In recent years, various concatenation coding-decoding schemes for magnetic recording have been investigated in which the concatenation codes used are actually error correction codes. Reports that the use of these error-correction codes leads to improved efficiency characteristics of the recording process have motivated us to propose a new concatenation coding-decoding scheme. In our concept, higher-dimensional parity check codes, which are well known in the digital communications area for their strong error correction capability, are combined with partial response-equalized magnetic recording channels. We also propose a novel variable-threshold soft-decision decoding method along with the higher-dimensional parity check code that combines error detection based on parity check line vectors (informal decision) with decision-making based on comparing the confidence level of each symbol to a threshold value (formal decision). After formulating this scheme, we conducted an investigation to compare its error rate characteristics with those of a system in current use, a 16/17(0.6.6) encoding/decoding system. In this comparison we observed a clear improvement using our scheme, specifically a 3.0-dB improvement in the SN ratio required to achieve a 10(-4) bit error rate. (c) 2005 Wiley Periodicals, Inc.