v u).sub.decimal →U=(U+1) mod [4]. 
    
     For example, the symbol (v u c)=(101) becomes (110) after a 45° phase rotation, i.e., U =(10) decimal  =2 is transformed to U=(U+1) mod [4]=3=(11) decimal . 
     Referring now to FIG. 2, a block diagram of an embodiment of a 45° phase invariant 8PSK encoder is shown. The encoder comprises a pair of encoding assemblies 102, 104, a differential encoder 122 and a convolutional encoder 124. The encoding assembly 102 includes a pair of multiplexers 106, 112 and a pair of differential encoders 108, 110 connected between the multiplexers. Like-vise, the encoding assembly 104 includes a pair of multiplexers 114, 120 and a pair of differential encoders 116, 118 connected between the multiplexers. The differential encoder 122 has an output connected to an input of the convolutional encoder 124. The differential encoders 108, 110, 116, 118, 122 are binary differential encoders of the type shown in FIG. 3. Referring again to FIG. 2, the convolutional encoder 124 is preferably a conventional rate 1/2 convolutional encoder, though it can also comprise a rate (n/n+1) convolutional encoder for punctured coding schemes. 
     The encoding operation for rate 5/6 TCM for a set of information bits a 5n+k , where n≧0 and 4≧k≧0 is now described. Bit a 5n  is input to differential encoder 122 and the output of encoder 122 is then encoded using the rate 1/2 convolutional encoder 124. The coded bits output from the convolutional encoder 124 are designated as (c&#39; 5n  c 5n ). Bits a 5n+1 , a 5n+2 , a 5n+3 , and a 5n+4  are referred to as uncoded bits since such bits are not convolutionally encoded. The uncoded bits a 5n+1 , a 5n+2 , a 5n+3 , a 5n+4  are differentially pre-encoded by the encoding assemblies 102, 104 to resolve the 45° phase ambiguity. More particularly, uncoded bits a 5n+2 , a 5n+4  are successively differentially encoded by the encoding assembly 102 while uncoded bits a 5n+1 , a 5n+3  are successively differentially encoded by the encoding assembly 104. The output bits from the encoding assemblies 102, 104 are denoted by v 5n , v&#39; 5n  and u 5n  and u&#39; 5n  respectively. The three-bit symbols are constructed as (v 5n  u 5n  c 5n ) and (v&#39; 5n  u&#39; 5n  c&#39; 5n ). It can be seen that each such three-bit symbol includes one coded bit per symbol, namely respective coded bits c 5n , c&#39; 5n . 
     From FIG. 2 it can also be seen that the three information streams have different rates. For instance, if the information rate is denoted by inf --  rate, then the input bit rate of the a 5n  path is equal ##EQU1## and the input bit rate of the other two paths is equal ##EQU2## Therefore, the output bit rate on each of the three output paths is equal to ##EQU3## 
     The particular logic by which the encoding assemblies select among possible paths is now described. As shown in FIG. 2, the multiplexers 106, 112, 114 and 120 have respective select inputs 106-1, 106-2, 112-1, 112-2, 114-1, 114-2, 120-1, 120-2. 
     Multiplexers 106, 114 are conventional 1:2 multiplexers. Multiplexers 112, 120 are conventional 2:1 multiplexers. The signals that are presented on these select inputs include the uncoded bits u 5n , u&#39; 5n  and coded bits c 5n , c&#39; 5n . In particular, for encoding assembly 102, multiplexers 106, 112 select a path from paths 108-1, 108-2 and 110-1, 110-2 according to the following logic: 
     If {(c&#39;=0) c=0} or if {(c&#39;=1) c=1&amp;(u&#39;=0) u=0} then path 108-1, 108-2 is 10 selected. 
     If {(c&#39;=1) c=1&amp;(u&#39;=1) u=1 } then path 110-1, 110-2 is selected. 
     For encoding assembly 104, multiplexers 114, 120 select a path from paths 116-1, 116-2 and 118-1, 118-2 according to the following logic: 
     If {(c&#39;=0) c=0} then path 116-1, 116-2 is selected. 
     If {(c&#39;=1) c=1} then path 118-1, 118-2 is selected. 
     Next, it can be seen that the differential pre-encoding provided by the encoding assemblies 102, 104 indeed resolves any 45° phase ambiguity rotation. First consider that it is desirable to differentially pre-encode the bit that can flip (110) value when it is rotated by 45°. As indicated in Table 2, the information bits are pre-coded as follows: 
     1. Bit c 5n  always transforms to (c 5n  ⊕1). Therefore, the information bit a 5n  should always be differentially pre-encoded. 
     2. The uncoded bit a 5n+1  is differentially pre-encoded with the previous bits a 5m+1  or a 5m&#39;+3 , where m and m&#39; are less than n, provided that c 5n  =c 5m  or c&#39; 5n  =c&#39; 5m&#39; , respectively. 
     3. The uncoded bit a 5n+3  is differentially pre-encoded with the previous bits a 5m+1  or a 5m&#39;+3  where m and m&#39; are less than n, provided that c&#39; 5n  =c 5m  or c&#39; 5n  =c 5m&#39; , respectively. 
     4. The uncoded bit a 5n+2  is differentially pre-encoded with the previous bits a 5m+2  or a 5m&#39;+4 , where m and m&#39; are less than n, provided that {c 5n  =c 5m  and u 5n  =u m  } or {c 5n  =c&#39; 5m&#39;   and u 5n  =u&#39; 5m&#39;  }, 
     5. The other uncoded bit a 5n+4  is differentially pre-encoded with the previous bits a 5m+2  or a 5m&#39;+4 , where m and m&#39; are less than n, provided {c&#39; 5n  =c 5m  or u&#39; 5n  =u 5m  } and {c&#39; 5n  =c&#39; 5m&#39;   or u&#39; 5n  =u&#39; 5m&#39;  }, respectively. 
     Referring now to FIG. 4, a block diagram of an embodiment of a 45° phase invariant 8PSK decoder is shown. The decoder includes 8PSK phase mapper 202, branch metrics calculator &amp; sector determination block 204, a pair of decoding assemblies 206, 208, a Viterbi decoder 226, a convolutional encoder 228 and a differential decoder 230. The decoding assembly 206 includes a pair of multiplexers 210, 216 and a pair of differential decoders 212, 214 connected between the multiplexers. Likewise, the decoding assembly 208 includes a pair of multiplexers 208, 224 and a pair of differential decoders 220, 222 connected between the multiplexers. The differential decoder 230 has an input connected to the output of Viterbi decoder 226. The differential decoders 212, 214, 220, 222, 230 are binary differential decoders of the type shown in FIG. 5. Referring again to FIG. 4, the convolutional encoder 228 is a conventional rate 1/2 convolutional encoder or alternatively a rate n/(n+1) convolutional encoder for punctured codes which also connects to the output of Viterbi decoder 226. 
     Phase mapper 202 receives signals that have been transmitted as 8PSK signals as described above. The received signals are converted to quantized I and Q components which are provided to branch metrics calculator &amp; sector determination block 204. Block 204 provides sector values and branch metrics corresponding to estimates for v 5n , v&#39; 5n , u 5n , U&#39; 5n , c 5n , c&#39; 5n , to the decoding assemblies 206, 208 and Viterbi decoder 226. Note that since the coding of the present invention provides 45° phase ambiguity resolution, a sector rotation is not required. 
     A decoded bit estimate a 5n  from Viterbi decoder 226 is re-encoded by the convolutional encoder 228 to deduce bits c 5n  and c&#39; 5n . Coded bits c 5n  and c&#39; 5n  are used with decoding assembly 208 to differentially decode the bits u 5n  and u&#39; 5n , respectively. The bits v 5n  and v&#39; 5n  are decoded in decoding assembly 206 using the bits {c 5n  and u 5n  } and {c&#39; 5n  and u&#39; 5n  }, respectively. Thus, the decoder provides decoded bits a 5n , a 5n+1 ,a 5n+2 , a 5n+3 , a 5n+4 . 
     The particular logic by which the decoding assemblies select among possible paths is now described. As shown in FIG. 4, the multiplexers 210, 216, 218, 224 have respective select inputs 210-1, 210-2, 216-1, 216-2, 218-1, 218-2, 2241, 2242. Multiplexers 210, 218 are conventional 1:2 multiplexers. Multiplexers 216, 224 are conventional 2:1 multiplexers. The signals that are presented on these select inputs include the uncoded bits u 5n , u&#39; 5n  and coded bits c 5n , c&#39; 5n . In particular, for decoding assembly 206, multiplexers 210, 216 select a path from paths 212-1, 212-2 and 214-1, 214-2 according to the following logic: 
     If {(c&#39;=1) c=1} or if {(c&#39;=0) c=0&amp;(u&#39;=1) u=1} then path 212-1, 212-2 is selected. 
     If {(c&#39;=0) c=0&amp;(u&#39;=0) u=0} then path 214-1, 2142 is selected. 
     For decoding assembly 208, multiplexers 218, 224 select a path from paths 220-1, 220-2 and 222-1, 222-2 according to the following logic: 
     If {(c&#39;=0) c=0} then path 220-1, 220-2 is selected. 
     If {(c&#39;=1) c=1} then path 222-1. 222-2 is selected. 
     While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.