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We present a general interleaver structure that can be systematically derived from any existing block interleaver. When used in a turbo code with proper encoding and decoding procedures, the proposed interleaver is capable of providing unbounded interleaving depth with bounded decoding delay. Given a fixed decoding delay, the new interleaver results in superior bit error rate (BER) performance. The algebraic properties of the associated turbo codes are examined to provide guidelines in design the permutation rule.