Abstract: This paper provides a conceptual description of data dependability, and proposes a primary scheme of a fault-tolerant computing system. One of the fundamental research topics for the scheme is data compression. Linear Feedback Shift Registers (LFSRs)are suggested to compress the data, but prone to aliasing errors due to some specific types of error patterns.Based on a penetrating mathemat ical analysis for various structures of LFSRs, necessary and sufficient conditions for aliasing errors are presented, and a design for data compressor is proposed which will prevent any aliasing double errors.Such prevention cannot be obtained by any extension of an LFSR.