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This paper describes an efficient redundancy reduction coding scheme for bi-level facsimile signals and field test results of a Group 3 facsimile machine applying this technique. The bi-level signal obtained by scanning documents is characterized by white-to-black or black-to-white edges. These edges cross successive scan lines smoothly in most cases. This scheme makes use of two-dimensional correlation by coding the difference in positions where an edge crosses successive scan lines. The performance of this scheme has been evaluated by computer simualtions for eight CCITT SG.XIV test documents scanned at an 8 lines/mm rate. This scheme reduces the entropy by 24 to 60 percent over the conventional run-length coding scheme and 2 to 10 percent over one of the currently proposed two-dimensional coding schemes, respectively. In a newly fabricated prototype model of a Group 3 machine using this technique, a run-length coded line is inserted every lines to prevent error propagation. In accordance with subjective test results, is set equal to two in that machine for the case of 3.85 lines/mm resolution and equal to four for the case of 7.7 lines/mm resolution. For these two levels of resolution, the average transmission times for the eight CCITT test documents are roughly equal to 49 s and 70 s, respectively, at a transmission rate of 4800 bits/s.