The main problem with the hardware implementation of turbo codes is the lack of parallelism in the MAP-based decoding algorithm. This paper proposes to overcome this problem by using a new family of turbo codes called Multiple Slice Turbo Codes. This family is based on two ideas: the encoding of each dimension with P independent tail-biting codes and a constrained interleaver structure that allows the parallel decoding of the P independent codewords in each dimension. The optimization of the interleaver is described. A high degree of parallelism is obtained with equivalent or better performance than thedvb-rcs turbo code. For very high throughput applications, the parallel architecture decreases both decoding latency and hardware complexity compared to the classical serial architecture, which requires memory duplication.