Energy-Efficient Decoders of Near-Capacity Channel Codes.

Channel coding has become essential in state-of-the-art communication and storage systems for ensuring reliable transmission and storage of information. Their goal is to achieve high transmission reliability while keeping the transmit energy consumption low by taking advantage of the coding gain provided by these codes. The lowest total system energy is achieved with a decoder that provides both good coding gain and high energy-efficiency. This thesis demonstrates the VLSI implementation of near-capacity channel decoders using the LDPC, nonbinary LDPC (NB-LDPC) and polar codes with an emphasis of reducing the decode energy. LDPC code is a widely used channel code due to its excellent error-correcting performance. However, memory dominates the power of high-throughput LDPC decoders. Therefore, these memories are replaced with a novel non-refresh embedded DRAM (eDRAM) taking advantage of the deterministic memory access pattern and short access window of the decoding algorithm to trade off retention time for faster access speed. The resulting LDPC decoder with integrated eDRAMs achieves state-of-the-art area- and energy-efficiency. NB-LDPC code achieves better error-correcting performance than LDPC code at the cost of higher decoding complexity. However, the factor graph is simplified, permitting a fully parallel architecture with low wiring overhead. To reduce the dynamic power of the decoder, a fine-grained dynamic clock gating technique is applied based on node-level convergence. This technique greatly reduces dynamic power allowing the decoder to achieve high energy-efficiency while achieving high throughput. The recently invented polar code has a similar error-correcting performance to LDPC code of comparable block length. However, the easy reconfigurability of code rate as well as block length makes it desirable in numerous applications where LDPC is not competitive. In addition, the regular structure and simple processing enables a highly efficient decoder in terms of area and power. Using the belief propagation algorithm with architectural and memory improvements, a polar decoder is demonstrated achieving high throughput and high energy- and area-efficiency. The demonstrated energy-efficient decoders have advanced the state-of-the-art. The decoders will allow the continued reduction of decode energy for the latest communication and storage applications. The developed techniques are widely applicable to designing low-power DSP processors.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108731/1/parkyoun_1.pd

Topological Code Architectures for Quantum Computation

This dissertation is concerned with quantum computation using many-body quantum systems encoded in topological codes. The interest in these topological systems has increased in recent years as devices in the lab begin to reach the fidelities required for performing arbitrarily long quantum algorithms. The most well-studied system, Kitaev\u27s toric code, provides both a physical substrate for performing universal fault-tolerant quantum computations and a useful pedagogical tool for explaining the way other topological codes work. In this dissertation, I first review the necessary formalism for quantum information and quantum stabilizer codes, and then I introduce two families of topological codes: Kitaev\u27s toric code and Bombin\u27s color codes. I then present three chapters of original work. First, I explore the distinctness of encoding schemes in the color codes. Second, I introduce a model of quantum computation based on the toric code that uses adiabatic interpolations between static Hamiltonians with gaps constant in the system size. Lastly, I describe novel state distillation protocols that are naturally suited for topological architectures and show that they provide resource savings in terms of the number of required ancilla states when compared to more traditional approaches to quantum gate approximation