DC-Free Multimode Code Design Using Novel Selection Criteria for Optical Recording Systems 553

J. Lee and K. A. S. Immink: DC-free Multimode Code Design Using Novel Selection Criteria for Optical Recording Systems 553 DC-free Multimode Code Design Using Novel Selection Criteria for Optical Recording Systems Jun Lee and Kees A. Schouhamer Immink, Fellow, IEEE Abstract — DC-free run-length limited codes have been the consisting of L > 3 codewords. The encoder evaluates the cornerstone of all three generations of optical recording, CD, quality of each codeword in the selection set, and then transmits DVD and BD. Research into very efficient coding methods is the codeword with the least DC-contribution. There are two key paramount for the upcoming fourth generation. Guided elements for multimode code design with DC-free property. Scrambling (GS) is an efficient coding method that has been One is a scrambler for translating source words into their reported in the literature. Under GS rules, a user word is corresponding selection sets, and the other is a good criterion for translated into a plurality of possible candidate words, and evaluating the quality of the candidate codewords. The spectral among the candidate words the encoder selects the codeword performance of the code greatly depends on both issues. with the least low-frequency spectral content. In our paper, we The best multimode coding scheme reported is guided will present results of our attempts to improve the performance scramble (GS) [6]. Originally, GS scheme is designed for fiber of GS-based codes. We will present new selection criteria and optic communication system required to DC-suppression, and evaluate their performance and complexity. Specifically, we its application is limited to the transmission system over fiber will evaluate the new selection criteria to the 2/3(1,7) parity cables. In recent, its application is moving toward optical preserving code used in Blu-Ray Disc. recording system requiring DC-free property. GS scheme exploits the linear shift feedback register as scrambler and Index Terms — Selection Criterion, GS, DC-free RLL code augmenting step for generating the distinct candidate codewords. The DC-control of GS scheme can be achieved by developing I. INTRODUCTION selection criterion, which is one of the key elements of The design of codes for optical recording is essentially the multimode code. The criteria developed can also be extended to design of the combined DC-free and runlength-limited any multimode coding scheme. Immink and Patrovics [4] (DCRLL) codes. An RLL constraint in optical recording plays a assessed the spectral performance of the GS scheme under crucial role for the reduction of channel impairments and clock conventional criteria. With the same redundancy, the simulation recovery. The DC-free property is for circumventing or reducing results show that the performance of GS scheme with short interaction between data written on disk and the servo systems codeword length is almost the same irrespective the selection that follow the track. In literatures [1][2], the design of DCRLL criteria, while that with long codeword length is very sensitive codes can be accomplished by several design techniques and to the selection criteria. This fact reveals that the selection has been mostly concentrated on byte-oriented DCRLL code criterion is indispensable for multimode code design with DC- with the small codeword length. The data recording industry has free property and certain application. been moving towards detection scheme that can function well at The criteria reported for evaluating the quality of the high code rate such as 16/17, 24/25 and 32/33. For certain candidate codewords are minimum running digital sum application, it is desirable that the code rate and codeword (MRDS), minimum squared weight (MSW) and minimum length of a modulation code for optical recording are even threshold overrun (MTO) [1][4][9]. The MRDS criterion that higher. However, unfortunately, the design of high-rate DCRLL selects a codeword with minimum absolute RDS at the end of code satisfying all of two constraints is far from obvious, and each codeword requires the simplest complexity, while its severely hampered by the large number of states of the finite- spectral performance is degraded as the length of codeword is state machine (FSM) which models the channel constraints increased. The MSW criterion that selects a codeword with the [3][4]. minimum variance of RDS among candidate codewords can One possible solution for achieving high capacity adopts a achieve the best performance irrespective of the codeword weakly constrained code, instead of perfectly RLL constrained length, while its complexity is large because it requires the code, for designing recording code. Recently, multimode coding squaring operation. The MTO criterion simply counts the scheme is issued for next-generation optical recording [4][5]. number of times that the absolute value of RDS in the codeword The coding scheme is one of methods for constructing weakly is larger than the threshold predetermined by trial and error. constrained code with DC-free property. In multimode codes, Then, it selects the codeword with minimum overrun. The each source word is translated into codewords of a selection set structure is simple compared to MSW, while it can select codeword with bad quality because it randomly chooses one if Jun Lee is with Digital Storage Research Laboratory, LG Electronics in there are codewords with the same penalty. This paper suggests Korea (e-mail: [email protected]). the minimum peak RDS (MPRDS) criterion that is simple to Kees A. Schouhamer Immink is with Institute for Experimental implement while its efficiency approaches that of the MSW Mathematics, Ellernstrasse 29-31, Essen, Germany (e-mail: criterion. The scheme does not require the exhaustive search of [email protected]). optimal threshold unlike MTO, and achieves the reasonable Contributed Paper Manuscript received December 1, 2008 0098 3063/09/$20.00 © 2009 IEEE Authorized licensed use limited to: Kees Immink. Downloaded on August 11, 2009 at 00:48 from IEEE Xplore. Restrictions apply. 554 IEEE Transactions on Consumer Electronics, Vol. 55, No. 2, MAY 2009 performance irrespective of the number of candidate codewords variance of sequences, the smaller its DC-content at low like MSW, and only requires simple components (adder and frequency. comparator) while MSW requires squaring operator in addition Code efficiency [1] is given by to that of conventional criteria for implementation. For (1− CN ( ))σ 2 improving the performance of criteria, we also propose the sign E = RDS (2.2) change (SC) aided criteria. SC criterion is appended to the (1− Rs ) 2 proposed and conventional criteria as sub-criterion, and then SC 2 where 1−C(N) and σ RDS are the redundancy and sum variance aided criteria reduce the probability selecting codewords with of maxentropic DC-free sequences, respectively, and R is the large DC-contribution among codewords with the same penalty. code rate of the implemented code, and s2 is variance of RDS Thus, SC aided criteria can achieve better DC-suppression than values obtained at every bit position of sequences produced by those without SC. We also suggest the absolute RDS criterion implemented code. It means how redundancy-sum variance (ABSRDS). This criterion is the simplified version of MSW product of implemented code approaches to that of because it uses absolute operation instead of the squaring maxentropic sequence. Maxentropic DC-free sequences operation of MSW for computing RDS variation. The scheme satisfy the following relationship between the sum variance achieves the best performance among the proposed schemes. In and the redundancy [1] addition, we introduce the complexity reduction (CR) versions 2 of new and conventional criteria, which are CRMSW, 0.2326 <(1−C(N)) σ RDS ≤ 0.25. (2.3) CRABSRDS, CRMPRDS and CRMTO. CR criterion sparsely Since the codeword length that we are targeting is very long evaluates each codeword instead of checking at each bit of the (greater than 50 bits), DSV is around 30. For large N, the codeword. The scheme requires definitely less complexity than redundancy-sum variance product of maxentropic sequences the conventional schemes, and the performance loss is not is approximately constant and equals 0.2326. Thus, E is given noticeable in the range investigated. For displaying certain by application of the proposed criteria, we apply the proposed 0.2326 E ≈ criteria to 2/3(1, 7) parity preserving (PP) code [7], and GS 2 . (2.4) scheme satisfying RLL constraints. For better DC-control of (1, (1− Rs ) 7) PP code, its encoding exploits look ahead (LA) algorithm that The efficiency in the equation (2.4) is used for discussing the looks ahead some codewords. From the simulation results, we performance of the proposed criteria. identify that the spectral performance of the proposed criteria The paper applies the proposed criteria to GS scheme, outperforms that of conventional criteria. which is a multimode coding scheme, for examining their This paper is organized as follows. We firstly start with some performance. Figure 1 represents the operation procedure of preliminaries in Section II. In Section III, we introduce the GS algorithm. In Figure 1, symbols T and ⊕ denote the shift conventional and proposed criteria, and analyze their spectral register and modulo-2 addition, respectively. The operation performance. Section IV applies the proposed criteria to two process of GS algorithm is executed as follows. In the first DCRLL coding for optical recording systems. Finally, Section V step, the source word X = {x1,…,xm}, xi ∈{0, 1}and i = 1,...,m, remarks conclusion. is preceded by all the possible binary sequences of length r-1 (r−1) to generate the L' = 2 vectors of B={b1,…,bL'}, bj = II. PRELIMINARIES {b1,...,bn} and j = 1,...,L'. In the second step, each vector of DC-free codes translate binary source sequences into binary length n=m+r−1 consisting of B is provided to linear shift channel sequences with spectral null at zero frequency.

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