A Class of High-Rate Low-Complexity Error-Detecting RLL Codes
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Class of High-Rate N/(N + 1) Low-Complexity Error-Detecting RLL Codes Anthony G. Bessios† Texas Instruments, Inc., Dallas, TX 75243, USA
Received 3 April 2000 and in revised form 24 August 2001 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) (Blaum, 1991). 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 Rc = 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. Keywords and phrases: run-length-limited constrained codes.
1. INTRODUCTION New high-rate RLL block codes are proposed in this paper. 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. Their error detection capability is limited to the codewords non-supported by the code, as well as to the weak constraint of k, I violations. Furthermore, the block mapping size grows exponentially with the user data word length N . Concatenation of conventional RLL codes with ECC can reduce the effectiveness of the ECC, especially with a sliding block encoder/decoder subject to error propagation [3]. The single-error correcting RLL codes combine RLL with single-error correcting capability via an increase of the codewords’ minimum distance dmin , but with the adverse effect of a lower rate, such as 8/21, 8/28 [3], or 1/3 and 7/17 [4]. In [5], it was proposed that the Hamming subcode block length is kept as large as possible to avoid rate loss for a single-error correcting ECC/RLL code. In [6], redundancy based on appended parity bits is used, or access to channel-side information is possible and sufficiently long †
The author is currently with Agere Systems, Milpitas, CA 95035, USA; Email: [email protected].
codewords are assumed, to construct high rate codes with single error correction capability. Single error detecting systematic RLL codes subject to rate loss are presented in [7], using m parity check bits to produce rates of RC = 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 erro
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