Abstract:
In the coding device and method, m-bit information words are converted into n-bit code words such that the coding rate m/n is greater than ⅔. The n-bit code words are divided into a first type and a second type, and into coding states of a first kind and a second kind such that an m-bit information word is converted into an n-bit code word of the first or second kind if the previous m-bit information word was converted into an n-bit code word of the first type and is converted into an n-bit code word of the first kind if the previous m-bit information word was converted into an n-bit code word of the second type. In one embodiment, n-bit code words of the first type end in zero, n-bit code words of the second type end in one, n-bit code words of the first kind start with zero, and n-bit code words of the second kind start with zero or one. Furthermore, in the embodiments, the n-bit code words satisfy a dk-constraint of (1, k) such that a minimum of 1 zero and a maximum of k zeros falls between consecutive ones. The coding device and method are employed to record information on a recording medium and thus create the recording medium. The coding device and method are further employed to transmit information. In the decoding method and apparatus, n-bit code words are decoded into m-bit information words. The decoding involves determining the state of a next n-bit code word, and based on the state determination, the current n-bit code word is converted into an m-bit information word. The decoding device and method are employed to reproduce information from a recording medium, and to receive information transmitted over a medium.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]     The present application is a continuation of application Ser. No. 09/707,947 filed on Nov. 8, 2000, and claims priority under 35 U.S.C. §119 to EPO Patent Application No. 99203739.0, filed Nov. 11, 1999, the entire contents of which are hereby incorporated by reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates to coding information, and more particularly, to a method and apparatus for coding information having improved information density. The present invention further relates to producing a modulated signal from the coded information, producing a recording medium from the coded information, and the recording medium itself. The present invention still further relates to a method and apparatus for decoding coded information, and decoding coded information from a modulated signal and/or a recording medium.  
       BACKGROUND OF THE INVENTION  
       [0003]     When data is transmitted through a transmission line or recorded onto a recording medium such as a magnetic disc, an optical disc or a magneto-optical disc, the data is modulated into code matching the transmission line or the recording medium prior to the transmission or recording.  
         [0004]     Run length limited codes, generically designated as (d, k) codes, have been widely and successfully applied in modern magnetic and optical recording systems. Such codes, and means for implementing such codes are described by K. A. Schouhamer Immink in the book entitled “Codes for Mass Data Storage Systems” (ISBN 90-74249-23-X, 1999). Run length limited codes are extensions of earlier non return to zero recording codes, where binary recorded “zeros” are represented by no (magnetic flux) change in the recording medium, while binary “ones” are represented by transitions from one direction of recorded flux to the opposite direction.  
         [0005]     In a (d, k) code, the above recording rules are maintained with the additional constraints that at least d “zeros” are recorded between successive “ones”, and no more than k “zeros” are recorded between successive “ones”. The first constraint arises to obviate intersymbol interference occurring because of pulse crowding of the reproduced transitions when a series of “ones” are contiguously recorded. The second constraint arises to ensure recovering a clock from the reproduced data by “locking” a phase locked loop to the reproduced transitions. If there is too long an unbroken string of contiguous “zeros” with no interspersed “ones”, the clock regenerating phase-locked-loop will fall out of synchronism. In, for example, a (1,7) code there is at least one “zero” between recorded “ones”, and there are no more than seven recorded contiguous “zeros” between recorded “ones”.  
         [0006]     The series of encoded bits is converted, via a modulo-2 integration operation, to a corresponding modulated signal formed by bit cells having a high or low signal value. A “one” bit is represented in the modulated signal by a change from a high to a low signal value or vice versa, and a “zero” bit is represented by the lack of change in the modulated signal.  
         [0007]     The information conveying efficiency of such codes is typically expressed as a rate, which is the quotient of the number of bits (m) in the information word to the number of bits (n) in the code word (i.e., m/n). The theoretical maximum rate of a code, given values of d and k, is called the Shannon capacity.  FIG. 1  tabulates the Shannon capacity C(d, k) for d=1 versus k. As shown, for a (1,7) code, the Shannon capacity, C(1,7), has a value of 0.67929. This means that a (1,7) code cannot have a rate larger than 0.67929. The practical implementation of codes requires that the rate be a rational fraction, and to date the above (1,7) code has a rate ⅔. This rate of ⅔ is slightly less than the Shannon capacity of 0.67929, and the code is therefore a highly efficient one. To achieve the ⅔ rate, 2 unconstrained data bits are mapped into 3 constrained encoded bits.  
         [0008]     (1,7) codes having a rate of ⅔ and means for implementing associated encoders and decoders are known in the art. U.S. Pat. No. 4,413,251 entitled “Method and Apparatus for Generating A Noiseless Sliding Block Code for a (1,7) Channel with Rate ⅔”, issued in the names of Adler et al., discloses an encoder which is a finite-state machine having 5 internal states. U.S. Pat. No. 4,488,142 entitled “Apparatus for Encoding Unconstrained Data onto a (1,7) Format with Rate ⅔”, issued in the name of Franaszek discloses an encoder having 8 internal states.  
         [0009]     However, a demand exists for even more efficient codes so that, for example, the information density on a recording medium or over a transmission line can be increased.  
       SUMMARY OF THE INVENTION  
       [0010]     In the converting method and apparatus according to the present invention, m-bit information words are converted into n-bit code words at a rate greater than ⅔. Consequently, the same amount of information can be recorded in less space, and information density increased.  
         [0011]     In the present invention, n-bit code words are divided into a first type and a second type, and into coding states of a first kind and a second kind such that an m-bit information word is converted into an n-bit code word of the first or second kind if the previous m-bit information word was converted into an n-bit code word of the first type and is converted into an n-bit code word of the first kind if the previous m-bit information word was converted into an n-bit code word of the second type. In one embodiment, n-bit code words of the first type end in zero, n-bit code words of the second type end in one, n-bit code words of the first kind start with zero, and n-bit code words of the second kind start with zero or one. Furthermore, in the embodiments according to the present invention, the n-bit code words satisfy a dk-constraint of (1, k) such that a minimum of 1 zero and a maximum of k zeros falls between consecutive ones.  
         [0012]     In other embodiments of the present invention, the coding device and method according to the present invention are employed to record information on a recording medium and create a recording medium according to the present invention.  
         [0013]     In still other embodiments of the present invention, the coding device and method according to the present invention are further employed to transmit information.  
         [0014]     In the decoding method and apparatus according to the present invention, n-bit code words created according to the coding method and apparatus are decoded into m-bit information words. The decoding involves determining the state of a next n-bit code word, and based on the state determination, the current n-bit code word is converted into an m-bit information word.  
         [0015]     In other embodiments of the present invention, the decoding device and method according to the present invention are employed to reproduce information from a recording medium.  
         [0016]     In still other embodiments of the present invention, the decoding device and method according to the present invention are employed to receive information transmitted over a medium. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0017]     The present invention will become more fully understood from the detailed description given herein below and the accompanying drawings which are given by way of illustration only, wherein like reference numerals designate corresponding parts in the various drawings, and wherein:  
         [0018]      FIG. 1  tabulates the Shannon capacity C(d, k) for d=1 versus k;  
         [0019]      FIG. 2  shows an example of how the code words in the various subgroups are allocated in to the various states in the first embodiment;  
         [0020]      FIG. 3  shows an embodiment for a coding device according to the invention;  
         [0021]      FIGS. 4A-4H  show a complete translation table according to the first embodiment for converting 9-bit information words into 13-bit code words;  
         [0022]      FIG. 5  illustrates the conversion of a series of information words into a series of code words using the translation table of  FIGS. 4A-4H ;  
         [0023]      FIG. 6  illustrates an embodiment of a recording device according to the present invention;  
         [0024]      FIG. 7  illustrates a recording medium and modulated signal according to the present invention;  
         [0025]      FIG. 8  illustrates a transmission device according to the present invention;  
         [0026]      FIG. 9  illustrates a decoding device according to the present invention;  
         [0027]      FIG. 10  illustrates a reproducing device according to the present invention;  
         [0028]      FIG. 11  illustrates a receiving device according to the present invention;  
         [0029]      FIG. 12  shows an example of how the code words in the various subgroups are allocated in to the various states in the second embodiment;  
         [0030]      FIGS. 13A-13C  show the beginning, middle and end portions of a translation table according to the second embodiment for converting 9-bit information words into 13-bit code words;  
         [0031]      FIG. 14  shows an example of how the code words in the various subgroups are allocated in to the various states in the third embodiment;  
         [0032]      FIGS. 15A-15C  show the beginning, middle and end portions of a translation table according to the third embodiment for converting 11-bit information words into 16-bit code words  
         [0033]      FIG. 16  shows an example of how the code words in the various subgroups are allocated in to the various states in the fourth embodiment; and  
         [0034]      FIGS. 17A-17C  show the beginning, middle and end portions of a translation table according to the fourth embodiment for converting 13-bit information words into 19-bit code words. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0035]     The general coding method according to the present invention will be described followed by a specific first embodiment of the coding method. Next, the general decoding method according to the present invention will be described in the context of the first embodiment. The various apparatuses according to the present invention will then be described. Specifically, the coding device, recording device, transmission device, decoding device, reproducing device and receiving device according to the present invention will be described. Afterwards, additional coding embodiments according to the present invention will be described.  
         [heading-0036]     Coding Method  
         [0037]     According to the present invention, an m-bit information word is converted into an n-bit code word such that the rate of m/n is greater than ⅔. The code words are divided into first and second types wherein the first type includes code words ending with “0” and the second type includes code words ending with “1.” As a result, the code words of the first type are divided into two subgroups E00 and E10, and code words of the second type are divided into two subgroups E01 and E11. Code word subgroup E00 includes code words that start with “0” and end with “0”, code word subgroup E01 includes code words that start with “0” and end with “1”, code word subgroup E10 includes code words that start with “1” and end with “0”, and code word subgroup E11 includes code words that start with “1” and end with “1”.  
         [0038]     The code words are also divided into at least one state of a first kind and at least one state of a second kind. States of the first kind include code words that only start with “0,” and states of the second kind include code words that start with either “0” or “1.” 
         [heading-0039]     Coding Method According to a First Embodiment  
         [0040]     In a first preferred embodiment of the present invention, 9-bit information words are converted into 13-bit code words. The code words satisfy a (d, k) constraint of (1, k), and are divided into 3 states of the first kind and 2 states of the second kind (a total of 5 states). In order to reduce the k-constraint, three code words, namely, “0000000000000”, “0000000000001”, and “0000000000010” are barred from the encoding tables. An enumeration of code words shows there are 231 code words in subgroup E00, 144 code words in subgroup E10, 143 code words in subgroup E01, and 89 code words in subgroup E11.  
         [0041]     To perform encoding, each 13-bit code word in each state is associated with a coding state direction. The state direction indicates the next state from which to select a code word in the encoding process. The state directions are assigned to code words such that code words that end with a “0” (i.e. code words in subgroups E10 and E00) have associated state directions that indicate any of the r=5 states, while code words that end with a “1” (i.e., code words in subgroups E01 and E11) have associated state directions that only indicate one of the states of the first kind. This ensures that the d=1 constraint will be satisfied; namely, after a code word ending in “1”, the next code word will start with “0”.  
         [0042]     Furthermore, while, as explained in more detail below, the same code word can be assigned to different information words in the same state, different states cannot include the same code word. In particular code words in subgroups E10 and E00 can be assigned 5 times to different information words within one state, while code words in subgroups E11 and E01 can be assigned 3 times to different information words within one state. As there are 231 code words in subgroup E00 and 144 code words in subgroup E10, there are 1875 (5*(231+144)) “code word-state direction” combinations for code words of the first type. There are 143 code words in subgroup E01 and 89 code words in E11, so that there are 696 (3*(143+89)) “code word-state direction” combinations for code words of the second type. In total 1875+696=2571 “code word-state direction” combinations exist.  
         [0043]     For m-bit information words, there are a total of 2 m  possible information words. So, for 9-bit information words, 2 9 =512 information words exist. Because there are five states in this encoding embodiment, 5 times 512=2561 of the “code word-state direction” combinations are needed. This leaves 2571−2561=10 remaining combinations.  
         [0044]     The available code words in the various subgroups are distributed over the states of the first and second kind in compliance with the restrictions discussed above.  FIG. 2  shows an example of how the code words in the various subgroups are allocated in this embodiment to the various states. As shown in  FIG. 2 , in this example, states  1 ,  2 , and  3  are states of the first kind and states  4  and  5  are states of the second kind. Taking the subgroup E00 of size 230 as an example, subgroup E00 has 76 code words in each of states  1 ,  2 , and  3  plus 1 code word in each of states  4  and  5 . And, taking state  1  as an example, in state  1  the number of “code word-state direction” combinations is 5×76+3×44=512, which means that 9-bit information words can be assigned. Remember, each code word of the first type can be assigned any one of the five different states as a state directions, and therefore used five time within a state; while each code word of the second type can only be assigned one of the three states of the first kind as a state direction because of the d=1 restriction, and therefore used three times within a state.  
         [0045]     It can be verified that from any of the r=5 coding states shown in  FIG. 2  there at least 512 information words that can be assigned to code words, which is enough to accommodate 9-bit information words. In the manner described above any random series of 9-bit information words can be uniquely converted to a series of code words.  
         [0046]      FIGS. 4A-4H  show a complete translation table according to this embodiment for converting 9-bit information words into 13-bit code words. Included in the translation table of  FIGS. 4A-4H  are the state direction assigned to each code word. Specifically, in  FIGS. 4A-4H , the first column shows the decimal notation of the information words in the second column. The third, fifth, seventh, ninth and eleventh columns show the code words (also referred to in the art as channel bits) assigned to the information words in states  1 ,  2 ,  3 ,  4  and  5 , respectively. The fourth, sixth, eighth, tenth and twelfth columns show by way of the respective digits  1 ,  2 ,  3 ,  4  and  5  the state direction of the associated code words in the third, fifth, seventh, ninth and eleventh columns, respectively.  
         [0047]     The conversion of a series of information words into a series of code words will be further explained with reference to  FIG. 5 . The first column of  FIG. 5  shows from top to bottom a series of successive 9-bit information words, and the second column shows in parenthesis the decimal values of these information words. The third column “state” is the coding state that is to be used for the conversion of the information word. The “state” is laid down when the preceding code word was delivered (i.e., the state direction of the preceding code word). The fourth column “code words” includes the code words assigned to the information words according to the translation table of FIGS.  4 A-H. The fifth column “next state” is the state direction associated with the code word in the fourth column and is also determined according to the translation table of FIGS.  4 A-H.  
         [0048]     The first word from the series of information words shown in the first column of  FIG. 5  has a word value of “1” in decimal notation. Let us assume that the coding state is state  1  (S 1 ) when the conversion of the series of information words is initiated. Therefore the first word is translated into code word “0000000000100” according to the state  1  set of code words from the translation table. At the same time the next state becomes state  2  (S 2 ) because the state direction assigned to code word “0000000000100” representing decimal value 1 in state  1  is state  2 . This means that the next information word (decimal value “3”) is going to be translated using the code words in state  2 . Consequently, the next information word, having a decimal value of “3”, is translated into code word “0001010001010”. Similar to the manner described above, the information words having the decimal values “5”, “12” and “19” are converted.  
         [heading-0049]     Decoding Method  
         [0050]     Hereinafter, decoding of n-bit code words (in this example 13-bit words) received from a recording medium will be further explained with reference to  FIGS. 4A-4H . For the purposes of description, assume that the word values of a series of successive code words received from, for example, a recording medium are “0000000000100”, “0001010001010”, “0101001001001”. From the translation table of  FIGS. 4A-4H , it is found that the first code word “0000000000100” is assigned to the information words “0”, “1”, “2”, “3” and “4” and state directions  1 ,  2 ,  3 ,  4  and  5 , respectively. The next code word value is “0001010001010”, and belongs to the set of code words in state  2 . This means that the first code word “0000000000100” had a state direction of  2 . The first code word “0000000000100” with a state direction of  2  represents the information word having a decimal value of “1”. Therefore, it is determined that the first code word represents information word “000000001” having a decimal value of “1”.  
         [0051]     Furthermore, the third code word “0101001001001” is a member of state  4 . Therefore, it is determined in the same manner as above that the second code word “0001010001010” represents the information word having the decimal value “3”. In the same manner other code words can be decoded. It is noted that both the current code word and the next code words are observed to decode the current code word into a unique information word.  
         [heading-0052]     Coding Device  
         [0053]      FIG. 3  shows an embodiment for a coding device  124  according to the invention. The coding device  124  converts m-bit information words into n-bit code words, where the number of different coding states r is represented by s bits. For example, when the number of coding states r=5, s equals 3. As shown, the coding device  124  includes a converter  50  for converting (m+s) binary input signals to (n+s) binary output signals. In a preferred embodiment, the converter  50  includes a read only memory (ROM) storing a translation table according to at least one embodiment of the present invention and address circuitry for addressing the translation table based on the m+s binary input signals. However, instead of a ROM, the converter  50  can include a combinatorial logic circuit producing the same results as the translation table according to at least one embodiment of the present invention.  
         [0054]     From the inputs of the converter  50 , m inputs are connected to a first bus  51  for receiving m-bit information words. From the outputs of the converter  50 , n outputs are connected to a second bus  52  for delivering n-bit code words. Furthermore, s inputs are connected to an s-bit third bus  53  for receiving a state word that indicates the instantaneous coding state. The state word is delivered by a buffer memory  54  including, for example, s flip-flops. The buffer memory  54  has s inputs connected to a fourth bus  55  for receiving a state direction to be loaded into the buffer memory  54  as the state word. For delivering the state directions to be loaded in the buffer memory  54 , the s outputs of the converter  50  are used.  
         [0055]     The second bus  52  is connected to the parallel inputs of a parallel-to-serial converter  56 , which converts the code words received over the second bus  52  to a serial bit string. A signal line  57  supplies the serial bit string to a modulator circuit  58 , which converts the bit string into a modulated signal. The modulated signal is then delivered over a line  60 . The modulator circuit  58  is any well-known circuit for converting binary data into a modulated signal such as a modula-2 integrator.  
         [0056]     For the purposes of synchronizing the operation of the coding device, the coding device includes a clock generating circuit (not shown) of a customary type for generating clock signals for controlling timing of, for example, the parallel/serial converter  58  and the loading of the buffer memory  54 .  
         [0057]     In operation, the converter  50  receives m-bit information words and an s-bit state word from the first bus  51  and the third bus  53 , respectively. The s-bit state word indicates the state in the translation table to use in converting the m-bit information word. Accordingly, based on the value of the m-bit information word, the n-bit code word is determined from the code words in the state identified by the s-bit state word. Also, the state direction associated with the n-bit code word is determined. The state direction, namely, the value thereof is converted into an s-bit binary word; or alternatively, the state directions are stored in the translation table as s-bit binary words. The converter  50  outputs the n-bit code word on the second bus  52 , and outputs the s-bit state direction on fourth bus  55 . The buffer memory  54  stores the s-bit state direction as a state word, and supplies the s-bit state word to the converter  50  over the third bus  53  in synchronization with the receipt of the next m-bit information word by the converter  50 . This synchronization is produced based on the clock signals discussed above in any well-known manner.  
         [0058]     The n-bit code words on the second bus  52  are converted to serial data by the parallel/serial converter  56 , and then the serial data is converted into a modulated signal by the modulator  58 .  
         [0059]     The modulated signal may then undergo further processing for recordation or transmission.  
         [heading-0060]     Recording Device  
         [0061]      FIG. 6  shows a recording device for recording information that includes the coding device  124  according to the present invention as shown in  FIG. 3 . As shown in  FIG. 6 , m-bit information is converted into a modulated signal through the coding device  124 . The modulated signal produced by the coding device  124  is delivered to a control circuit  123 . The control circuit  123  may be any conventional control circuit for controlling an optical pick-up or laser diode  122  in response to the modulated signal applied to the control circuit  123  so that a pattern of marks corresponding to the modulated signal are recorded on the recording medium  110 .  
         [0062]      FIG. 7  shows by way of example, a recording medium  110  according to the invention. The recording medium  110  shown is a read-only memory (ROM) type optical disc. However, the recording medium  110  of the present invention is not limited to a ROM type optical disk, but could be any type of optical disk such as a write-once read-many (WORM) optical disk, random accessible memory (RAM) optical disk, etc. Further, the recording medium  110  is not limited to being an optical disk, but could be any type of recording medium such as a magnetic disk, a magneto-optical disk, a memory card, magnetic tape, etc.  
         [0063]     As shown in  FIG. 7 , the recording medium  110  according to one embodiment of the present invention includes information patterns arranged in tracks  111 . Specifically,  FIG. 7  shows an enlarged view of a track  111  along a direction  114  of the track  111 . As shown, the track  111  includes pit regions  112  and non-pit regions  113 . Generally, the pit and non-pit regions  112  and  113  represent constant signal regions of the modulated signal  115  (zeros in the code words) and the transitions between pit and non-pit regions represent logic state transitions in the modulated signal  115  (ones in the code words).  
         [0064]     As discussed above, the recording medium  110  may be obtained by first generating the modulated signal and then recording the modulated signal on the recording medium  110 . Alternatively, if the recording medium is an optical disc, the recording medium  110  can also be obtained with well-known mastering and replica techniques.  
         [heading-0065]     Transmission Device  
         [0066]      FIG. 8  shows a transmission device for transmitting information that includes the coding device  124  according to the present invention as shown in  FIG. 3 . As shown in  FIG. 8 , m-bit information words are converted into a modulated signal through the coding device  124 . A transmitter  150  then further processes the modulated signal, to convert the modulated signal into a form for transmission depending on the communication system to which the transmitter belongs, and transmits the converted modulated signal over a transmission medium such as air (or space), optical fiber, cable, a conductor, etc.  
         [heading-0067]     Decoding Device  
         [0068]      FIG. 9  illustrates a decoder according to the present invention. The decoder performs the reverse process of the converter of  FIG. 3  and converts n-bit code words of the present invention into m-bit information words. As shown, the decoder  100  includes a first look-up table (LUT)  102  and a second LUT  104 . The first and second LUTs  102  and  104  store the translation table used to create the n-bit code words being decoded. Where K refers to time, the first LUT  102  receives the (K+1)th n-bit code word and the second LUT  104  receives the output of the first LUT  102  and the Kth n-bit code word. Accordingly, the decoder  100  operates as a sliding block decoder. At every block time instant the decoder  100  decodes one n-bit code word into one m-bit information word and proceeds with the next n-bit code word in the serial data (also referred to as the channel bit stream).  
         [0069]     In operation, the first LUT  102  determines the state of the (K+1)th code word from the stored translation table, and outputs the state to the second LUT  104 . So the output of the first LUT  102  is a binary number in the range of 1, 2, . . . , r (where r denotes the number of states in the translation table). The second LUT  104  determines the possible m-bit information words associated with Kth code word from the Kth code word using the stored translation table, and then determines the specific one of the possible m-bit information words being represented by the n-bit code word using the state information from the first LUT  102  and the stored translation table.  
         [0070]     For the purposes of further explanation only, assume the n-bit code words are 13-bit code words produced using the translation table of  FIGS. 4A-4H . Then, referring to  FIG. 5 , if the (K+1)th 13-bit code word is “0001010001010” the first LUT  102  determines the state as state  2 . Furthermore, if the Kth 13-bit code word is “0000000000100”, then the second LUT  104  determines that the Kth 13-bit code word represents one of the 9-bit information words having a decimal value of 0, 1, 2, 3 or 4. And, because the next state or state direction of state  2  is supplied by the first LUT  102 , the second LUT  104  determines that the Kth 13-bit code word represents the 9-bit information word having a decimal value of 1 because the 13-bit code word “0000000000100” associated with a state direction of  2  represents the 9-bit information word having a decimal value of 1.  
         [heading-0071]     Reproducing Device  
         [0072]      FIG. 10  illustrates a reproducing device that includes the decoder  100  according to the present invention as shown in  FIG. 9 . As shown, the reading device includes an optical pick-up  122  of a conventional type for reading a recording medium  110  according to the invention. The recording medium  110  may be any type of recording medium such as discussed previously. The optical pick-up  122  produces an analog read signal modulated according to the information pattern on the recording medium  110 . A detection circuit  125  converts this read signal in conventional fashion into a binary signal of the form acceptable to the decoder  100 . The decoder  100  decodes the binary signal to obtain the m-bit information words.  
         [heading-0073]     Receiving Device  
         [0074]      FIG. 11  illustrates a receiving device that includes the decoder  100  according to the present invention as shown in  FIG. 9 . As shown, the receiving device includes a receiver  160  for receiving a signal transmitted over a medium such as air (or space), optical fiber, cable, a conductor, etc. The receiver  160  converts the received signal into a binary signal of the form acceptable to the decoder  100 . The decoder  100  decodes the binary signal to obtain the m-bit information words.  
         [heading-0075]     Coding Method According to a Second Embodiment  
         [0076]      FIGS. 12 and 13 A- 13 C illustrate another embodiment of the present invention. According to this embodiment, the greater than ⅔ rate is achieved by converting 9-bit information words into 13-bit code words; wherein the number of coding states r equals 13, and 8 of the coding states are coding states of the first kind and 5 of the coding states are coding states of the second kind. Also, the code words satisfy a (d, k) constraint of (1, k).  FIG. 12  corresponds to  FIG. 2  of the first embodiment, and illustrates the division of code words among the states in this second embodiment.  
         [0077]     As described above, code words that end with a “0”, i.e. code words in subgroups E00 and E10, are allowed to enter any of the r=13 states, while code words that end with a “1” i.e. code words in subgroups E01 and E11, may only enter the states of the first kind(State  1  to State  8 ).  
         [0078]     Therefore, code words in subgroups E00 and E10 can be assigned 13 times to different information words, while code words in subgroups E01 and E11 can be assigned 8 times to different information words. Referring to  FIG. 12 , subgroup E00 has 24 code words in state  1  and the subgroup E01 has 25 code words in state  1 . So the number of “code words-state direction” combinations is (13×24)+(8×25)=512, which means that 9-bit information words can be assigned. It can be verified that from any of the r=13 coding states there at least 512 information words that can be assigned to code words, which is enough to accommodate 9-bit information words.  
         [0079]      FIGS. 13A-13C  illustrate the beginning, middle and end portions of the translation table for this second embodiment in the same fashion that  FIGS. 4A-4H  illustrated the translation table for the first embodiment.  
         [heading-0080]     Coding Method According to a Third Embodiment  
         [0081]      FIGS. 14 and 15 A- 15 C illustrate another embodiment of the present invention. According to this embodiment, the greater than ⅔ rate is achieved by converting 11-bit information words into 16-bit code words; wherein the number of coding states r equals 13, and 8 of the coding states are coding states of the first kind and 5 of the coding states are coding states of the second kind. Also, the code words satisfy a (d, k) constraint of (1, k).  FIG. 14  corresponds to  FIG. 2  of the first embodiment, and illustrates the division of code words among the states in this third embodiment. It can be verified that from any of the r=13 coding states there at least 2048 information words that can be assigned to code words, which is enough to accommodate 11-bit information words.  
         [0082]      FIGS. 15A-15C  illustrate the beginning, middle and end portions of the translation table for the third embodiment in the same fashion that  FIGS. 4A-4H  illustrated the translation table for the first embodiment.  
         [heading-0083]     Coding Method According to a Fourth Embodiment  
         [0084]      FIGS. 16 and 17 A- 17 C illustrate another embodiment of the present invention. According to this embodiment, the greater than ⅔ rate is achieved by converting 13-bit information words into 19-bit code words; wherein the number of coding states r equals 5, and 3 of the coding states are coding states of the first kind and 2 of the coding states are coding states of the second kind. Also, the code words satisfy a (d, k) constraint of (1, k).  FIG. 16  corresponds to  FIG. 2  of the first embodiment, and illustrates the division of code words among the states in this fourth embodiment. It can be verified that from any of the r=5 coding states there at least 8192 information words that can be assigned to code words, which is enough to accommodate 13-bit information words.  
         [0085]      FIGS. 17A-17C  illustrate the beginning, middle and end portions the translation table for the fourth embodiment in the same fashion that  FIGS. 4A-4H  illustrated the translation table for the first embodiment.  
         [0086]     The invention has been described in detail with particular reference to preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention.