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This paper presents a high-efficiency parallel architecture for a turbo decoder using a quadratic permutation polynomial (QPP) interleaver. Conventionally, two half-iterations for different component codewords alternate during the decoding flow. Due to the initialization calculation and pipeline delays in every half-iteration, the functional units in turbo decoders will be idle for several cycles. This inactive period will degrade throughput, especially for small blocks or high parallelism. To resolve this issue, we impose several constraints on the QPP interleaver and rearrange the processing schedule; then the following half-iteration can be executed before the completion of the current half-iteration. Thus, it can eliminate the idle cycles and increase the efficiency of functional units. Based on this modified schedule with 100% efficiency, a parallel turbo decoder which contains 32 radix-24 SISO decoders is implemented with 90 nm technology to achieve 1.4 Gb/s while decoding size-4096 blocks for 8 iterations.