Abstract
Fix-free codes are a type of variable length codes with both prefix-free and suffix-free properties, and there are two types of fix-free codes: symmetric fix-free codes and asymmetric fix-free codes. In this paper, we mainly discuss symmetric fix-free codes. First, the existence of symmetric fix-free codes is studied in detail, and some necessary and sufficient conditions are proposed. We also discuss the problem of achieving synchronization of symmetric fix-free codes, which is important in application. We then establish a scheme with synchronizing codewords to resolve this problem.
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