Conference Paper

Error detecting runlength-limited sequences

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Abstract

Codes based on runlength-limited sequences are the state of the art corner stone of current disk recorders, whether their nature is magnetic or optical. The error detecting or correcting capabilities of runlength limited sequences are quite poor. In this paper, the author presents an algebraic approach for constructing runlength-limited block codes of fixed codeword length that impart some error detecting capabilities

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... These are (d = 0, k) codes, where d and k denote, respectively , the minimum and maximum run-length of zeros between ones in an unprecoded channel data stream. There are several RLL codes with or without enhanced error control capabilities [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. The (d = 0, k/I) RLL codes use gated-partition logic to achieve high rates such as 8/9 [1] and 16/17 [2], while focusing on the k, I (interleave) constraints. ...
... Single error detecting systematic RLL codes subject to rate loss are presented in [7], using m parity check bits to produce rates of R C = N/(N + 1 + m). Finally, in [8] the error detecting modulation codes with 3–4 times larger block length than conventional RLL of the same rate, alleviate the code rate overhead due to the appended parity, but they increase the system's probability of error. In [8], code rate reduction is avoided by choosing the odd or the even sequences only, whichever provides sufficient number of codewords satisfying constraints d, k. ...
... Finally, in [8] the error detecting modulation codes with 3–4 times larger block length than conventional RLL of the same rate, alleviate the code rate overhead due to the appended parity, but they increase the system's probability of error. In [8], code rate reduction is avoided by choosing the odd or the even sequences only, whichever provides sufficient number of codewords satisfying constraints d, k. Not all rates are feasible for every block length due to insufficient number of available codewords, and the obtained rates are lower than the conventional 8/9, and 16/17 RLL codes. ...
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We present a new methodology for the construction of high-rate channel modulation run-length-limited RLL (0,k) codes. Simple modulation encoders and decoders are constructed, with low error propagation during decoding. They combine partial error detection capability (PED) to boost the performance of a concatenated outer Error Correction Code (ECC) [1]. Moreover, current systems are using low redundancy ECC, and the overall rate is mainly determined by the inner modulation code rate, which critically is to be maintained high. Code rates R c=N/(N+1), for example, 16/17, 24/25 and higher are achievable, with efficiency exceeding 0.94 and 0.96, respectively. The proposed fixed length block decodable codes, are generalized schemes of the type N/(N+1)(d=0,k=[N/2]) for N≥5.
... In general, an RLL(d,k) code can be described as finite state machine by a state transition diagram [50] as shown in Figure 5-7. The state transition diagram has k+1 states, which are denoted by σ 1 ,...,σ k 1 + . ...
... RLLWhile the sums of each row provide the actual numbers of successor states of each state, the term 2 p defines the required successor states of each state.The state transition matrix D q as defined in Section 5.2.1 would obey the (d,k)-constraints, but unfortunately it does in general not fulfill the requirement of Equation 5-15. However, there exist several different methods for deriving from D q a proper state transition matrix as summarized by Immink in[50]. In the following the sliding block code algorithm of Adler et al.[52][53] is introduced, since this method results in general in the lowest logic complexity for the implementation. ...
... In recent years, some attention has been given (examples include [6] [7] [8] [9] [10]) to the problem of designing (d; k)-constrained codes with error-correction capabilities. This research has been motivated by the idea that some of the inherent redundancy of (d; k)-constrained codes can be exploited towards error correction. ...
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