Patent Publication Number: US-9852757-B2

Title: Systems and methods for decoding using run-length limited (RLL) codes

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present disclosure is a divisional of U.S. patent application Ser. No. 14/694,401 (now U.S. Pat. No. 9,431,053), filed on Apr. 23, 2015, which claims the benefit of Singapore Patent Application No. 10201401781X, filed 24 Apr. 2014. The entire disclosures of the applications referenced above are incorporated herein by reference. 
    
    
     FIELD 
     The present disclosure generally relates to run-length limited (RLL) codes, and more particularly, to dc-free k constrained codes for hard disk drive (HDD) systems with dedicated servo. 
     BACKGROUND 
     Hard disk drive (HDD) systems with dedicated servo show potential to achieve higher recording density as compared to conventional servo systems that share the surface area of the medium with data on the same track. For example, by adding a dedicated servo recording layer in between the conventional perpendicular recording data layer and the soft-underlayer (SUL), nearly all the surface of the data layer can be used for data recording. However, one challenge of the dedicated servo system is the interference between the data signal recorded on the data layer and the servo signal recorded on the servo layer. In this regard, since the servo signal of the dedicated servo is designed at dc, the dc-free constrained codes have the ability to reduce the interference between the data and servo signals. 
     In HDD systems with dedicated servo, there are generally two types of code constraints to be satisfied in the channel sequences. Namely, the maximum run length limited (RLL) constraint (also known as the k constraint) and the dc-free constraint. The k constraint specifies the maximum number of consecutive zeros between two ones in the channel sequences to facilitate timing recovery of the channel readback signal. The dc-free constraint, on the other hand, is used to suppress the dc component of the channel sequences to reduce the interference between the data signal and the servo signal of the dedicated servo. 
     A straightforward way of constructing the k constrained code is by using table look-up. However, this approach cannot achieve high code rates as the size of the corresponding look-up tables will be huge and are not affordable for practical hardware application. In certain conventional methods, an enumerative coding scheme may be used to design high rate k constrained codes with long codeword lengths. However, it has been found that the enumerative coding scheme can lead to serious error propagation during decoding. A single error in the received word may result in massive amounts of decoded errors. In other conventional methods, an interleaving scheme may be used to achieve high code rates by interleaving coded and uncoded symbols, where the coded symbols are obtained from a low-rate k constrained base code. More recently, a nibble replacement coding technique has been disclosed which uses various k constrained codes that achieve higher code efficiencies than those disclosed previously. However, the nibble replacement method designs the k constrained codes in the non-return-to-zero-inverse (NRZI) format rather than in the non-return-to-zero (NRZ) format. 
     SUMMARY 
     A method of encoding an input data into a codeword that satisfies a k constraint includes partitioning the input data into a plurality of data blocks comprising a first data block and a plurality of remaining data blocks; performing a first analysis of the plurality of data blocks for modifying each of the plurality of remaining data blocks that satisfies a first predetermined criterion; performing a second analysis of the plurality of data blocks after the first analysis for modifying each of the plurality of data blocks that satisfies a second predetermined criterion; and converting each bit of the plurality of data blocks after the second analysis to produce the codeword in Non-Return-to-Zero (NRZ) format that satisfies the k constraint. 
     In other features, the performing a first analysis comprises replacing each of the plurality of remaining data blocks that satisfies the first predetermined criterion. The performing a second analysis comprises replacing each of the plurality of data blocks that satisfies the second predetermined criterion. 
     In other features, the first predetermined criterion comprises whether a current data block of the plurality of remaining data blocks has a decimal value less than a predetermined value. 
     In other features, the second predetermined criterion comprises whether a current data block of the plurality of data blocks contains a predetermined set of binary bits and whether a data block immediately before the current data block contains a predetermined bit at a predetermined bit position. The performing a second analysis comprises replacing each of the plurality of data blocks that satisfies the second predetermined criterion with a predetermined data block. 
     In other features, the predetermined set of binary bits contains all binary ‘1’ bits, the predetermined bit at the predetermined bit position is a binary ‘1’ bit at the least significant bit of the data block, and the predetermined data block contains all binary ‘0’ bits. 
     In other features, the partitioning the input data comprises partitioning the input data into a plurality of single-bit data blocks and the plurality of data blocks comprising the first data block and the plurality of remaining data blocks, when the k constraint is an odd k constraint. 
     In other features, the number of single-bit data blocks corresponds to the number of data blocks. 
     In other features, the second predetermined criterion comprises whether a current data block of the plurality of data blocks contains a predetermined set of binary bits and whether a corresponding single-bit data block matches a predetermined bit. The performing a second analysis comprises replacing each of the plurality of data blocks that satisfies the second predetermined criterion with a predetermined data block. 
     In other features, the predetermined set of binary bits contains all binary ‘1’ bits, the predetermined bit is a binary ‘1’ bit, and the predetermined data block contains all binary ‘0’ bits. 
     In other features, the method further comprises interleaving the plurality of single-bit data blocks and the plurality of data blocks after the second analysis to produce the codeword, that satisfies the k constraint. 
     In other features, the method further comprises encoding the input data with a dc-free constraint to produce the codeword in NRZ format that satisfies the k constraint and the dc-free constraint. 
     In other features, the input data is encoded with a dc-free constraint based on a guided scrambling technique, and wherein the codeword is selected based on a minimum squared weight selection criterion. 
     A method of decoding a codeword that satisfies a k constraint into an output data includes converting each bit of the codeword being in Non-Return-to-Zero (NRZ) format; extracting, from the converted codeword, a plurality of data blocks comprising a first data block and a plurality of remaining data blocks; performing a first analysis on the plurality of data blocks for modifying each of the plurality of data blocks that satisfies a first predetermined criterion; and performing a second analysis on the plurality of data block after the first analysis for modifying each of the plurality of data blocks that satisfies a second predetermined criterion to obtain the output data. 
     In other features, the performing a first analysis comprises replacing each of the plurality of data blocks that satisfies the first predetermined criterion. The performing a second analysis comprises replacing each of the plurality of data blocks that satisfies the second predetermined criterion. 
     In other features, the first predetermined criterion comprises whether a current data block of the plurality of data blocks contains a predetermined set of binary bits The performing a first analysis comprises replacing each of the plurality of data blocks that satisfies the first predetermined criterion with a predetermined data block. 
     In other features, the predetermined set of binary bits contains all binary ‘0’ bits and the predetermined data block contains all binary ‘1’ bits. 
     In other features, the second predetermined criterion comprises whether the most significant bit of the first data block has a predetermined bit. 
     In other features, the predetermined bit is a binary ‘1’ bit. 
     In other features, the extracting from the converted codeword comprises extracting a plurality of single-bit data blocks and the plurality of data blocks comprising the first data block and the plurality of remaining data blocks, when the k constraint is an odd k constraint. 
     In other features, the number of single-bit data blocks corresponds to the number of data blocks. 
     In other features, the method further comprises concatenating the plurality of single-bit data blocks with the plurality of data blocks to obtain the output data after the modifying in the second analysis. 
     In other features, the codeword further satisfies a dc-free constraint. 
     An encoder for encoding an input data into a codeword that satisfies a k constraint includes a partitioning module configured to partition the input data into a plurality of data blocks comprising a first data block and a plurality of remaining data blocks; a first analysis module configured to perform a first analysis of the plurality of data blocks for modifying each of the plurality of remaining data blocks that satisfies a first predetermined criterion; a second analysis module configured to perform a second analysis of the plurality of data blocks after the first analysis for modifying each of the plurality of data blocks that satisfies a second predetermined criterion; and a conversion module configured to convert each bit of the plurality of data blocks after the second analysis to produce the codeword in Non-Return-to-Zero (NRZ) format that satisfies the k constraint. 
     A decoder for decoding a codeword that satisfies a k constraint into an output data includes a conversion module configured to convert each bit of the codeword being in Non-Return-to-Zero (NRZ) format; an extraction module configured to extract, from the converted codeword, a plurality of data blocks comprising a first data block and a plurality of remaining data blocks; a first analysis module configured to perform a first analysis on the plurality of data blocks for modifying each of the plurality of data blocks that satisfies a first predetermined criterion; and a second analysis module configured to perform a second analysis on the plurality of data block after the first analysis module for modifying each of the plurality of data blocks that satisfies a second predetermined criterion to obtain the output data. 
     A hard disk drive system includes a dedicated servo medium including a data recording layer and a servo layer; a spindle motor configured to rotate the dedicated servo medium; an encoder of claim  23  for encoding data to be stored on the data recording layer; and a write head coupled to the encoder and operable to write the codewords in Non-Return-to-Zero (NRZ) format from the encoder onto the data recording layer. 
     A hard disk drive system includes a dedicated servo medium including a data recording layer and a servo layer; a spindle motor configured to rotate the dedicated servo medium; a read head operable to read codewords from the data recording layer; and a decoder of claim  24  for decoding the codewords in Non-Return-to-Zero (NRZ) format read from the data recording layer. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       Examples of the present disclosure will be better understood and readily apparent to one of ordinary skill in the art from the following written description, by way of example only, and in conjunction with the drawings, in which: 
         FIG. 1  depicts an overview of a method of encoding an input data into a codeword in NRZ format that satisfy a k constraint according to the present disclosure; 
         FIG. 2  depicts a schematic block diagram of an example of method of encoding an input data into a codeword in NRZ format that satisfy a k constraint according to the present disclosure, for the case where the k constraint is even; 
         FIG. 3  depicts a schematic block diagram of an example of method of encoding an input data into a codeword in NRZ format that satisfy a k constraint according to according to the present disclosure, for the case where the k constraint is odd; 
         FIG. 4  depicts an overview of an example of method of decoding a codeword in NRZ format that satisfy a k constraint into an output data according to the present disclosure; 
         FIG. 5  depicts a schematic block diagram of an example of method of decoding a codeword in NRZ format that satisfy a k constraint into an output data according to according to the present disclosure, for the case where the k constraint is even; 
         FIG. 6  depicts a schematic block diagram of an example of method of decoding a codeword in NRZ format that satisfy a k constraint into an output data according to the present disclosure, for the case where the k constraint is odd; 
         FIG. 7  depicts a schematic block diagram of an example of method of encoding and decoding of dc-free k constrained codes according to the present disclosure; 
         FIG. 8  depicts a plot of an example of the power spectrum densities (PSD) of a designed rate R=0.9941, k=14 dc-free constrained code with a fixed p=5, but with different selection criteria for the guided scrambling (GS) technique; 
         FIGS. 9A and 9B  depict plots of an example of the PSDs of dc-free k constrained codes according to the present disclosure; 
         FIGS. 10A to 10C  depict plots of an example of RRO spectrum results of dc-free k constrained codes according to the present disclosure; 
         FIG. 11  depicts a schematic block diagram of an example of an encoder for encoding an input data into a codeword in NRZ format with a k constraint according to the present disclosure; 
         FIG. 12  depicts a schematic block diagram of an example of a decoder for decoding a codeword in NRZ format with a k constraint into an output data according to the present disclosure; and 
         FIG. 13  depicts a simplified schematic block diagram of an example of a hard disk drive system according to the present disclosure. 
     
    
    
     DESCRIPTION 
     Examples of the present disclosure provide RLL coding methods for constructing RLL constrained codes with high efficiency (e.g., high code rate). In some examples, the RLL constraint imposed is the maximum RLL constraint, also known in the art as the k constraint. Therefore, k constrained codes with high efficiency are constructed. In further examples, the k constraint codes are further imposed with a dc-free constraint to construct highly efficient dc-free k constrained codes suitable for HDD systems with dedicated servo to reduce or minimize the interference between the data and servo signals. In this regard, the k constrained codes are constructed in Non-Return-to-Zero (NRZ) format (rather than Non-Return-to-Zero Inverted (NRZI) format) for facilitating easy construction of dc-free constrained codes as the dc-free constraint needs to be imposed on NRZ format data. Doing so advantageously avoids the use of NRZI to NRZ converter during encoding and the NRZI to NRZ converter during detection and decoding, thus simplifying the implementation complexity. 
       FIG. 1  depicts an overview of a method  100  of encoding an input data into a codeword (in NRZ format) that satisfy a k constraint according to the present disclosure. The method  100  comprises a step  102  of partitioning the input data into a plurality of data blocks comprising a first data block and a plurality of remaining data blocks, a step  104  of performing a first analysis of the plurality of data blocks for modifying each of the plurality of remaining data blocks that satisfy a first predetermined criterion, a step  106  of performing a second analysis of the plurality of data blocks after the first analysis for modifying each of the plurality of data blocks that satisfy a second predetermined criterion, and a step  108  of converting/modifying each bit of the plurality of data blocks after the second analysis to produce the codeword into NRZ format that satisfy the k constraint. 
     For a better understanding, the method  100  will now be described more fully with reference to  FIGS. 2 and 3 , in which examples of the disclosure are shown. This disclosure may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein. Rather, these examples are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. 
       FIG. 2  depicts a schematic block diagram of a method  200  of encoding an input data  202  into a codeword  208  (in NRZ format) that satisfy a k constraint according to an example embodiment of the present disclosure, for the case where the k constraint is even. The input data  202  may be an (n−1)-bit information word which is partitioned into a first data block  205  of (q−1)-bit (which may be referred to as a pivot data block) and subsequent/remaining (L−1) data blocks  206  of q-bit. It will be appreciated to a person skilled in the art that data blocks may also be referred to as nibbles. Accordingly, there are L blocks in the plurality of data blocks  204  and the input data  202  is encoded into a codeword  208  of n-bit in NRZ format that satisfy the k constraint. The integer n is a multiple of the integer q, that is, n=Lq, where q is the data block size and L is the number of q-bit data block  204  in a codeword  208 . For example, as shown in  FIG. 2 , the input data  202  may be a 31-bit information word which is partitioned into a first/pivot data block  205  of 3-bit (U 0 ), and remaining 7 data blocks  206  of 4-bit (U 1  to U 7 ). 
     Subsequently, a first analysis of the plurality of data blocks  204  is performed. In the example embodiment, the first analysis corresponds to the encoding method of the nibble replacement technique disclosed in K.A.S. Immink, “High-Rate Maximum Runlength Constrained Coding Schemes Using Nibble Replacement”, the contents of which is hereby incorporated by reference in its entirety for all purposes. Following the nibble replacement technique, a pivot bit equal to, for example, ‘1’ is appended to the beginning of the first data block  205 , thus obtaining a q-bit first data block  205 . The value of the pivot bit may be determined by the encoder. The pivot bit indicates that at least one of the remaining data blocks  206  has been modified, for example, a binary ‘1’ bit indicates that at least one remaining data block  206  has been modified, whereas a binary ‘0’ bit indicates that none of the remaining data blocks  206  has been modified. 
     In other features, performing the first analysis comprises replacing each of the plurality of remaining data blocks  206  that satisfy the first predetermined criterion. In this regard, the sequence of remaining data blocks  206  are scanned to determine whether a current data block has a decimal value less than a predetermined value (w) (first predetermined criterion). For example, the predetermined value may be set to 1 as shown in  FIG. 2 , but it will be appreciated that the predetermined value may be set to other values as appropriate such as 2. A remaining data block which satisfy the first predetermined criterion may be referred to as an admissible data block or nibble, whereas a remaining data block which does not satisfy the first predetermined criterion may be referred to as an inadmissible data block or nibble. 
     In general, all inadmissible data blocks will be replaced with data blocks whose decimal representation is larger than or equal to the predetermined value (w). Therefore, all admissible data blocks will be transmitted without modification to the second analysis, whereas all inadmissible data blocks will be replaced according to the nibble replacement technique. In particular, the first found inadmissible data block is replaced with the first/pivot data block  205 . After that, the pivot bit is set to binary ‘0’ (to indicate that a remaining data block has been modified), and the address and the decimal value of the first found inadmissible data block are converted into binary data and stored in remaining q−1 bits of the first block  205 . The first analysis then continues to scan and replace as long as the first predetermined criterion is met, until the end of the remaining data blocks  206 . More specifically, the process treats a replaced data block as a pivot data block in a similar manner as performed in the first replacement, and a subsequently found inadmissible data block is replaced by the current pivot data block and so on until all inadmissible data blocks are replaced. In the example embodiment of  FIG. 2 , the plurality of data blocks  220  after the first analysis is represented as X 0  to X 7 , which can then be subjected to the second analysis. 
     For illustration purposes only, an example of the nibble replacement technique will now be described. Let w=1, q=3 and L=4 and the input data=‘11 000 110 111’. It will be appreciated that the spaces between the data blocks are provided for clerical convenience. A binary ‘1’ bit is appended to the first data block to obtain ‘111 000 110 111’. In this example, the only remaining data block that satisfy the first predetermined criterion is the data block ‘000’ since this has a decimal value of 0 which is less than the predetermined value of 1. Therefore, this inadmissible data block is replaced with the first/pivot data block ‘111’. In addition, the first/pivot bit of the first/pivot data block is set to 0 and the remaining bits of the first/pivot data block is modified to store information indicating the address and decimal value of the inadmissible data block. Based on this, the first data block is modified to ‘001’. In this example, since no other remaining data blocks is found to satisfy the first predetermined criterion, no further modifications to the remaining data blocks are required. Therefore, the plurality of data blocks  220  after the first analysis is ‘001 111 110 111’, which can then be subjected to the second analysis. 
     However, the above first analysis (i.e., the encoding method of the nibble replacement technique) generates an even k constrained sequence/codeword in NRZI format. According to examples of the present disclosure, it is noted that a k constraint in NRZI format allows at most k+1 number of consecutive ‘+1’s or ‘−1’s in the channel sequence in NRZ format. If a conversion of changing a ‘0’ to a ‘−1’ and a ‘1’ to a ‘+1’ is carried out in the channel sequence in NRZI format, the NRZ sequence obtained would have at most k number of consecutive ‘−1’s, which do not violate the k constraint. However, the number of consecutive ‘+1’s in the sequence obtained can be greater than k+1, hence violates the k constraint. To address this, the subsequent second analysis according to examples of the present disclosure prohibits the occurrence of greater than k+1 number of consecutive ‘+1’s, and ensures that the maximum number of consecutive ‘+1’s or ‘−1’s is at most k+1 in the encoded NRZ sequence/codeword. 
     The second analysis according to the present disclosure will now be described. In other features, performing the second analysis comprises modifying/replacing each of the plurality of data blocks  220  that satisfy the second predetermined criterion. In this regard, the sequence of data blocks  220  from the first analysis are scanned to determine whether a current data block of the plurality of data blocks  220  contains a predetermined set of binary bits and whether a data block immediately before the current data block contains a predetermined bit at a predetermined bit position (second predetermined criterion). If so, the current data block is replaced with a predetermined data block. For example, the predetermined set of binary bits contains all binary ‘1’ bits, the predetermined bit at the predetermined bit position is a binary ‘1’ bit at the least significant bit of the data block, and the predetermined data block contains all binary ‘0’ bits. 
     Referring to the example of  FIG. 2 , the plurality of data blocks  220  are represented by X i , where i=0, 1, . . . L−1. In the example of  FIG. 2 , as mentioned above, L=8 and q=4. In the second analysis, the plurality of data blocks  220  is scanned to determine whether a current data block X i  matches a predetermined set of binary bits, i.e., an all binary ‘1’ data block of q-bit (i.e., whether X i =[1111]), and whether a data block (X i-1 ) immediately before the current data block contains a predetermined bit of “1” at the least significant bit (i.e., whether X i-1 (q)=1). If so, the current data block X i  is replaced with the predetermined data block of all binary ‘0’ data block of q-bit, i.e., [0000] and outputted as Y i  having the modified/replaced value. Otherwise, the current data block X i  is not modified and simply outputted as Y i  having the same value as X i  as shown in  FIG. 2 . In this way, a rate 31/32 and k=6 constrained codeword in NRZ format is obtained in the example. Note that the code rate is the same with that of the code that can be designed in NRZI format, and no advantageously NRZI to NRZ converter is needed during encoding. 
     Therefore, according to an example embodiment, the second analysis may be implemented by the following general equation:
 
For all  i=L− 1, if  X   i =[11 . . . 1] and  X   i-1 ( q )=1, set  Y   i =[00 . . . 0];  Equation (1)
         else set X i =[00 . . . 0];   end       

     After performing the second analysis, each bit of the plurality of data blocks  240  obtained (i.e., Y 0  to Y 7 ) is converted to produce the n-bit codeword  208  in NRZ format that satisfy the k constraint (k even constraint). In a preferred embodiment, the binary ‘0’ bit is converted to ‘−1’ and the binary ‘1’ bit is converted to ‘+1’. 
       FIG. 3  depicts a schematic block diagram of a method  300  of encoding an input data  302  into a codeword  308  (in NRZ format) that satisfy a k constraint according to an example embodiment of the present disclosure, for the case where the k constraint is odd. In this case, the input data  302  is partitioned into a plurality of single-bit data blocks  305  and a plurality of data blocks (multi-bit data blocks)  306  comprising a first data block and a plurality of remaining data blocks. For example, as shown in  FIG. 3 , the input data  302  may be a 15-bit information word  302  which is partitioned into 4 single-bit data blocks  305  (a 0 , a 1 , a 2 , and a 3 ) and 4 multi-bit data blocks  306  having bits represented as U 0  to U 10 . In this example, the multi-bit data blocks  306  comprise a first data block of (q−1)-bits (i.e., 2 bits) and 3 remaining data blocks each of q-bits (i.e., 3 bits). Therefore, the number of single-bit data blocks corresponds to the number of multi-bit data blocks. 
     In the example embodiment, the length of the plurality of data blocks  306  is set to be n even −1, which is equal to the information word length of a code with an even k even  constraint, and the number (L) of multi-bit data blocks  306  is set to be equal to that of the corresponding k even  constrained code. Therefore, the code word length at the output of the encoder is given by n odd =n even +L. 
     Subsequently, a first analysis is performed on the plurality of data blocks  306  in the same manner as described hereinbefore with reference to  FIG. 2 . That is, the plurality of data blocks  306  is encoded into an even k even  constrained codeword by using the nibble replacement technique as described hereinbefore to obtain L data blocks (X 0 , X 1 , X 2 , and X 3 )  320 . The nibble replacement technique will not be repeated for clarity and conciseness. 
     Similarly, the above first analysis (i.e., the encoding method of the nibble replacement technique) generates an odd k constrained sequence/codeword in NRZI format. According to examples of the present disclosure, it is noted that if a conversion of changing a ‘0’ to a‘−1’ and a ‘1’ to a ‘+1’ is carried out in the channel sequence in NRZI format, the NRZ sequence obtained would have at most k number of consecutive ‘−1’s, which do not violate the k constraint. However, the number of consecutive ‘+1’s in the sequence obtained can be greater than k+1, hence violates the k constraint. To address this, the subsequent second analysis according to examples of the present disclosure prohibits the occurrence of greater than k+1 number of consecutive ‘+1’s, and ensures that the maximum number of consecutive ‘+1’s or ‘−1’s is at most k+1 in the encoded NRZ sequence/codeword. 
     The second analysis according to the present disclosure will now be described. In other features, performing the second analysis comprises modifying/replacing each of the plurality of data blocks  320  that satisfy the second predetermined criterion. In this regard, the sequence of data blocks  320  from the first analysis are scanned to determine whether a current data block of the plurality of data blocks  320  contains a predetermined set of binary bits and whether a corresponding single-bit data block contains a predetermined bit (the second predetermined criterion). If so, the current data block is replaced with a predetermined data block. For example, the predetermined set of binary bits contains all binary ‘1’ bits, the predetermined bit is a binary ‘1’ bit, and the predetermined data block contains all binary ‘0’ bits. 
     Referring to the example of  FIG. 3 , in the second analysis, the plurality of data blocks  320  is scanned to determine whether a current data block X i  matches a predetermined set of binary bits, i.e., an all binary ‘1’ data block of q-bit (i.e., whether X i =[111]), and whether a corresponding single-bit data block a i  matches a predetermined bit (i.e., binary ‘1’ bit) (i.e., whether a i =1). If so, the current data block X i  is replaced with the predetermined data block of all binary ‘0’ data block of q-bit, i.e., [000] in this example and outputted as Y i  having the modified/replaced value. Otherwise, the current data block X i  is not modified and simply outputted as Y i  having the same value as X i . In this way, a rate 15/16 and k=5 constrained code in NRZ format is obtained in the example. Note that the code rate is the same with that of the code that can be designed in NRZI format, and advantageously, no NRZI to NRZ converter is needed during encoding. 
     Therefore, according to an example embodiment, the second analysis may be implemented by the following general equation:
 
For all  i=L− 1, if  X   i =[11 . . . 1] and  a   i =1, set  Y   i =[00 . . . 0];  Equation (2)
         else set X i =[00 . . . 0];   end       

     After performing the second analysis, the plurality of data blocks  340  obtained (i.e., Y 0  to Y 7 ) is interleaved with the plurality of single-bit blocks  305  correspondingly to obtain a combined codeword  360 , preferably in the format of [a 0 Y 0 a 1 Y 1  . . . a L-1 Y L-1 ] as shown in  FIG. 3 . Subsequently, each bit of the combined codeword  360  is converted to produce the n-bit codeword  308  in NRZ format that satisfy the k constraint (k odd constraint). In a preferred embodiment, the binary ‘0’ bit is converted to ‘−1’ and a binary ‘1’ bit is converted to ‘+1’. 
       FIG. 4  depicts an overview of a method  400  of decoding a codeword (in NRZ format) that satisfy a k constraint into an output data according to the present disclosure. The method  400  comprises a step  402  of converting/modifying each bit of the codeword  208 ,  308  being in NRZ format, a step  404  of extracting, from the converted codeword, a plurality of data blocks comprising a first data block and a plurality of remaining data blocks, a step  406  of performing a first analysis on the plurality of data blocks for modifying each of the plurality of data blocks that satisfy a first predetermined criterion, and a step of  408  performing a second analysis on the plurality of data block after the first analysis for modifying each of the plurality of data blocks that satisfy a second predetermined criterion to obtain the output data. 
     For a better understanding, the method  400  will now be described more fully with reference to  FIGS. 5 and 6 , in which examples of the disclosure are shown. This disclosure may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein. Rather, these examples are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. 
       FIG. 5  depicts a schematic block diagram of a method  500  of decoding a codeword  208  (in NRZ format) that satisfy a k constraint into an output data  202  according to an example embodiment of the present disclosure, for the case where the k constraint is even. The received codeword  208  may be an n-bit codeword  208  which is first modified by converting bit ‘−1’ to ‘0’ and bit ‘+1’ to ‘1’ in the received n-bit codeword  208 . 
     Subsequently, a plurality of data blocks, comprising a first data block  505  and a plurality of remaining data blocks  506 , is extracted from the modified/converted codeword. In the example shown in  FIG. 5 , a first data block  505  of q-bit (which may be referred to as a pivot data block) and subsequent/remaining (L−1) data blocks  506  of q-bit are extracted from the converted n-bit codeword, where q=4, L=8 and n=32. The integer n is a multiple of integer q, that is, n=Lq, where q is the data block size and L is the number of q-bit data blocks. For example, as shown in  FIG. 5 , the received data  208  may be a 32-bit codeword and the first data block  505  and the remaining 7 data blocks  506  extracted/retrieved may be 4-bit each. 
     A first analysis is then performed on the plurality of data blocks  240  for modifying each of the plurality of data blocks  240  that satisfy a first predetermined criterion. In other features, performing the first analysis comprises modifying/replacing each of the plurality of data blocks  240  that satisfy the first predetermined criterion. In this regard, the sequence of data blocks  240  are scanned to determine whether a current data block of the plurality of data blocks  240  contains a predetermined set of binary bits. If so, the current data block is replaced with a predetermined data block. For example, the predetermined set of binary bits contains all binary “0” bits and the predetermined data block contains all binary “1” bits. 
     Referring to the example of  FIG. 5 , the plurality of data blocks  240  are represented by Y 0  to Y 7 . In the first analysis, the plurality of data blocks  240  are scanned to determine whether a current data block Y i  contains a predetermined set of binary bits, which in this example is an all binary ‘0’ data block of q-bit (i.e., whether Y i =[0000]). If so, the current data block Y i  is replaced with the predetermined data block of all binary “1” data block of q-bit, i.e., [1111] and outputted as X i  having the replaced/modified value. Otherwise, the current data block Y i  is not modified and simply outputted as X i  having the same value as Y i  as shown in  FIG. 5 . it can be appreciated that the above decoding process is the inverse of the second analysis of the encoding process illustrated in  FIG. 2 . During decoding, an all binary ‘0’ data block of q-bit (i.e., whether Y i =[0000]) can be confirmed to be generated during the second analysis of the encoding process shown in  FIG. 2 , as the first analysis of the encoding process (i.e., the encoding method of the nibble replacement) would forbid the generation of an all binary ‘0’ data block of q-bit. 
     Therefore, according to an example embodiment, the first analysis of the decoding process may be implemented by the following general equations:
 
For all  i=L− 1, if  Y   i =[00 . . . 0], set  X   i =[11 . . . 1];  Equation (3)
         else set X i =Y i ;   end       

     Subsequently, a second analysis is performed on the plurality of data blocks  220  after the first analysis for modifying each of the plurality of data blocks  220  that satisfy a second predetermined criterion. In the example embodiment, the second analysis corresponds to the decoding method of the nibble replacement technique disclosed in K.A.S. Immink as mentioned hereinbefore, the contents of which has been incorporated by reference in its entirety for all purposes. In particular, following the decoding method of the nibble replacement technique, the second predetermined criterion comprises whether the most significant bit of the first data block  508  has a predetermined bit. In other features, the most significant bit of the first data block  508  is the first/pivot bit and the predetermined bit is a binary ‘1’ bit. In this case, if the pivot bit of the first data block  508  is a binary ‘1’ bit, the (n−1)-bit information word (output data) can be recovered by simply removing the pivot bit. This is because a pivot bit having a value of ‘1’ indicates that no modifications were made to the original (n−1)-bit information word during encoding. On the other hand, if the pivot bit is a binary “0” bit, the decoding process recursively replaces the data blocks  220  that were replaced/modified during the encoding process based on the address and decimal values stored in the replaced/modified data blocks. The decoding process halts when the most significant bit of a replaced/modified data block equals binary ‘1’ and outputs the original information word (output data)  202 . 
       FIG. 6  depicts a schematic block diagram of a method  600  of decoding a codeword (in NRZ format) that satisfy a k constraint into an output data according to an example embodiment of the present disclosure, for the case where the k constraint is odd. The received codeword may be an n-bit codeword  308  which is first modified by converting bit ‘−1’ to ‘0’ and bit ‘+1’ to ‘1’ in the received n-bit codeword  308 . 
     Subsequently, a plurality of single-bit data blocks  305  and a plurality of data blocks (multi-bit data blocks)  340  are extracted/retrieved from converted codeword. The plurality of data blocks  340  comprises a first data block and a plurality of remaining data blocks. In the example shown in  FIG. 6 , the received codeword  308  may be a 16-bit codeword from which is extracted 4 single-bit data blocks (a 0 , a 1 , a 2 , and a 3 )  305  and 4 data blocks (Y 0 , Y 1 , Y 2 , Y 3 )  340 . 
     A first analysis is then performed on the plurality of data blocks  340  for modifying each of the plurality of data blocks that satisfy a first predetermined criterion in the same manner as described hereinbefore with reference to  FIG. 5  and thus will not be repeated for clarity and conciseness. After the first analysis, a plurality of data blocks X 0  to X 3    320  is obtained as shown in  FIG. 6 . 
     Subsequently, a second analysis is performed on the plurality of data blocks (X 0  to X 3 )  320  after the first analysis for modifying each of the plurality of data blocks that satisfy a second predetermined criterion. In particular, the plurality of data blocks Xi is decoded using the decoding method of the nibble replacement technique as described hereinbefore and thus will not be repeated for clarity and conciseness. After the second analysis, a plurality of data blocks containing U 0  to U 10  is obtained as shown in  FIG. 6 . 
     The plurality of data blocks output from the second analysis is then concatenated with the plurality of single-bit data blocks  305  as shown in  FIG. 6  to recover the (n−1)-bit original information word (output data)  302 . In the example, the single-bit data blocks a 0 a 1 a 2 a 3  are concatenated with the plurality of multi-bit data blocks containing bits U 0  to U 10  to obtain output data a 0  . . . a 3 U 0  . . . U 10 . 
     As mentioned hereinbefore, in further examples, the k constraint codes are further imposed with a dc-free constraint to construct highly efficient dc-free k constrained codes suitable for HDD systems with dedicated servo to reduce or minimize the interference between the data and servo signals. In this regard, according to an embodiment, the method  100  further comprises encoding the input data with a dc-free constraint to produce the codeword that satisfy the k constraint and the dc-free constraint. In other features, the input data is encoded with a dc-free constraint based on a guided scrambling (GS) technique and the codeword is selected based on a minimum squared weight (MSW) selection criterion. For a better understanding, the method  100  of this embodiment will now be described in further details with reference to  FIG. 7 , in which an example of the disclosure is shown. This disclosure may, however, be embodied in many different forms and should not be construed as limited to the example. Rather, the example is provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. 
       FIG. 7  depicts a schematic block diagram of a method  700  of encoding and decoding of dc-free k constrained codes according to an example embodiment of the present disclosure. In this example embodiment, the GS technique is used to generate the dc-free codes because it was found to be a very efficient method to suppress the dc component of the channel sequence. The GS technique is known in the art and thus need not be described in detail herein. In this example embodiment, the GS technique is combined with the above-described k constrained coding techniques by appending p binary redundant bits to each information word, and thus each information word can be represented by a member of a selection set consisting of 2 p  codewords. After that, the “best” codeword in the selection set is selected to be transmitted over the channel  712  according to a selection criterion (preferably based on a MSW selection criterion, which will be described later below) that suppresses the dc component of the channel sequence. 
     Referring to  FIG. 7 , during encoding, the m 1  user data bits  702  are appended with p redundant bits, to generate a selection set of 2 p  super blocks. The p+m 1 =n−1 bits super block is then scrambled using a feedback register scrambler  704 . After that, the scrambled super block is converted into n-bits k constrained code (in NRZ format) through a k constrained encoder  706  in the same manner as described hereinbefore with reference to  FIG. 2 or 3  according to examples of the present disclosure. The above scrambling and encoding steps are repeated 2 p  times for all possible combinations of the p redundant bits. A selection module  710  then chooses and transmits one codeword preferably according to a MSW selection criterion as will be described below that suppresses the dc component of the channel sequence. 
     During decoding, the codewords received/detected from the channel  712  is first input into a k constrained decoder  716  for decoding in the same manner as described hereinbefore with reference to  FIG. 4 or 5  according to examples of the present disclosure. The decoded data block is then de-scrambled through a de-scrambler  718 . After removing the p redundant bits, the input information word  720  is recovered. 
     In the above method  700  to design dc-free k constrained codes, the selection criterion to select the “best” word from the selection set helps to achieve efficient dc suppression. In this regard, conventionally, the most widely used criterion for the design of dc-free codes is the minimum running digital sum (MRDS) criterion imposed at the end of each codeword. However, although the RDS reflects the disparity of the channel sequence, it does not directly represent the energy of the channel sequence at dc. Therefore, to address this problem and against conventional teaching, the example embodiment uses the minimum squared weight (MSW) criterion for choosing a codeword which has been surprisingly found to result in more dc suppression than the conventional MRDS criterion, for a given number of redundant bits p. Without wishing to be bound by theory, it is believed that this is because the sum of the squared RDS values at each bit position of the codeword, defined as 
                       w   sq     =       ∑     i   =     -   ¥       n     ⁢     z   i   2         ,           (   4   )               
shows exactly the energy of the channel sequence at dc.
 
     As an example illustration,  FIG. 8  depicts a plot of the power spectrum densities (PSD) of a designed rate R=0.9941, k=14 dc-free constrained code with a fixed p=5, but with different selection criteria for GS (i.e., MSW and MRDS criteria) to illustrate the difference in dc suppression between the two criteria. As can be seen, the MSW criterion  802  gains over the MRDS criterion  804  by around 8 dB more dc suppression. This corresponds to 2.5 times reduction in the signal amplitude. Therefore, adopting the MSW criterion to select the best codeword in the GS technique has been found to advantageously result in significantly better dc suppression. 
     Further simulation results will now be disclosed for illustration purposes. By using the code design methods as described hereinbefore according to examples of the present disclosure, various dc-free constrained codes fitting to different data storage systems can be designed.  FIGS. 9A and 9B  illustrate the PSDs of some examples of dc-free k constrained codes designed according to example examples of the present disclosure. From  FIG. 9A , it can be observed that for a fixed codeword length n and hence the k constraint, the amount of dc suppression increases with increase of p. However, increasing p would lead to more code rate loss. On the other hand, as can be seen from  FIG. 9B , for a fixed number of redundant bits p, the amount of dc suppression increases with decrease of n (hence the k constraint). However, decreasing n while fixing p would also lead to more code rate loss. In practical dedicated servo system, depending on the level of the interference between the data layer and the servo layer, the codeword length n and the number of redundant bits p should be chosen to achieve a satisfactory level of dc suppression which can be indicated by the PSD of the repeatable runout (RRO) of the system. The RRO is a key parameter indicating the interference to the servo system of HDDs. The higher the RRO PSD, the larger the level of interference, and the less accurate of the performance of the servo system. 
     RRO simulations were carried out for dedicated servo with the newly designed dc-free k constrained codes, and the obtained RRO spectrum with random data and with dc-free codes are shown in  FIG. 10A  and  FIG. 10B . Note that  FIG. 10C  shows the expanded view of  FIG. 10B  with frequency restricted to 0˜11.5 KHz. During the RRO simulations, the data to servo ratio is set to K=5 (i.e. amplitude of data signal is 5 times of servo signal amplitude). Each set of data sequence consists of 700×4096 or 700×4032 code bits. Each 1 set of 4096 or 4032 bits are used to estimate 1 position error signal (PES) point, thus leading to 700 PES points each revolution. The revolutions per minute (RPM) is set to 5400, and the servo sampling rate is 63K Hz. As can be seen, the RRO simulations results show that codes with more dc suppression result in better RRO performance. This will advantageously lead to less track offset and track mis-registration, and hence improve the data recovery performance of dedicated servo. Note that the profile of the RRO PSD with dc-free codes shows a triangle shape, unlike the square shape of that with the random data (see  FIG. 10A ). This indicates that the total noise power with dc-free codes is even smaller than that shown by the maximum amplitude of RRO spectrum. In practice, the choice of a specific dc-free k constrained codes depends on the amount of dc-suppression required by the system and the affordable code rate loss. 
     According to the present disclosure, there is provided an encoder  1100  for encoding an input data into a codeword (in NRZ format) with a k constraint, corresponding to method  100  as described hereinbefore with reference to  FIG. 1 . As schematically illustrated in  FIG. 11 , the encoder  1100  comprises a partitioning module  1102  configured to partition the input data into a plurality of data blocks comprising a first data block and a plurality of remaining data blocks, a first analysis module  1104  configured to perform a first analysis of the plurality of data blocks for modifying each of the plurality of remaining data blocks that satisfy a first predetermined criterion, a second analysis module  1106  configured to perform a second analysis of the plurality of data blocks after the first analysis for modifying each of the plurality of data blocks that satisfy a second predetermined criterion, and a conversion module  1108  configured to convert/modify each of the plurality of data blocks after the second analysis to produce the codeword in NRZ format with the k constraint. 
     According to the present disclosure, there is provided a decoder  1200  for decoding a codeword with a k constraint into an output data, corresponding to method  400  as described hereinbefore with reference to  FIG. 4 . As schematically illustrated in  FIG. 12 , the decoder  1200  comprising a conversion module  1202  configured to convert/modify each bit of the codeword being in NRZ format, an extraction module  1204  configured to extract, from the converted codeword, a plurality of data blocks comprising a first data block and a plurality of remaining data blocks, a first analysis module  1206  configured to perform a first analysis on the plurality of data blocks for modifying each of the plurality of data blocks that satisfy a first predetermined criterion, and a second analysis module  1208  configured to perform a second analysis on the plurality of data block after the first analysis module for modifying each of the plurality of data blocks that satisfy a second predetermined criterion to obtain the output data. 
     It will be appreciated to a person skilled in the art that the encoder  1100  and decoder  1200  may be software module(s) realized by computer program(s) or set(s) of instructions executable by a computer processor to perform the required functions, or may be hardware module(s) being functional hardware unit(s) designed to perform the required functions. It will also be appreciated that a combination of hardware and software modules may be implemented. 
     In a preferred embodiment, there is provided a hard disk drive system  1300  having incorporated therein the above-described encoder  1100  for encoding an input data into a codeword in NRZ format with a k constraint to be stored on a disk and/or the above-described decoder  1200  for decoding a codeword in NRZ format with a k constraint read from the disk into an output data. According to an example embodiment with reference to  FIG. 13 , the system  1300  comprises a dedicated servo medium  1302  including a data recording layer  1304  and a servo layer  1305 , a spindle motor (not shown) configured to rotate the plurality of the dedicated servo medium, the above-described encoder  1100  for encoding data to be stored on the data recording layer  1304  (through the read/write channel  1308 ), and a write head  1306  coupled to the encoder  1100  (through the read/write channel  1308 ) and operable to write the codewords in NRZ format from the encoder  1100  onto the data recording layer  1304 . The system  1300  preferably also include a read head (which may be integrated with the write head  1306 ) operable to read codewords in NRZ format from the data recording layer  1304 , and the above-described decoder  1200  for decoding the codewords in NRZ format read from the data recording layer  1304 . For example, it will be appreciated that the encoder  1100  and the decoder  1200  may be stored in a memory device/component  1310  of a host computer or controller  1312  and executable by a computer processor  1314 . 
     Some portions of the description are explicitly or implicitly presented in terms of algorithms and functional or symbolic representations of operations on data within a computer memory. These algorithmic descriptions and functional or symbolic representations are the means used by those skilled in the data processing arts to convey most effectively the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities, such as electrical, magnetic or optical signals capable of being stored, transferred, combined, compared, and otherwise manipulated. 
     Unless specifically stated otherwise, and as apparent from the following, it will be appreciated that throughout the present specification, discussions utilizing terms such as “scanning”, “calculating”, “determining”, “replacing”, “generating”, “initializing”, “outputting”, or the like, refer to the action and processes of a computer system, or similar electronic device, that manipulates and transforms data represented as physical quantities within the computer system into other data similarly represented as physical quantities within the computer system or other information storage, transmission or display devices. 
     The present specification also discloses apparatus for performing the operations of the methods. Such apparatus may be specially constructed for the required purposes, or may comprise a general purpose computer or other device selectively activated or reconfigured by a computer program stored in the computer. The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various general purpose machines may be used with programs in accordance with the teachings herein. Alternatively, the construction of more specialized apparatus to perform the required method steps may be appropriate. 
     In addition, the present specification also implicitly discloses a computer program or software/functional module, in that it would be apparent to the person skilled in the art that the individual steps of the methods described herein may be put into effect by computer code. The computer program is not intended to be limited to any particular programming language and implementation thereof. It will be appreciated that a variety of programming languages and coding thereof may be used to implement the teachings of the disclosure contained herein. Moreover, the computer program is not intended to be limited to any particular control flow. There are many other variants of the computer program, which can use different control flows without departing from the spirit or scope of the disclosure. 
     Furthermore, one or more of the steps of the computer program may be performed in parallel rather than sequentially. Such a computer program may be stored on any computer readable medium. The computer readable medium may include storage devices such as magnetic or optical disks, memory chips, or other storage devices suitable for interfacing with a general purpose computer. The computer program when loaded and executed on such a general-purpose computer effectively results in an apparatus that implements the steps of the methods described herein. 
     The software or functional modules described herein may also be implemented as hardware modules. More particularly, in the hardware sense, a module is a functional hardware unit designed for use with other components or modules. For example, a module may be implemented using discrete electronic components, or it can form a portion of an entire electronic circuit such as an Application Specific Integrated Circuit (ASIC). Numerous other possibilities exist. Those skilled in the art will appreciate that the system can also be implemented as a combination of hardware and software modules. 
     While examples of the disclosure have been particularly shown and described with reference to specific examples, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims. The scope of the disclosure is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced. 
     The foregoing description is merely illustrative in nature and is in no way intended to limit the disclosure, its application, or uses. The broad teachings of the disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent upon a study of the drawings, the specification, and the following claims. It should be understood that one or more steps within a method may be executed in different order (or concurrently) without altering the principles of the present disclosure. Further, although each of the embodiments is described above as having certain features, any one or more of those features described with respect to any embodiment of the disclosure can be implemented in and/or combined with features of any of the other embodiments, even if that combination is not explicitly described. In other words, the described embodiments are not mutually exclusive, and permutations of one or more embodiments with one another remain within the scope of this disclosure. 
     Spatial and functional relationships between elements (for example, between modules, circuit elements, semiconductor layers, etc.) are described using various terms, including “connected,” “engaged,” “coupled,” “adjacent,” “next to,” “on top of,” “above,” “below,” and “disposed.” Unless explicitly described as being “direct,” when a relationship between first and second elements is described in the above disclosure, that relationship can be a direct relationship where no other intervening elements are present between the first and second elements, but can also be an indirect relationship where one or more intervening elements are present (either spatially or functionally) between the first and second elements. As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A OR B OR C), using a non-exclusive logical OR, and should not be construed to mean “at least one of A, at least one of B, and at least one of C.” 
     In the figures, the direction of an arrow, as indicated by the arrowhead, generally demonstrates the flow of information (such as data or instructions) that is of interest to the illustration. For example, when element A and element B exchange a variety of information but information transmitted from element A to element B is relevant to the illustration, the arrow may point from element A to element B. This unidirectional arrow does not imply that no other information is transmitted from element B to element A. Further, for information sent from element A to element B, element B may send requests for, or receipt acknowledgements of, the information to element A. 
     In this application, including the definitions below, the term “module” or the term “controller” may be replaced with the term “circuit.” The term “module” may refer to, be part of, or include: an Application Specific Integrated Circuit (ASIC); a digital, analog, or mixed analog/digital discrete circuit; a digital, analog, or mixed analog/digital integrated circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor circuit (shared, dedicated, or group) that executes code; a memory circuit (shared, dedicated, or group) that stores code executed by the processor circuit; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system-on-chip. 
     The module may include one or more interface circuits. In some examples, the interface circuits may include wired or wireless interfaces that are connected to a local area network (LAN), the Internet, a wide area network (WAN), or combinations thereof. The functionality of any given module of the present disclosure may be distributed among multiple modules that are connected via interface circuits. For example, multiple modules may allow load balancing. In a further example, a server (also known as remote, or cloud) module may accomplish some functionality on behalf of a client module. 
     The term code, as used above, may include software, firmware, and/or microcode, and may refer to programs, routines, functions, classes, data structures, and/or objects. The term shared processor circuit encompasses a single processor circuit that executes some or all code from multiple modules. The term group processor circuit encompasses a processor circuit that, in combination with additional processor circuits, executes some or all code from one or more modules. References to multiple processor circuits encompass multiple processor circuits on discrete dies, multiple processor circuits on a single die, multiple cores of a single processor circuit, multiple threads of a single processor circuit, or a combination of the above. The term shared memory circuit encompasses a single memory circuit that stores some or all code from multiple modules. The term group memory circuit encompasses a memory circuit that, in combination with additional memories, stores some or all code from one or more modules. 
     The term memory circuit is a subset of the term computer-readable medium. The term computer-readable medium, as used herein, does not encompass transitory electrical or electromagnetic signals propagating through a medium (such as on a carrier wave); the term computer-readable medium may therefore be considered tangible and non-transitory. Non-limiting examples of a non-transitory, tangible computer-readable medium are nonvolatile memory circuits (such as a flash memory circuit, an erasable programmable read-only memory circuit, or a mask read-only memory circuit), volatile memory circuits (such as a static random access memory circuit or a dynamic random access memory circuit), magnetic storage media (such as an analog or digital magnetic tape or a hard disk drive), and optical storage media (such as a CD, a DVD, or a Blu-ray Disc). 
     In this application, apparatus elements described as having particular attributes or performing particular operations are specifically configured to have those particular attributes and perform those particular operations. Specifically, a description of an element to perform an action means that the element is configured to perform the action. The configuration of an element may include programming of the element, such as by encoding instructions on a non-transitory, tangible computer-readable medium associated with the element. 
     The apparatuses and methods described in this application may be partially or fully implemented by a special purpose computer created by configuring a general purpose computer to execute one or more particular functions embodied in computer programs. The functional blocks, flowchart components, and other elements described above serve as software specifications, which can be translated into the computer programs by the routine work of a skilled technician or programmer. 
     The computer programs include processor-executable instructions that are stored on at least one non-transitory, tangible computer-readable medium. The computer programs may also include or rely on stored data. The computer programs may encompass a basic input/output system (BIOS) that interacts with hardware of the special purpose computer, device drivers that interact with particular devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, etc. 
     The computer programs may include: (i) descriptive text to be parsed, such as HTML (hypertext markup language), XML (extensible markup language), or JSON (JavaScript Object Notation) (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. As examples only, source code may be written using syntax from languages including C, C++, C#, Objective-C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl, Pascal, Curl, OCaml, Javascript®, HTML5 (Hypertext Markup Language 5th revision), Ada, ASP (Active Server Pages), PHP (PHP: Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, MATLAB, SIMULINK, and Python®. 
     None of the elements recited in the claims are intended to be a means-plus-function element within the meaning of 35 U.S.C. §112(f) unless an element is expressly recited using the phrase “means for,” or in the case of a method claim using the phrases “operation for” or “step for.”