Abstract:
A method and apparatus encoding and decoding data for storage on a mass storage device is described. The code used is a 5/6 rate code in which a maximum transition run constraint is imposed. This code is designed for use with an EEPR4 read channel and provides a Euclidian squared free distance, d 2 free, of 10 when used with an EEPR4 partial response filter and a Viterbi decoder.

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to the field of coding data; particularly, the present invention relates to encoding of data for use with a partial response maximum-likelihood read channel. 
     BACKGROUND OF THE INVENTION 
     This invention relates to coding techniques for use with magnetic storage media. Designs for magnetic storage media systems must simultaneously maximize the density of information stored on the media and ensure that the storage system has adequate error tolerance. These two goals are always in tension. The features of a read channel that maximize the permissible storage density on the storage media also tend to reduce the error tolerance of the storage device and read channel. 
     Storage density can be maximized with the use of a partial response maximum likelihood (PRML) read channel. A PRML read channel always includes a partial response filter and a maximum likelihood decoder. The partial response filter provides an output signal that represents a mathematical combination of the stored bits from a moving window of adjacent bits in the sequence of stored bits on the magnetic media. The output of the filter is then fed to a decoder that determines the sequence of bits most likely to have produced the filter output. Use of a partial response filter in the read channel permits higher density storage of data on the magnetic media. See H. Kobayashi, D. T. Tang, “Application of Partial-responsc Channel Coding to Magnetic Recording Systems”,  IBM Journal of Research &amp; Development , July 1970, pp. 368-375. 
     The decoder in a PRML read channel uses a maximum-likelihood sequence detection algorithm such as the Viterbi algorithm. The decoder converts the output of the partial response filter into a sequence of binary values representing the sequence of bits stored onto the magnetic media. Methods for decoding PRML read channels using trellis decoders are shown, for example, in Jack W. Wolf &amp; Gottfried Ungerboeck, “Trellis Coding for Partial Response Channels,”  IEEE Transactions on Communications , vol. COM-34, Aug. 1986, pp. 765-773, and G. David Forney, “The Viterbi Algorithm,”  Proceedings of the IEEE , March 1973, pp. 268-278, which are herein incorporated by reference. 
     Write and read channels for magnetic storage devices often employ encoding of the sequence of bits that is to be stored on the magnetic device. Encoding of the symbols to be recorded onto the magnetic storage media can be used to increase the noise tolerance of the entire system. The most common measure of noise signal tolerance of a trellis decoder is the minimum free squared Euclidean distance of the set of permissible paths through the trellis, d 2   free . The minimum free squared Euclidean distance measures the minimum difference in the path distance of any two paths in the trellis that start and end at the same node. One method of increasing the minimum free squared Euclidean distance of a read channel is to encode the sequence of symbols that are to be recorded onto the magnetic storage media. Encoding limits the set of permissible trellis paths and can be used to disallow alternative trellis paths that produce the worst case minimum free squared Euclidean distance measure. By disallowing these paths, the minimum free squared Euclidean distance of the remaining paths is improved. 
     Encoding, however, comes at a cost in that it expands the number of bits required to store a fixed amount of user source data on the disk. The rate of a code indicates the relationship between the number of bits of user data encoded and the number of bits of encoded data stored on the storage media. In a rate 5/6 code, five bits of user data are encoded into six bits of encoded data that are stored. It is always possible to increase the minimum free squared Euclidean distance of any encoding scheme by increasing the coding overhead and decreasing the rate of the code. Increasing the rate of the code used necessitates a decrease in the storage density that may be used. 
     One type of code that can be used for encoding is the class of Maximum Transition Run (MTR) codes. MTR codes have the property that the number of consecutive ‘1’ symbols is limited to some maximum transition run length. In the non return to zero inverse (NRZI) convention often used in analysis of magnetic storage systems, a ‘1’ symbol indicates the existence of a transition in the magnetic state stored, and a ‘0’ symbol indicates that the current state is maintained. The MTR code used in the subject invention limits the maximum sequence of consecutive ‘1’ symbols to two. Limiting the number of consecutive ‘1’ symbols to two is equivalent to limiting the number of consecutive state transitions to two or less. Patterns of three or more consecutive transitions cause most of the errors in read channel detection systems, so using codes that eliminate these patterns produces significant error reduction dividends. See Jaekyun Moon &amp; Barrett Brickner, “Maximum Transition Run Codes for Data Storage Systems,”  IEEE Transactions oil Magnetics , vol. 32, September 1996, pp. 3992-3994. 
     The central problem, therefore, for any designer of encoding and decoding channels for a storage device is to develop a coding procedure which maximizes the density of user data that may be stored on the magnetic media. This involves a trade-off between the coding rate used and the density of storage that may be achieved using any particular code. The designer&#39;s goal is to develop a code which maximizes the coding rate and provides a minimum free squared Euclidean distance that ensures the error detection margin required to support a particular storage density. 
     SUMMARY OF THE INVENTION 
     The present invention describes an apparatus and a method for encoding and decoding data. The inventive encoding system can be used with a storage medium that employs a partial response filter with the transfer function h(D)=(1−D)(1+D) 3 , where D represents the delay operator. This is known as an extended-extended partial response channel of Class 4 (EEPR4). 
     The subject encoding system and read channel employ a rate 5/6 code. The code is an MTR code with the property that codewords are selected so that runs of consecutive ‘1’ symbols are limited to two or less ‘1’ symbols, and runs of consecutive ‘0’ symbols are limited to runs of six or less of such ‘0’ symbols. For this reason the code can be identified as a rate 5/6 MTR(2,6) code. 
     The code employed in the inventive encoding system and read channel has a minimum free squared Euclidean distance of 10, when used with an EEPR4 read channel. This value is large enough to provide an adequate margin of error for use in a magnetic disk drive system. Use of this code makes it possible to use an EEPR4 filter in the read channel, which would not be possible if a coding scheme with a lesser minimum free squared Euclidean distance was used. 
     An advantage of the present invention is that it provides a high density, rate 5/6 code that affords a minimum free squared Euclidean distance of 10 when used in an EEPR4 system. 
     Another advantage of the present invention is that it permits the use of an EEPR4 read channel, which makes possible higher read densities than would be afforded with lower-order partial response filters. 
     The foregoing, and other features and advantages of the invention, will be apparent from the following, more particular, description of the preferred embodiments of the invention, the accompanying drawings and the appended claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram illustrating the overall architecture of a write encoder and read channel decoder that can be used to implement the present invention. 
     FIG. 2 is an idealized EEPR4 partial response filter in accordance with the present invention. 
     FIG. 3 is a decoding trellis for use by a Viterbi detector in detecting an EEPR4 filtered signal in accordance with the present invention. 
     FIG. 4 is a sequence of boolean equations that can be used to implement the encoding algorithm performed by the rate 5/6 MTR encoder of the present invention. 
     FIG. 5 is a sequence of boolean equations that can be used to implement the decoding algorithm performed by the rate 5/6 MTR decoder of the present invention. 
     FIG. 6 is a block diagram illustrating the overall architecture of a disk drive storage device built utilizing the write encoder and read channel decoder of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The preferred embodiment of the present invention and its advantages are best understood by reference to FIGS. 1 through 6, where like reference numbers indicate like elements. 
     FIG. 1 illustrates a functional block diagram of the write encoder  20  and read channel decoder  30  for a hard disk drive system. The bidirectional interface  10  interconnects the write encoding circuitry and read channel circuit with a drive controller (not shown) through I/O bus  11 . Data to be written to the hard disk drive is conveyed over bidirectional interface  10  to write encoder  20  where it is encoded. The output of write encoder  20  from the output buffer  24  is a differential analog signal which can be used with external magnetic read/write circuitry to write the data to the hard disk media. When data is read from the hard disk, the differential analog signal read from the disk is received by automatic gain control clement  31  in read channel decoder  30 . Read channel decoder  30  filters and decodes the signal to recover the data stored on the disk. The decoding performed by read channel decoder  30  reverses the encoding performed by write encoder  20  when the data was written to the disk. The decoded data is then transferred across I/O bus  11  to the drive controller. 
     The detailed operation of write encoder  20  will now be described. The external drive controller passes data that is to be written to write encoder  20  over I/O bus  11 . A rate 5/6 MTR encoder  21  is coupled to the bidirectional interface. Data that is to be written to the disk drive is received at bidirectional interface  10  in an unencoded fonn, and is passed through bidirectional interface  10  to rate 5/6 MTR encoder  21 . Rate 5/6 MTR encoder  21  converts this raw data into an encoded format, in accordance with the code described in detail below. This code encodes five bits of raw data received from the drive controller into six bits of encoded data that will be stored on the disk drive. While this has the effect of expanding the number of bits that must be stored on the disk drive, the use of the code permits denser storage of the drive media, more than offsetting the 20% overhead that results from the use of the 5/6 code. The output from the encoder can be thought of as a sequence of six-bit codewords {y k }(={y 0 , y 1 , . . . y k , . . . }), where each y k  represents a separate six-bit codeword. 
     Rate 5/6 MTR encoder  21  receives a sequence of symbols from interface circuitry  10 . Each received symbol is five-bits wide. Encoder  21  converts each five-bit symbol received into an encoded output symbol that is made up of six-bits. In the discussion that follows, and in accordance with standard practice, data words are identified as a sequence of ‘0’ and ‘1’ characters, with the most significant bit (MSB) on the left and the least significant bit (LSB) on the right. The “first” bit in the codeword is synonymous with the MSB and the “last” bit in the codeword is synonymous with the LSB. In practice, it is purely a matter of definition as to whether the LSB or MSB is transmitted first when a word is transmitted serially, and the disclosed system can be implemented either way. 
     Source and codewords are processed sequentially in time by write encoder  20 . This processing is pipelined so that processing of multiple codewords is proceeding simultaneously at different points in write encoder  20 . When code or source words are described as the “current” or “preceding” or “previous” words, this indicates the nature of the sequential relationship between the two words. The “current” word follows directly after the “previous” or “preceding” word in the sequence of code or source words that is processed by the encoder/read channel. 
     The encoding algorithm used by rate 5/6 MTR encoder  21  has four steps. These steps must be performed in the order indicated. The operations performed in some of these steps are determined not only by the contents of the current source word but also by the encoded output codeword produced when the previous source word was encoded. 
     Step 1: 
     The first step of the conversion can be done as a table lookup. The five bits of the received symbol are used as an index into one of two translation tables. Each translation table includes 32 entries, so that each received sequence corresponds to a specific index in the table. Each entry in the table is occupied by a six-bit translation that will serve to represent the five-bit received symbol. The encoder determines which table to use based upon whether the previous encoded codeword had a ‘0’ or a ‘1’ in its last bit position. If the previous codeword had a ‘0’ in its last bit position, then the “State-0” table should be used, otherwise the “State-1” table is used. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 “STATE-0” Conversion Table 
               
             
          
           
               
                   
                 Input 
                 Output 
               
               
                   
                   
               
               
                   
                 00000 
                 000000 
               
               
                   
                 00001 
                 000001 
               
               
                   
                 00010 
                 000010 
               
               
                   
                 00011 
                 000001 
               
               
                   
                 00100 
                 000100 
               
               
                   
                 00101 
                 000101 
               
               
                   
                 00110 
                 000110 
               
               
                   
                 00111 
                 100101 
               
               
                   
                 01000 
                 001000 
               
               
                   
                 01001 
                 001001 
               
               
                   
                 01010 
                 001010 
               
               
                   
                 01011 
                 100100 
               
               
                   
                 01100 
                 001100 
               
               
                   
                 01101 
                 001101 
               
               
                   
                 01110 
                 100010 
               
               
                   
                 01111 
                 100000 
               
               
                   
                 10000 
                 010000 
               
               
                   
                 10001 
                 010001 
               
               
                   
                 10010 
                 010010 
               
               
                   
                 10011 
                 101001 
               
               
                   
                 10100 
                 010100 
               
               
                   
                 10101 
                 010101 
               
               
                   
                 10110 
                 010110 
               
               
                   
                 10111 
                 101101 
               
               
                   
                 11000 
                 011000 
               
               
                   
                 11001 
                 011001 
               
               
                   
                 11010 
                 011010 
               
               
                   
                 11011 
                 101100 
               
               
                   
                 11100 
                 101000 
               
               
                   
                 11101 
                 101010 
               
               
                   
                 11110 
                 110100 
               
               
                   
                 11111 
                 110101 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 “STATE-1” Conversion Table 
               
             
          
           
               
                   
                 Input 
                 Output 
               
               
                   
                   
               
               
                   
                 00000 
                 000000 
               
               
                   
                 00001 
                 000001 
               
               
                   
                 00010 
                 000010 
               
               
                   
                 00011 
                 000001 
               
               
                   
                 00100 
                 000100 
               
               
                   
                 00101 
                 000101 
               
               
                   
                 00110 
                 000110 
               
               
                   
                 00111 
                 100101 
               
               
                   
                 01000 
                 001000 
               
               
                   
                 01001 
                 001001 
               
               
                   
                 01010 
                 001010 
               
               
                   
                 01011 
                 100100 
               
               
                   
                 01100 
                 001100 
               
               
                   
                 01101 
                 001101 
               
               
                   
                 01110 
                 100010 
               
               
                   
                 01111 
                 100000 
               
               
                   
                 10000 
                 010000 
               
               
                   
                 10001 
                 010001 
               
               
                   
                 10010 
                 010010 
               
               
                   
                 10011 
                 101001 
               
               
                   
                 10100 
                 010100 
               
               
                   
                 10101 
                 010101 
               
               
                   
                 10110 
                 010110 
               
               
                   
                 10111 
                 101101 
               
               
                   
                 11000 
                 011000 
               
               
                   
                 11001 
                 011001 
               
               
                   
                 11010 
                 011010 
               
               
                   
                 11011 
                 101100 
               
               
                   
                 11100 
                 101000 
               
               
                   
                 11101 
                 101010 
               
               
                   
                 11110 
                 110010 
               
               
                   
                 11111 
                 110110 
               
               
                   
                   
               
             
          
         
       
     
     It will be observed that the “State-0” and “State-1” conversion tables differ only in the last two entries. 
     When the “States-1” table is used, the encoder must under undertake one additional step that does not apply when the “State-0” table is used. If the received source word sequence to be translated using the “State-1” table is either ‘11110’ or ‘11111’, the last bit of the previous codeword output of the encoder to use a different encoder must be inverted. The fact that the last bit has been inverted should not cause the encoder to use a different encoding table with the current source word. For example, if the previous encoded codeword is ‘110101’, the encoder will use the “State-1” table with the current source word. If the current source word is ‘11111’, the encoder must invert the last bit of the previous encoded codeword, making it ‘110100’. This does not, however, mean that the encoder should now use the “State-0” table to encode the current source word. Instead it will continue to use the “State-1” table, encoding ‘11111’ as ‘110110’. 
     Step 2: 
     If the translated six-bit output produced from Step 1 is ‘000000’ and the first bit of the following codeword is ‘0’, then the last two bits of the current codeword must be changed to logical ‘1’s so that the current codeword becomes ‘000011’. If this condition does not apply, the codeword passes through step two unchanged. 
     Step 3: 
     If the previous codeword has a ‘0’ as its last bit, and the current six-bit output produced from step two has five zeroes in its first five bits, then the first two bits of the current codeword are modified to become logical ones. If this condition does not apply, the codeword passes through step three unchanged. 
     Step 4: 
     If the previous codeword ends with a sequence of zeroes and the current codeword starts with a sequence of zeroes, and the combined length of these sequences is seven bits or greater, then the last two bits of the previous codeword are modified to become logical ones. If this condition does not apply, the codeword passes through step four unchanged. 
     The encoding steps performed by rate 5/6 MTR encoder  21  can be performed by a sequence of boolean logic operations. The boolean equations shown in FIG. 4 implement the function of rate 5/6 MTR encoder  21 . In these equations the five-bit symbol x k  represents the symbol that is provided as an input to rate 5/6 MTR encoder  21 . The binary variables X 1   k ,X 2   k ,X 3   k ,X 5   k , represent the five bits of symbol x k , with X 1   k  representing the first bit in the symbol and X 5   k  the last. The corresponding six-bit codeword produced as an output from rate 5/6 MTR encoder  21  is identified by the symbol y k . The six bits that make up y k , are identified as y 1   k , y 2   k , y 3   k , y 4   k , y 5   k , y 6   k . The input to rate 5/6 MTR encoder  21  is made up of a continuous sequence of five-bit symbols, x 1 , x 2 , . . . , x k−1 , x k , x k+1 , . . . . The output from rate 5/6 MTR encoder  21  is likewise made up of a continuous sequence of six-bit codewords, y 1 , y 2 , . . . , y k−1 , y k , y k+1 , . . . . The equations in FIG. 4 employ a number of intermediate variables, including a sequence of six-bit codewords g 1 , g 2 , . . . , g k−1 , g k , g k+1 , In the equations in FIG. 4, boolean logical OR operations are indicated as additions or with the ‘+’ symbol, and logical AND operations are indicated as multiplication of two binary symbols or with the ‘.’ symbol. 
     Turning again to FIG. 1, a parallel to serial converter  22  is coupled to the six-bit wide parallel output of rate 5/6 MTR encoder  21 . Parallel to serial converter  22  serializes the six-bit wide output of rate 5/6 MTR encoder  21 , which allows the encoded data to be written to the disk drive in a serial format. The serial output of parallel to serial converter  22 , which can be represented as serial binary sequence {w i }, is coupled to a write precompensation circuit ( 23 ). 
     The purpose of the precompensation circuit is to incrementally delay or advance the time at which signal pulses appear in the stream of data values to be written to the magnetic media. The precompensation circuit must determine which pulses need to be shifted. It does this by sorting them into groups based upon the presence of adjacent pulses. The user of write encoder  20  determines how much each group of pulses should be shifted. The shifting parameters are fixed based upon the characteristics of a particular magentic storage drive and can be adjusted separately for each drive device manufactured. 
     The output of precompensation circuit  23  is connected to output buffer  24  which is used to drive an encoded output signal that can be used with a standard hard disk drive write circuit or other storage media circuitry to store the encoded data onto magnetic media. 
     A detailed description of the operation of read channel decoder  30  will now be given. 
     Read channel decoder  30  receives data from an external disk drive read circuit (not shown). The disk drive read circuit produces a differential analog signal which is provided as an input to automatic gain control (AGC) circuit  31 . The AGC circuit is a standard feature of disk drive circuitry that amplifies the differential signal received from the external read/write circuitry. The gain on this amplifier is adjusted to maintain constant signal amplitude at the input to an EEPR4 filter  32 . 
     EEPR4 filter  32  is an analog circuit. The input signal provided to EEPR4 Filter  32  by AGC  31  and the output signal from filter  32  are continuous-time analog waveforms. The analog input signal to EEPR4 filter  32  represents a sequence {ŵ i } of binary values read from the storage media. Similarly, the output from filter  32  represents a sequence {v i } of discrete multilevel output values. 
     EEPR4 filter  32  is best described in terms of with reference to a discrete time model  200  of an EEPR4 filter. Discrete time model  200  operates on a sequence of discrete inputs, each of which is a binary sample of two possible values. From this input sequence, the discrete time model produces a sequence of discrete multi-level output values. In contrast, EEPR4 filter  32  is an analog circuit that operates on a continuous input signal and produces therefrom a continuous output signal. As noted above, however, the analog input and output signals to and from EEPR4 filter  32  represent discrete time sequences of binary or multi-level values. The relationship between the binary input sequences and the multi-level output sequences conveyed by these analog inputs and outputs is identical to the relationship between the discrete time input and output sequences of discrete time model  200 . 
     In FIG. 2, discrete time model  200  is illustrated. The schematic shown in FIG. 2 is a discrete time model of an extended extended partial response class  4  filter. It is not a schematic representation of the analog circuitry found in EEPR4 filter  32 . Model EEPR4 filter  200  is a finite response filter. The filter receives a sequence of binary input values {ŵ i } selected from the set of {+1, −1} and produces an output sequence {{circumflex over (v)} i } of multilevel symbols selected from the set {+6, +4, +2, 0, −2, −4, −6}. The model filter employs four unit delay blocks  201   a-d  that store previous elements of the input sequence so that five consecutive sequence members {ŵ i−4 , ŵ i−3 , ŵ i−2 , ŵ i−1 , ŵ i } are available to the filter simultaneously. The sequence members are scaled and added in accordance with the EEPR4 filter equation h(D)=(1−D)(1+D) 3 , where D represents the unit delay operator. Equivalently, the encoder output sequence, {v i }, is related to the binary input sequence, {w i }, by: v i =w i +2w i−1 −2w i−3 −w i−4 . 
     Turning again to FIG. 1, the manner in which filter circuitry  32  implements model EEPR4 filter  200  will now be described. 
     Filter circuitry  32  comprises a low-pass filter  41 /and a finite impulse response (FIR) filter  42 . Low-pass filter  41  is coupled to the output of AGC circuit  31 . Low-pass filter  41  is a continuous time filter, the output of which is coupled to FIR filter  42 . In the preferred embodiment of the invention, low-pass filter  41  has programmable cutoff, boost and group delay settings. Low-pass filter  41  performs two functions. First, it filters out noise signals that have frequencies outside the bandwidth of the signal read from the magnetic storage device. Second, low-pass filter  41  shapes the pulse stream read from the magnetic storage device. The result of this shaping, when combined with the effect of FIR filter  42 , is to produce a partial response filtering effect, so that the output of low-pass filter  41  and FIR filter  42  represents the pulse sequence originally stored on the disk filtered through a class  4  partial response filter. The programmable settings for the cutoff, boost and group delay characteristics of low-pass filter  41  must be set in accordance with the particular properties of the magnetic storage media and the disk drive read circuitry of storage device used with read channel decoder  30 . 
     FIR filter  42  is used for fine shaping of the sampled read signal to make it perform the function of model EEPR4 filter  200 . The output of EEPR4 filter  32  is an analog continuous time waveform, which is fed as an input to analog to digital (A/D) converter  33 . A/D converter  33  takes the analog output of EEPR4 filter  32  and converts it a sequence of discrete multilevel output samples {v i }. The multilevel output from the filter circuitry, {v i }, is coupled to the input of an EEPR4 detector ( 34 ). EEPR4 detector  34  is a maximum likelihood Viterbi detector. Each element in the sequence can take on one of the set of values {+6, +4, +2, 0, −2, −4, −6}. These values cannot be decoded directly into corresponding stored bit values. Rather, each symbol in the {v i } sequence corresponds to a one-bit transition through the state trellis for EEPR4 detector  34 . The detector algorithm tracks all possible paths that might be used to traverse the state trellis and selects the path which best fits the sequence of transition symbols received by the decoder. Once the “best fit” path has been determined, the stored bit values that produced the “best fit” state transition path are identified and EEPR4 detector  34  provides, at its output, a sequence {{circumflex over (v)} i } of stored bit values. 
     The Viterbi detection algorithm used in EEPR4 detector  34  employs the state transition trellis given in FIG.  3 . The nodes on the left and right hand sides of the trellis indicate the starting and ending states, respectively, of EEPR4 detector  34 . 
     The trellis indicates which transitions are possible as EEPR4 detector  34  advances one bit at a time through a sequence of bits to be decoded. Every permissible transition is represented as a line in the trellis, and the values indicated near each permissible transition represent the expected output from the EEPR4 encoder during that transition. These expected transition values may be combined with the multi-level transition symbol actually received (v i ) to create branch metrics for the Viterbi decoder. Using the branch metrics the most likely path can be determined. 
     EEPR4 detector  34  produces an output sequence {{circumflex over (v)} i } of serial bits. In order to decode this sequence of bits they must be reassembled into six-bit wide codewords. This reassembly is done by serial to parallel circuitry  35 . To assemble the serial sequence of data into six-bit codewords, serial to parallel circuitry  35  must have an indication of which bits in the serial sequence {{circumflex over (v)} i } represent the first or last bit of a six-bit codeword. This information is provided to serial to parallel  35  by synchronization circuitry (not shown). The synchronization circuitry recovers the boundaries of the six-bit codewords by monitoring patterns in the data received. 
     Serial to parallel circuitry  35  produces an output sequence of six-bit words {ŷ k } which represents the best estimate of the serial sequence {y k } that was written to the disk. The rate 5/6 MTR code used in the inventive PRML read channel makes it impossible for certain sequences of bits to appear in the sequence {y k } produced by rate 5/6 MTR encoder  21 . Therefore these disallowed sequences must also not appear in the output sequence {ŷ k } of EEPR4 detector  34 . If a disallowed sequence is identified by EEPR4 detector  34  as the most likely sequence, the detector should not provide this sequence as its output. Instead, EEPR4 detector  34  should provide the most likely sequence that is not disallowed by the rate 5/6 MTR code used. 
     Rate 5/6 MTR decoder  36  takes each six-bit word output from serial to parallel circuitry  35  and reverses the encoding performed by rate 5/6 MTR encoder  21 . The decoding operation performed by rate 5/6 MTR decoder  36  has four steps. These steps must be performed in the order indicated. In step three, the content of a first codeword received by decoder  36  may be altered as a consequence of the content of the next codeword received by decoder  36 . Whether any changes will be made to a particular input codeword in step 3 cannot be determined until steps 1 through 2 have been conducted for the next codeword. This creates a dependancy in the processing of received codewords. Step three of the decoding process cannot proceed for one codeword until steps one and two have been performed on the following codeword. 
     Step 1: 
     If the last two bits of a codeword are both ‘1’, then replace the last two bits of the codeword with the symbol sequence ‘00’. 
     Step 2: 
     If the first five bits of a codeword are ‘11000’, then replace the first five bits of the codeword with the symbol sequence ‘00000’. 
     Step 3: 
     If the first three bits of the current codeword are ‘110’ and the last two bits of the current codeword are ‘10’, then invert the last bit of the previous codeword. 
     Step 4: 
     The modified codeword can now be translated using the decoding table. Examination of the table reveals that it contains only 32 entries, so that all possible comvinations of six-bit inputs do not have entries. This is a result of the fact that steps one through three of the decoding process prevent many possible combinations from occurring. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Decoding Table 
               
             
          
           
               
                   
                 Input 
                 Output 
               
               
                   
                   
               
               
                   
                 000000 
                 00000 
               
               
                   
                 000001 
                 00001 
               
               
                   
                 000010 
                 00010 
               
               
                   
                 100001 
                 00011 
               
               
                   
                 000100 
                 00100 
               
               
                   
                 000101 
                 00101 
               
               
                   
                 000110 
                 00110 
               
               
                   
                 100101 
                 00111 
               
               
                   
                 001000 
                 01000 
               
               
                   
                 001001 
                 01001 
               
               
                   
                 001010 
                 01010 
               
               
                   
                 100100 
                 01011 
               
               
                   
                 001100 
                 01100 
               
               
                   
                 001101 
                 01101 
               
               
                   
                 100010 
                 01110 
               
               
                   
                 100000 
                 01111 
               
               
                   
                 010000 
                 10000 
               
               
                   
                 010001 
                 10001 
               
               
                   
                 010010 
                 10010 
               
               
                   
                 101001 
                 10011 
               
               
                   
                 010100 
                 10100 
               
               
                   
                 010101 
                 10101 
               
               
                   
                 010110 
                 10110 
               
               
                   
                 101101 
                 10111 
               
               
                   
                 011000 
                 11000 
               
               
                   
                 011001 
                 11001 
               
               
                   
                 011010 
                 11010 
               
               
                   
                 101100 
                 11011 
               
               
                   
                 101000 
                 11100 
               
               
                   
                 101010 
                 11101 
               
               
                   
                 110010 
                 11110 
               
               
                   
                 110110 
                 11111 
               
               
                   
                   
               
             
          
         
       
     
     The decoding steps performed by rate 5/6 MTR decoder  36  can be performed by a sequence of boolean logic operations. The boolean equations shown in FIG. 5 implement the function of rate 5/6 MTR decoder  36 . In these equations the six-bit codeword provided as an input to rate 5/6 MTR decoder  36  is identified by the symbol ŷ k . The six bits that make up ŷ k  are identified as ŷ 1   k , ŷ 2   k , ŷ 3   k , ŷ 4   k , ŷ 6   k . The five bit symbol {circumflex over (x)} k  represents the decoded symbol that is produced as an output from rate 5/6 MTR decoder  36 . The binary variables ({circumflex over (x)} 1   k , {circumflex over (x)} 2   k , {circumflex over (x)} 3   k , {circumflex over (x)} 4   k , {circumflex over (x)} 5   k ) represent the five bits of symbol {circumflex over (x)} k , with {circumflex over (x)} 1   k , representing the first bit in the symbol and {circumflex over (x)} k  the last. The input to rate 5/6 MTR decoder  36  is made up of a continuous sequence of six-bit codewords, ŷ 1 , ŷ 2 , . . . ŷ k−1 , ŷ k , ŷ k+1 , . . . . The output from rate 5/6 MTR decoder  36  is likewise made up of a continuous sequence of five-bit symbols, {circumflex over (x)} 1 , {circumflex over (x)} 2 , . . . , {circumflex over (x)} k−1 , {circumflex over (x)} k , {circumflex over (x)} k+1 , . . . . The equations in FIG. 5 employ a number of intermediate variables, including a sequence of six-bit codewords {circumflex over (z)} 1 , {circumflex over (z)} 2 , . . . , {circumflex over (z)} k−1 , {circumflex over (z)} k , {circumflex over (z)} k+1 , . . . 
     The operation of the invented encoding and decoding system in the context of a hard disk drive system is best illustrated with reference to FIG.  6 . Hard disk drive unit  50  is connected to a host computer  60  by way of SCSI bus  70 . The SCSI interface is a standardized protocol for interconnecting peripheral devices to microcomputers. Inside hard disk drive unit  50 , SCSI bus  70  is connected to drive controller  51 . Drive controller  51  is designed to receive control messages and data from host computer  60  and to transfer data and status information back to host computer  60 . Drive controller  51  is connected to encoder/decoder interface  10  and digital signal processor (DSP)  52 . The connection between drive controller  51  and encoder/decoder interface  10  is bidirectional. Drive controller  51  can pass data that is to be written to the hard disk to encoder/decoder interface  10  and receive data that has been read from the hard disk from encoder/decoder interface  10 . Information relating to the position on the disk where data is to be read or written is passed from drive controller  51  to DSP  52 . DSP  52  is connected to and controls the movement of actuator  55 . Actuator  55  controls the location of write head  56  and read head  57 . DSP  52  is also connected to spin motor phase locked loop (PLL)  53 . Both DSP  52  and spin motor PLL  53  are connected to spin motor  54 , which controls the spinning of the magnetic disks. 
     Data to be stored onto the hard disk drive passes from drive controller  51  to the encoder/decoder interface  10 . Encoder/decoder interface  10  then passes the data to write channel circuitry  20 , where it is encoded. The output from write encoder  20  is provided to write head  56 . Data is read from the hard disk by read head  57 , and provided at the input to read channel circuitry  30 , where the data is decoded. Decoded data is passed from the output of read channel circuitry  30  to encoder/decoder interface  10 , where it is passed to drive controller  51 . 
     FIG. 6 indicates only one possible deployment of the invented encoding and decoding systems. Any number of variations on this design are possible. For instance, the connection between host computer  60  and drive controller  51  need not be implemented through a SCSI bus. An IDE/ATA bus is often used for this purpose instead of a SCSI bus. It is also possible to build a hard disk drive without an integrated drive controller or DSP. Other variations in the design are possible 
     While the invention has been particularly shown and described with reference to the presently 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 in the appended claims. 
     While the encoding and decoding apparatus and methods described herein have been related in the context of an encoding and decoding channel for a magnetic storage device, the underlying encoding and decoding apparatus and methods could be used in connection with storage devices. The disclosed encoding and decoding apparatus and methods can be incorporated in storage devices using magnetic storage media, such as tape drives, or non-magnetic storage media, such as optical storage devices. In addition, the disclosed encoding and decoding apparatus and methods can be used to encode and decode data for transmission in communication channels and networking systems.