Trellis-based postprocessing of Viterbi decisions for noise decorrelation and compensation of nonlinear distortion (with application to magnetic recording channels)

This paper presents a new concatenated decoding algorithm for partial response channels in which the inner decoder is a low-complexity suboptimal Viterbi decoder that operates in the presence of linear or nonlinear intersymbol interference and/or correlated noise, and the outer decoder (or “postprocessor”) is used to introduce “non-redundant error correction” (error correction in the absence of channel coding), by taking advantage of the knowledge of the components of the channel response neglected by the inner decoder. The postprocessor operates by searching a trellis where the number of states is determined by the maximum length of error events expected, and is independent of the length of the channel impulse response. By contrast, the number of states of an optimal Viterbi decoder would increase exponentially with the length of the channel response. Therefore this algorithm allows long channel responses, typically arising from noise decorrelation, to be efficiently decoded. The primary example used is the partial response class IV (PR IV) magnetic recording channel. We show that when the postprocessor is used to compensate the nonlinearity of this channel, it typically yields a 2 dB gain over the (linear) PR IV Viterbi decoder. If, in addition, it is used for noise decorrelation, it yields a 3 dB gain. The algorithm can also be used to jointly decode a DC-free code of the type described by Knudson et al. (see Proceedings of GLOBECOM 93). The complexity of the trellis-based postprocessor is low, and it becomes even lower when DC-free codes are simultaneously decoded