To meet the evolving data rate requirements of emerging wireless communication technologies, many parallel architectures have been proposed to implement high throughput turbo decoders. However, concurrent memory reading/writing in parallel turbo decoding architectures leads to severe memory conflict problem, which has become a major bottleneck for high throughput turbo decoders. In this paper, we propose a flexible and efficient VLSI architecture to solve the memory conflict problem for highly parallel turbo decoders targeting multi-standard 3G/4G wireless communication systems. To demonstrate the effectiveness of the proposed parallel interleaver architecture, we implemented an HSPA+/LTE/LTE-Advanced multi-standard turbo decoder with a 45nm CMOS technology. The implemented turbo decoder consists of 16 Radix-4 MAP decoder cores, and the chip core area is 2.43 mm^2. When clocked at 600 MHz, this turbo decoder can achieve a maximum decoding throughput of 826 Mbps in the HSPA+ mode and 1.67 Gbps in the LTE/LTE-Advanced mode, exceeding the peak data rate requirements for both standards.