Conference Paper

Combinatorial construction of high rate runlength-limited codes

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Abstract

New combinatorial construction techniques are proposed which convert binary user information into a (0,k) constrained sequence having the virtue that at most k `zeroes' between logical `ones' will occur. In this way sequences are constructed which have a limited runlength. These codes find application in optical and magnetic recording systems. The new construction methods provide efficient, high rate codes with a low complexity. The low complex combinatorial structure of the encoder and the decoder ensure a very fast and efficient parallel conversion of binary information to codewords and vice versa. Specifically, we present the combinatorial structures to convert 16 data bits into a 17 bit constrained sequence to obtain an optimum (0,4) code, a (0,6) code with at most one byte error propagation, and a (0,6/6)-code, respectively. Serious error propagation is avoided by using constrained codes with several unconstrained positions, which are reserved to store the parity bits of an error control code which protects the constrained codeword

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... The FRB algorithm compares favorably with enumerative [15],[[17],Chap.6],[19], and combinatorial [20],[60] encoding: two important existing methods to generate (0, k) sequences. Specifically, the FRB encoding/decoding is simpler than enumeration , while achieving (asymptotically) similarly high encoding rates. ...
... Details of a rate 16/17, k = 6 code based on this technique can be found in [[17], pp.102103. Some other combinatorial constructions for high-rate (0, k) codes are discussed in [60]. An alternative to combinatorial techniques is to use enumerative coding (see [[17], ...
... The iterative pre-processing ideas were also extended to build fixed-rate (0, G/I) codes in Chapter 7.6. Two important existing methods to generate (0, k) sequences use enumerative [[17],Chap.6],[19], and combinatorial [20],[60] encoding. The FRB encoding/decoding is simpler than enumeration, while achieving (asymptotically) similarly high encoding rates. ...
Article
Run-Length-Limited (RLL) channels are found in digital recording systems like the Hard Disk Drive (HDD), Compact Disc (CD), and Digital Versatile Disc (DVD). This thesis presents novel encoding algorithms for RLL channels based on a simple technique called bit stuffing. First, two new capacity-achieving variable-rate code constructions are proposed for (d,k) constraints. The variable-rate encoding ideas are then extended to (0,G/I) and other RLL constraints. Since variable-rate codes are of limited practical value, the second half of this thesis focuses on fixed-rate codes. The fixed-rate bit stuff (FRB) algorithm is proposed for the design of simple, high-rate (0,k) codes. The key to achieving high encoding rates with the FRB algorithm lies in a novel, iterative pre-processing of the fixed-length input sequence prior to bit stuffing. Detailed rate analysis for the proposed FRB algorithm is presented, and upper and lower bounds on the asymptotic (in input block length) encoding rate are derived. Several system-level issues of the proposed FRB codes are addressed, and FRB code parameters required to design rate 100/101 and rate 200/201 (0,k) codes are tabulated. Finally, the proposed fixed-rate encoding is extended to (0,G/I) constraints. Ph.D. Committee Chair: McLaughlin, Steven; Committee Member: Barnwell, Thomas; Committee Member: Barry, John; Committee Member: Fekri, Faramarz; Committee Member: Tetali, Prasad
... This codeword is protected by a systematic enor control code. The e parity bits are inserted in the codeword in a specific manner [21], such that the resulting sequence I c H c ,p.l .c · 1;1 ,·'C lp' l c ·1~1 Fig. 3. Block diagram of CC-EC Scheme II, a two-step modulation and error control coding scheme. ...
... The construction of a ( 0, G I I) code [2], [22] is in general more difficult than is the construction of a (0, k) code, because both the global (0, G) constraints and the (0, I) constraints on the interleaved sequences of elements with odd and even indices have to be fulfilled. In [23], a combinatorial construction of a rate 8/9, (0, 4/4) code and a rate 8/9, (0, 3/6) code have been presented, and in [14], [21], and [24], a rate 16/17, (0, 6/6) code has been presented. ...
... Otherwise, the constraints on the odd and even subsequence are violat~d. As an example, consider the rate 16/17, (0, 6/6) code [21]. By inserting pairs of unconstrained po- Table look-up can be employed to convert the other eight-bit source words into ten-bit codewords. ...
... This translates to low hardware requirements for the encoder and the decoder. Another method with similar aims but for a different class of line codes is described in [50,51]. ...
... A 8 -b it long code-word has one bit inserted in the middle.The maximum run-length in this code word was two before the insertion and it becomes three afterwards.However, by correctly designing the line code, it is possible in most cases to incorporate the inserted bits within the maximum run-length. This can be achieved by designing the line code to have unconstrained bit positions where single bits can be inserted w ithout affecting the maximum run[50]. Such a code has the property th a t it can be encoded and decoded independently of the value of those bits.Furthermore, in certain error correcting and line code combinations, it is possi ble to leave some of the information symbols uncoded and to distribute them , together with the parity symbols, in available unconstrained bit positions of the run-length limited sequence. ...
Thesis
Channel coding is an important consideration influencing the design of a communications system. In particular, error control coding is used to detect and/or correct errors and line coding to modify the characteristics of the transmitted signal to suit other constraints of the channel, such as restricted frequency response. This thesis explores aspects of channel coding for such constrained channels with emphasis given to error control coding. Specifically, the hrst chapter of this thesis presents a general overview of channel coding, presents the organisation of the thesis and details the main contributions. The second chapter gives an overview of the principles of error control coding and line coding and explains a few terms that are connnonly used in the remainder of the thesis. One kind of constrained channel investigated here is the binary asymmetric error channel, where error transitions from one to zero occur with different probability than from zero to one. Error correcting codes for this channel and their properties are investigated in the third chapter. The fourth chapter introduces disparity control coding, and proposes a new error control coding structure that satisfies disparity constraints for both binary asymmetric and symmetric error channels. Run length limited channels are the subject of the hfth chapter. A new coding structure is proposed that offers advantages in performance over the one conventionally used for error control in such channels. The sixth chapter introduces peak power constraints present in multi-carrier systems. Codes that can be used limit the peak to average power ratio of such systems are presented and the application of the coding structure of the fifth chapter is also discussed. The final chapter brings the thesis to a conclusion by summarising the main results and proposing areas where further work may be fruitful.
... Fortunately, a block encoder/decoder architecture with acceptable implementation complexity for the constraints proposed here can always be designed by well known enumerative techniques [5]. A particularly efficient architecture based on the combinatorial techniques of [6] for one of the considered constraints is presented in [9] and outlined in Section V. ...
... In practice, there is always intertrack interference (ITI), i.e., the read head picks up magnetization from an adjacent track. Therefore, the channel output is given by (6) where is the discrete-time impulse response of the head to the adjacent track, and is the sequence recorded on that track. We assume that the noise is white. ...
Article
Full-text available
During the past few years, significant progress has been made in defining high capacity constraints which prohibit specified differences between constrained sequences, thus ensuring that the minimum distance between them is larger than for the uncoded system. However, different constraints which avoid the same prescribed set of differences may have different capacities, and codes into such constraints may have different complexity of encoder/decoder architecture and different performance on more realistic channel models. These issues, which have to be considered in application of distance enhancing codes, are discussed here. We define several distance enhancing constraints which support design of high rate codes. We also define weak constraints for which the minimum distance between sequences may be the same as for the uncoded system but the number of pairs of sequences at tile minimum distance is smaller. These constraints support design of even higher rate codes. We discuss the implementation issues of both types of constraints as well as their performance on the ideal channel and channels with colored noise and intertrack interference
... This imposes limitations on the block length and the achievable rate. The majority of codes have a rate 8/9, and only recently, codes with longer block lengths have been developed, either by using algorithms [4], [14], [15] or by interleaving a short block code with uncoded bits [15]–[17]. The latter methods increase the rate and limit error propagation, but the constraints of the resulting code are certainly not the best possible for the given rate. ...
Article
Full-text available
We present advanced combinatorial techniques for constructing maximum runlength-limited (RLL) block codes and maximum transition run (MTR) codes. These codes find widespread application in recording systems. The proposed techniques are used to construct a high-rate multipurpose modulation code for recording systems. The code, a rate 16/17, (0,3,2,2) MTR code, that also fulfills (0,15,9,9) RLL constraints is a high-rate distance-enhancing code with additional constraints for improving timing and gain control. The encoder and decoder have a particularly efficient architecture and allow an instantaneous translation of 16-bit source words into 17-bit codewords and vice versa. The code has been implemented in Lucent read-channel chips and has excellent performance
... 2. Possible realization of combined guided scrambling and MRL coding, where the sequence selector anticipates post-processing with an MRL code. uncoded source symbols as described in [4], [5]. One can get an additional degree of freedom in the selection of the scrambled sequences by using a strategy where the interspersed bits are observed and the source symbols of the underlying constrained code are transformed only if the overall constraints are violated, or, interestingly, the encoder may select one of the two possible sequences based on the overall constraints. ...
Conference Paper
Methods are developed to effectively combine guided scrambling and maximum run-length limited codes in order to impose a guaranteed maximum run-length constraint. It will be demonstrated that the combination of guided scrambling and a well-chosen maximum run-length limited code may offer a sound trade-off between overall code rate and performance in terms of the probability of violating the channel constraints.
... ) codes [25], [33], MTR( ) codes [26], and PRML( ) codes [27] . The MTR code design methodologies presented in this section are based on the use of the state transition diagrams for MTR constraints and the application of the look-ahead coding technique and violation detection combined with substitution. ...
... The high rate´¼ Ð Ö µ codes presented in [5], [6] are particularly suitable for the construction of higher rate codes because of their tight constraints. This is achieved by interspersing the codewords with uncoded source symbols as described in [4], [5]. One can get an additional degree of freedom in the selection of the scrambled sequences by using a strategy where the interspersed bits are observed and the source symbols of the underlying constrained code are transformed only if the overall constraints are violated, or, interestingly, the encoder may select one of the two possible sequences based on the overall constraints. ...
Article
Guided scrambling generates for each possible source word a unique set of candidate codewords and selects the "best" word subject to certain given channel constraints. This is an effective technique to generate long and highly efficient codes that satisfy the given channel constraints with high probability. These codes are referred to as weak constrained codes, because the guided scrambling method cannot guarantee that all constraints are satisfied. One of the common constraints, the maximum run-length constraint, is of particular importance, because sequences that violate this constraint are likely to cause loss of timing. For this reason, methods are developed in conjunction with guided scrambling to impose a guaranteed maximum run-length constraint. The performance of combined guided scrambling and maximum run-length limited codes is analyzed. It will be demonstrated that the combination of guided scrambling and a well-chosen maximum run-length limited code may offer a sound trade-off between overall code rate and performance in terms of the probability of violating the channel constraints.
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Self-clocking five bit record playback system
  • G Milligan