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Limited search trellis decoding algorithms have great potentials of realizing low power due to their largely reduced computational complexity compared with the widely used Viterbi algorithm. However, because of the lack of operational parallelism and regularity in their original formulations, the limited search decoding algorithms have been traditionally ruled out for applications demanding very high throughput. We believe that, through appropriate algorithm and hardware architecture co-design, certain limited search trellis decoding algorithms can become serious competitors to the Viterbi algorithm for high-throughout applications. Focusing on the well-known T-algorithm, this paper presents techniques at the algorithm and VLSI architecture levels to design fully parallel T-algorithm limited search trellis decoders. We first develop a modified T-algorithm, called SPEC-T, to improve the algorithmic parallelism. Then, based on the conventional state-parallel register exchange Viterbi decoder, we develop a parallel SPEC-T decoder architecture that can effectively transform the reduced computational complexity at the algorithm level to the reduced switching activities in the hardware. We demonstrate the effectiveness of the SPEC-T design solution in the context of convolutional code decoding. Compared with state-parallel register exchange Viterbi decoders, the SPEC-T convolutional code decoders can achieve almost the same throughput and decoding performance, while realizing up to 56% power savings. For the first time, this work provides an approach to exploit the low power potential of the T-algorithm in very high throughput applications.