Abstract:
Techniques are provided herein to improve the decoding efficiency in a wireless receiver to obtain a correctly decoded data string. A state metric matrix from a received codeword is used to generate active state metric matrices for time instances of the received codeword, and then a differential metric matrix is generated from information in the active state metric matrices. Based on the differential metric matrix a maximum likelihood path and one or more alternative paths are identified. A first decoded data string corresponding to the maximum likelihood path and a plurality of second decoded data strings corresponding to the one or more alternative paths are derived. Integrity of the respective decoded data strings is examined to obtain the correct decoded data string based on the first and second decoded data strings.

Description:
CROSS REFERENCE 
     The present application claims the benefit of U.S. Provisional Application Ser. 60/851,417, which was filed on Oct. 13, 2006. 
    
    
     BACKGROUND 
     Trellis codes, such as convolutional codes, trellis and bit-interleaved coded modulations, are commonly used to improve the performance of communications networks. However, a decoded message obtained by a receiver might still contain errors as a result of the impairment of channel conditions and/or insufficient protection due to a low redundancy rate. 
     Data exchanged in a wireless communications network is typically protected by an error detection code (EDC). A commonly used EDC algorithm is a cyclic redundancy code (CRC), which pads parity bits to the data. The EDC encoded data subsequently passes through a multi-state convolutional code encoder with a code rate of k/n. A convolutional code is terminated by a zero-padding or a tail-biting technique. In general, a convolutional code has a code rate of k/n; however, it is more practical to use a convolutional code with a code rate of 1/n in order to obtain higher rates through puncturing methods. 
     The decoding system of a receiver in a wireless communications network comprises a convolutional code decoder (e.g. a Maximum Likelihood decoder employing the Viterbi algorithm) and an EDC decoder. The EDC decoder examines the data decoded by the convolutional decoder to determine if a CRC error exists. Conventional methods for decoding messages may not always yield desired results or may use a considerable amount of time and resources due to the impairment of channel conditions and/or insufficient protection. 
     As such, what is desired is a method and system for improving decoding efficiency in a wireless communications network. 
     SUMMARY 
     The present invention discloses a method and system for improving the decoding efficiency in a wireless receiver to obtain a correct decoded data string. The method comprises generating an active state metric matrix of a receiving codeword, calculating a differential metric matrix pertinent to the active state metric matrix, identifying a maximum likelihood path and one or more alternative paths based on the differential metric matrix, deriving first decoded data string corresponding to the maximum likelihood path, deriving a plurality of second decoded data strings corresponding to the one or more alternative paths respectively, examining the integrity of the first decoded data string; and examining the integrity of the plurality of second decoded data strings after the first decoded data string is determined erroneous, wherein the wireless receiver obtains the correct decoded data string. 
     The construction and method of operation of the invention, however, together with additional objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings accompanying and forming part of this specification are included to depict certain aspects of the invention. The invention may be better understood by reference to one or more of these drawings in combination with the description presented herein. It should be noted that the features illustrated in the drawings are not necessarily drawn to scale. 
         FIG. 1  is a simplified trellis diagram illustrating the decoding process of an eight-state trellis code employing the Viterbi algorithm. 
         FIG. 2  illustrates a method for improving decoding efficiency in accordance with an embodiment of the present invention. 
         FIG. 3  illustrates a decoding system that employs an ML decoder and an EDC decoder to decode zero-padding trellis codes in accordance with an embodiment of the present invention. 
         FIG. 4  illustrates a decoding system that employs an ML decoder and an EDC decoder to decode tail-biting trellis codes in accordance with an embodiment of the present invention. 
         FIG. 5  is a simplified trellis diagram illustrating the decoding process of an ML decoder employing the Viterbi algorithm and a sliding window algorithm in accordance with an embodiment of the present invention. 
         FIG. 6  is a block diagram illustrating a decoding system that employs an ML decoder and an EDC decoder to decode zero-padding trellis codes by using a sliding window algorithm in accordance with an embodiment of the present invention. 
         FIG. 7  is a block diagram illustrating a decoding system that employs an ML decoder and an EDC decoder to decode tail-biting trellis codes by using a sliding window algorithm in accordance with an embodiment of the present invention. 
     
    
    
     DESCRIPTION 
     The following detailed description of the invention refers to the accompanying drawings. The description includes exemplary embodiments, not excluding other embodiments, and changes may be made to the embodiments described without departing from the spirit and scope of the invention. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. 
     The present invention discloses a method for improving the performance of a decoding system in which a Maximum Likelihood (ML) decoder and an error detection code (EDC) decoder are used to attain data efficiently by reconstructing receiving codewords. A decoding system employing the disclosed method requires fewer system resources than those using conventional methods and attains data more efficiently by generating multiple alternative codewords. For example, the improvement in coding gain is more than 1 dB for an additive white Gaussian noise (AWGN) channel and about 1 to 2 dBs for a fading channel. In addition, there is substantial coding gain when multiple codewords are encoded with a convolutional code and protected by a single EDC. 
     In one embodiment of the present invention, a decoding system comprises an s-sate ML decoder for codewords of length l, i.e. there are l time instances in a trellis. The decoding process creates a state metric matrix SM of size s×l. The ML decoder processes receiving codewords, constructs a simplified trellis diagram from time instances t 1  to t l , and generates a state metric matrix (SM) and potential maximum likelihood paths. The state metric matrix (SM) holds the metrics of the states of all time instances. In other words, each element of an SM represents the state metric of a time instance computed according to the Viterbi algorithm. 
     Out of all the states of a time instance, q states are selected as active states, where q is determined according to a predetermined rule. An active state metric matrix (ASM) of size q×2 keeps the active state metrics of two consecutive time instances. The q×2 ASM has two columns. Assuming that the current time instance is t, the first and second columns reflect the active state metrics of t−1 and t, respectively. The indices of q active states of the current time instance t are stored in an active state list A. 
     A path history matrix P of size q×l keeps the path history of all the potential ML paths during the decoding process. The metrics of all possible paths that go through an active state at a time instance are calculated. The difference between the metrics of the most reliable and the second most reliable paths is stored in the corresponding element of a differential metric matrix Δ of size q×l. Subsequently, a divergence list D of size c is generated using the differential metric matrix Δ. and it is used to construct alternative codewords. 
       FIG. 1  is a simplified trellis diagram illustrating the decoding process of an eight-state trellis code employing the Viterbi algorithm in accordance with an embodiment of the present invention. A column represents a time instance t i . A circle represents a state  110  of the ML decoder at a time instance while a shaded circle represents an active state  112  of the ML decoder at a time instance. A solid line represents an ML path  120  while a dotted line illustrates alternative paths  130  and  132 . 
     Based on state metric matrix information generated in the decoding process, an ML decoder employing a trace-back algorithm identifies a path representing the receiving codeword as an ML path. An alternative path, which also represents the receiving codeword, follows the ML path for a period of time, diverges from it at time instance i, and merges with it at time instance j, where i&lt;j. 
     As shown in  FIG. 1 , an alternative path  130  from time instances t 1  to t 12  diverges from the ML path  120  in the 5 nd  state at time instance t 3 , and merges with it in the 2 th  state at time instance t 5 . Another alternative path  132  from time instances t 1  to t 12  diverges from the ML path  120  in the 6 th  state at time instance t 7  and merges with it in the 7 th  state at time instance t 4 . 
       FIG. 2  illustrates a method  200  for improving decoding efficiency in accordance with an embodiment of the present invention. In step  210 , the ML decoder processes a receiving codeword, computes the state metrics, and generates an active state metric matrix (ASM), a path history matrix P, and an active state list A for each time instance. 
     At any time instance t, a q×2 ASM has two columns. The 1 st  column (the preceding time instance column) represents the active state metrics of t−1, and the 2 nd  column (the current time instance column) represents the active state metrics of the current time t. 
     The metrics of all s-states at a time instance are computed, and q states with the most reliable metrics are identified, where q is determined according to a predetermined rule. These q states are considered as the active states of the current time instance. The metrics of the q states are stored in the 2 nd  column of the ASM, namely the current time instance column. 
     The indices of the q active states of the current time instance are stored in a temporary table T 1  while those of the q active states of the preceding time instance are stored in another temporary table T 2 . The elements of the temporary table T 2  are inserted into the current time instance column in a path history matrix P. The elements of the temporary table T 2  are stored in an active list A. 
     The active state metrics of all succeeding time instances are generated in the same way as described below. First, the active state metrics of the current time instance column are shifted from the 2 nd  column to the 1 st  column. Second, the active state metrics of the succeeding time instance are calculated based on the active state metrics of the current time instance. In other words, the active state metrics of the current time instance become the active state metrics of the preceding time instance in relation to the succeeding time instance. For example, three consecutive time instances are denoted as x, y, and z. In the case of y being the current time, the 1 st  column in the ASM represents the active state metrics of time instance x; the 2 nd  column represents those of time instance y. In the case of z being the current time, the 1 st  column in the ASM represents the active state metrics of time instance y; the 2 nd  column represents those of time instance z. 
     Step  220  shows the generating of a differential metric matrix Δ by the ML decoder. First, the metrics of all possible paths going through each state of a time instance are calculated. Second, for each state, the path with the most reliable metric is designated as the surviving path while the path with the second most reliable metric is designated as the best alternative path. Lastly, the difference between the metrics of the surviving path and the best alternative path of each state is stored in a differential metric matrix Δ. 
     In the case that some active states of the current time instance are related to only one active state of the preceding time instance, the metrics of the elements of the current time instance in the differential metric matrix that do not have corresponding elements in the preceding time instances are set to a predetermined maximum value. The reason for choosing a maximum value is that no alternative path passes through the active state of the current time instance. 
     In step  230 , the receiving codeword is processed and a trace-back algorithm is executed to identify an ML path and generate a divergence list D, as shown. The information about the ML path is used to obtain a code sequence that represents the decoded codeword, which is subsequently converted to the decoded data. 
     The state metrics in the differential metric matrix Δ, related to the ML path, are examined. The indices of a predetermined number (c) of active states with the smallest metrics related to the ML path are retrieved, ordered and stored in a divergence list D, which is used to facilitate the construction of alternative codewords. 
     In step  240 , the decoded data is received and the EDC decoder checks for errors. If no error exists, the data is sent to the next processing unit of the receiving chain of the wireless receiver. If, however, an error is detected, a technique for finding alternative codewords is employed. 
     Step  250  shows the process of finding an alternative codeword. Constructing an alternative codeword begins with choosing one element from the divergence list D; namely an index. A trace-back algorithm re-traces an alternative path starting from the active state that corresponds to the chosen index. The trace-back process continues until the alternative path converges with the original ML path. During the process of generating an alternative codeword, a portion of the original ML code sequence is replaced with a segment of an alternative code sequence, which results in an alternative codeword. The alternative codeword is fed to the EDC decoder to check for errors. The process, which includes generating an alternative codeword, sending the alternative data to the EDC decoder, and checking for errors, continues until correct data is obtained or all c alternative codewords generated from the divergence list D are examined and deemed corrupted. 
     The present invention builds on two common approaches for terminating the trellis of a trellis code: zero-padding and tail-biting.  FIG. 3  illustrates a decoding system  300  that employs an ML decoder and an EDC decoder to decode zero-padding trellis codes in accordance with an embodiment of the present invention. The decoding system  300  comprises a state metric matrix generator  310 , a differential metric matrix generator  320 , a trace-back module  330 , an EDC decoder  340 , and an alternative codeword generator  350 . 
     Three components of the decoding system  300  (the state metric matrix generator  310 , the differential metric matrix generator  320 , and the trace-back module  330 ) form a codeword-decoding module  306 . The other two components (the EDC decoder  340  and the alternative codeword generator  350 ) form a data-checking module  308 . 
     An input bit stream  302  represents a receiving codeword. Following the process described in step  210  of  FIG. 2 , the state metric matrix generator  310  processes the entire bit stream  302 , calculates the state metrics of all time instances, and generates an active state metric matrix (ASM), a path history matrix P, and an active state list A. Based on the ASM, the differential metric matrix generator  320  calculates a differential metric matrix Δ and a divergence list D following the process described in step  220 . 
     After the receiving codeword is processed, the trace-back module  330  identifies an ML path corresponding to the code sequence representing the codeword. The information about the ML path is used to obtain the code sequence representing the decoded codeword, which is subsequently converted to the decoded data. 
     For a trellis terminated by using a zero-padding technique, the initial metrics in the ASM are set as follows: The first element of the fist column in the ASM corresponds to the zero state, and the metric of the first element is set to a predetermined highest reliability value. The metrics of the remaining elements of the fist column are set to a predetermined lowest reliability value. The first element of the active state list A corresponds to the index of the zero state, namely 0. The rest of the elements in the active state list A are set to a value indicating that the index of the state is ‘Not Available.’ 
     After receiving the decoded data, the EDC decoder  340  checks for errors. If no error exists, the decoded data  304  is sent to the next processing unit of the receiving chain of the wireless receiver. If, however, a error is detected, a technique for finding alternative codewords is employed (see step  250 ). A signal  342  is sent to the alternative codeword generator  350  to find an alternative codeword. Subsequently, the alternative data is fed to the EDC decoder  330  to check for errors. The trace-back process continues until correct data is obtained or the alternative codeword generator  350  exhausts all alternative codewords. 
       FIG. 4  illustrates a decoding system  400  that employs an ML decoder and an EDC decoder to decode tail-biting trellis codes in accordance with an embodiment of the present invention. The decoding system  400  comprises a trace-back extension module  410 , a codeword-decoding module  306  and a data-checking module  308 . 
     For a trellis that is terminated by using a tail-biting technique, its starting state, which is also the ending state, is unknown. Therefore, the initial values of the elements of the active state metric matrix ASM and the active state list A are initialized in such a way that each of the states is likely to be the starting state, i.e. all states have the same predetermined metric. 
     When the process of decoding the receiving codeword reaches the end of the bit stream  302 , the ML decoder repeats the process from the beginning of the bit stream  302  for a predetermined number of time instances w t     j   , where w t     j    is preferred to be bigger than 5 log 2  S and S is the number of states. Afterwards, the trace-back module  330  randomly selects an active state at time instance t j  and runs the trace-back algorithm. 
     After tracing back w t     j    time instances, the trace-back module  330  considers the state that the trace-back path passes through at time instance 0 (if w t     j   =5 log 2  S) as the starting state of the trellis. Because of the circular nature of tail-biting trellis codes, the ending state of the trellis becomes known after the starting state is identified. The trace-back process continues from the last time instance of the trellis, to the time instance 0 and then an ML path is identified. The part of the simplified trellis diagram between t 0  and t j , is traced-back twice by the trace-back extension module  410 . 
     The information about the ML path is used to obtain the code sequence that represents the decoded codeword, which is subsequently converted to the decoded data. Subsequently, the decoded data is forwarded to the data decoding module  308  to verify the integrity of the decoded data. The data-decoding module  308  either obtains correct decoded data or exhausts all the alternative codewords (see step  250 ). 
     One way to further reduce system resources required for processing a receiving codeword using the disclosed method is to divide a receiving codeword into segments. Instead of processing the entire receiving codeword, the ML decoder processes the receiving codeword one segment at a time. The processing of a segment of the receiving codeword by the ML decoder is similar to sliding a window of a predetermined size w over the receiving codeword. As a result, the technique is commonly known as a sliding window algorithm. 
       FIG. 5  is a simplified trellis diagram  500  illustrating the decoding process of trellis code employing the Viterbi algorithm and a sliding window algorithm in accordance with an embodiment of the present invention. A window  520  of a predetermined size w represents a segment of the receiving codeword. Furthermore, the window  520  is partitioned into two: the first sub-window  522 , which contains a convergent path, and the second sub-window  524 , which contains non-convergent paths. How the window is partitioned may be determined by channel conditions, which are unknown. 
     The ML path of the receiving codeword comprises convergent paths, each of which is a partial ML path of a window. Ideally, the first sub-window  522  has the same size as the window  520  and the second sub-window  524  has a size of zero. However, in reality, the window  520  always includes a number of non-convergent paths. As a result, the second sub-window  524  must be part of the succeeding window, i.e. any consecutive windows overlap where non-convergence paths are present. Without any prior knowledge about how the window is partitioned, an ML decoder can still produce the best result if the overlapping areas w o  of the consecutive windows has a predetermined size larger than 5 log 2  S, i.e. w o &gt;5 log 2  S. 
     In the diagram  500 , the current window  520  covers the area between time instances t 2  and t 11 . There is an overlapping area of the current window  520  and the preceding window  510 . There is also an overlapping area of the current window  520  and the succeeding window  530 . The overlapping areas include non-convergent paths. 
       FIG. 6  is a block diagram illustrating a decoding system  600  that employs an ML decoder and an EDC decoder to decode zero-padding trellis codes by using a sliding window algorithm in accordance with an embodiment of the present invention. The decoding system  600  comprises a signal path  608 , a codeword-decoding module  306  and a data-checking module  308 . 
     The codeword-decoding module  306  operates in the same way as described in  FIG. 3 . Instead of processing the entire bit stream  302 , the codeword-decoding module  306  employing a sliding window algorithm processes one segment of the bit stream  302  at a time and identifies a partial ML path of each window. After a partial ML path is identified, a signal is sent to the state metric matrix generator module  310  to begin processing the next window. 
     After the entire receiving codeword is processed, the ML path comprising partial ML paths from one or more windows is identified. After the decoded data is obtained, it is forwarded to the data-checking module  308 . The data-checking module  308  either obtains correct decoded data or exhausts all the alternative codewords. During the decoding process, it is important not to generate duplicate ML paths in the overlapping areas of the windows. 
       FIG. 7  is a block diagram illustrating a decoding system  700  that employs an ML decoder and an EDC decoder to decode tail-biting trellis codes by using a sliding window algorithm in accordance with an embodiment of the present invention. The decoding system  700  comprises a trace-back extension module  710 , a signal path  708 , a codeword-decoding module  306  and a data-checking module  308 . 
     The trellis in the decoding system  700  is initialized in the same way as the one in the system  400 . Processing the receiving codeword by using a sliding window algorithm is completed in the same way as it is for the system  600 . When the process of decoding the receiving codeword reaches the end of the bit stream  302 , the ML decoder repeats the process from the beginning of the bit stream  302  for a predetermined number of time instances w t     f   , where w t     f   &gt;5 log 2  S. Afterwards, the trace-back module  330  randomly selects an active state at time instance t f  and runs the trace-back algorithm. 
     The trace-back extension module  710  traces back the part of the simplified trellis diagram, between t 0  and t f , of size w t     f    twice. This operation is performed by using the variables M and A that are initialized according to the preceding window. 
     The trace-back module  330  identifies an ML path that corresponds to the code sequence representing the receiving codeword. The ML path comprises partial ML paths of each window. After the decoded data is obtained, it is forwarded to the data-checking module  308 . The data-checking module  308  either obtains correct decoded data or exhausts all the alternative codewords. During the decoding process, it is important not to generate duplicate ML paths in the overlapping area of the windows. 
     The above illustration provides many different embodiments or embodiments for implementing different features of the invention. Specific embodiments of components and processes are described to help clarify the invention. These are, of course, merely embodiments and are not intended to limit the invention from that described in the claims. 
     Although the invention is illustrated and described herein as embodied in one or more specific examples, it is nevertheless not intended to be limited to the details shown, since various modifications and structural changes may be made therein without departing from the spirit of the invention and within the scope and range of equivalents of the claims. Accordingly, it is appropriate that the appended claims be construed broadly and in a manner consistent with the scope of the invention, as set forth in the following claims.