Low Complexity Techniques for Low Density Parity Check Code Decoders and Parallel Sigma-Delta ADC Structures

Since their rediscovery in 1995, low-density parity-check (LDPC) codes have received wide-spread attention as practical capacity-approaching code candidates. It has been shown that the class of codes can perform arbitrarily close to the channel capacity, and LDPC codes are also used or suggested for a number of important current and future communication standards. However, the problem of implementing an energy-efficient decoder has not yet been solved. Whereas the decoding algorithm is computationally simple, with uncomplicated arithmetic operations and low accuracy requirements, the random structure and irregularity of a theoretically well-defined code does not easily allow efficient VLSI implementations. Thus the LDPC decoding algorithm can be said to be communication-bound rather than computation-bound. In this thesis, a modification to the sum-product decoding algorithm called earlydecision decoding is suggested. The modification is based on the idea that the values of the bits in a block can be decided individually during decoding. As the sumproduct decoding algorithm is a soft-decision decoder, a reliability can be defined for each bit. When the reliability of a bit is above a certain threshold, the bit can be removed from the rest of the decoding process, and thus the internal communication associated with the bit can be removed in subsequent iterations. However, with the early decision modification, an increased error probability is associated. Thus, bounds on the achievable performance as well as methods to detect graph inconsistencies resulting from erroneous decisions are presented. Also, a hybrid decoder achieving a negligible performance penalty compared to the sum-product decoder is presented. With the hybrid decoder, the internal communication is reduced with up to 40% for a rate-1/2 code with a length of 1152 bits, whereas increasing the rate allows significantly higher gains. The algorithms have been implemented in a Xilinx Virtex 5 FPGA, and the resulting slice utilization and energy dissipation have been estimated. However, due to increased logic overhead of the early decision decoder, the slice utilization increases from 14.5% to 21.0%, whereas the logic energy dissipation reduction from 499 pJ to 291 pJ per iteration and bit is offset by the clock distribution power, increased from 141 pJ to 191 pJ per iteration and bit. Still, the early decision decoder shows a net 16% estimated decrease of energy dissipation