In this paper, we study different schemes to parallelize trellis algorithms for efficient implementation on a GPU. We consider parallelization schemes at the packet-level, subblock-level and trellis-level to increase the number of threads in a GPU implementation. At the trellis-level, we consider state-level, forward-backward traversal and branch-metric parallelism. To evaluate the performance of the different schemes, an LTE uplink Turbo decoder is implemented on an NVIDIA GTX470 GPU. Tradeoffs between throughput, latency and bit error rate are presented. Our most balanced configuration is simultaneously processing multiple subblocks in a packet in conjunction with recovery schemes and trellis-level parallelism, which can achieve a throughput of 19.65 Mbps with a latency of 0.56 ms at bit error rate of 10^-5 for 1.3 dB channel SNR. We also show how different combinations of parallelization schemes can be used to satisfy systems with widely varying requirements of throughput, latency and bit error rate.