Coded modulation schemes with turbo and list detection for high-order partial response channels

Structured Set Partition (SSP) of PR channel output words was proved to be a useful tool to increase linear densities when combined with multilevel concatenated coding. In this paper, we describe a method for constructing SSP´s with good spectra of minimum Euclidean distances using multiple embedded linear subspaces and their cosets. Examples of some simple SSP precoders are provided. Bit-error-rate (BER) performances of various partial responses and multilevel modulation schemes are compared using bit-by-bit simulations. Partial responses are defined by the classical and modified target polynomials, while multilevel modulation schemes include (1) an SSP, (2) a set of conventional block codes with different error correcting capabilities, and (3) a variety of iterative decoders such as the List Trellis Decoder (LTD), the BCJR algorithm, and soft decoders for low-density parity check codes. Simulation results show that the ME²PR4 channel with two iterations of LTD using only two paths in the list gives gains of 3.3 dB and 3.8 dB at BER 10^-6 compared to the 16/17 (0,6/6) coded E²PR4 channel for linear densities 2.5 and 3.0, respectively. The LTD scheme does not use soft decisions or additional distance-enhancing constraints, like d=1, maximum-transition-run (MTR), or quasi-MTR codes. An additional coding gain of 0.5-1.0 dB can be achieved by combining the BCJR algorithm (instead of LTD) with the soft decoding of low density parity check codes