An Analysis on Optimal Rates of BDB Encoders for RLL and MTR Systems
Panu Chaichanavong · IEEE Transactions on Information Theory · 2005
In most recording channels, modulation codes are employed to transform user data to sequences that satisfy some desirable constraint. Run-length-limited (RLL(d,k)) and maximum transition run (MTR(j,k)) systems are examples of constraints that improve timing and detection performance. A modulation encoder typically takes the form of a finite-state machine. Alternatively, a look-ahead encoder can be used instead of a finite-state encoder to reduce complexity. Its encoding process involves a delay called look-ahead. If the input labeling of a look-ahead encoder allows block decodability, the encoder is called a bounded-delay-encodable block-decodable (BDB) encoder. These classes of encoders can be viewed as generalizations of the well-known deterministic and block-decodable encoders. Other related classes are finite-anticipation and sliding-block decodable encoders. In this paper, we clarify the relationship among these encoders. We also discuss the characterization of look-ahead and BDB encoders using the concept of path-classes. To minimize encoder complexity, look-ahead is desired to be small. We show that for nonreturn to zero inverted (NRZI) versions of RLL|,(0,k),RLL(1,k), and RLL(d,infin), a BDB encoder does not yield a higher rate than an optimal block-decodable encoder. However, for RLL(d,k) such that dges4 and d+2lesk