Modulation codes for precoded partial response channels

[d, k] Modulation codes for 1/(1⊕D²) precoded PR4 channels (PPR4) and 1/(1⊕D⊕D²⊕D³) precoded EPR4 channels (PEPR4) are proposed in this paper. They differ from conventional (d, k) constrained codes in the sense that they provide PPR with a direct control over separation between transitions during writing and the number of consecutive zero-samples during reading. Their Finite State Machines (FSM), which have the same Shannon Capacity as their counterparts of (d, k) codes, are constructed. For comparison with the 2/3 (1;7) code, a 2/3 [1, 6] code for PPR4 and a 2/3 [1, 5] code for PEPR4 are designed. They have a 5-state encoder and 8-bit decoding window, and an 8-state encoder and 9-bit decoding window, respectively. Their power spectra are calculated. As an example, error rate performances of (1, 7) PR4ML, (1, 7) PPR4ML, and [1, 6] PPR4ML are simulated under the Lorentzian model with both medium and electronic noises at various channel recording density. The result shows that the [1, 6] PPR4ML outperforms both the (1, 7) PR4ML and the (1, 7) PPR4ML consistently. More importantly, the [d, k] precoded PR (PPR) prevents error propagation which (1, 7) PR may suffer from, and deals with non-linearity more effectively than (1, 7) PPR. The technique presented in this paper is applicable to other extended PPR or precoded generalized PR (PGPR)