Rate and Performance Enhancement of LDPC Coded Schemes

In the first part of the dissertation, a novel collection of punctured codes decoding (CPCD) technique that considers a code as a collection of its punctured codes is proposed. Two forms of CPCD, serial CPCD that decodes each punctured code serially and parallel CPCD that decodes each punctured code in parallel, are discussed. In contrast to other modifications of Low-density parity-check (LDPC) decoding documented in the literature, the proposed CPCD technique views a LDPC code as a collection of punctured LDPC codes, where all punctured codes are derived from the original LDPC code by removing different portions of its parity bits. CPCD technique decodes each punctured code separately and exchanges extrinsic information obtained from that decoding among all other punctured codes for their decoding. Hence, as the iterations increase, the information obtained in the decoding of punctured codes improve making CPCD perform better than standard decoding. LDPC codes have received significant interest in a variety of communication systems due to their superior performance and reasonable decoding complexity. Numerical results demonstrate that CPCD can significantly improve the performance, or significantly increase the code rate of LDPC codes. It is demonstrated that both serial and parallel CPCD have about the same decoding complexity compared with standard sum product algorithm (SPA) decoding. It is also demonstrated that while serial CPCD has about the same decoding delay compared with standard SPA decoding, parallel CPCD can decrease the decoding delay, however, at the expense of processing power. Furthermore, it is demonstrated that similar improvements in performance and decoding delay can be achieved by applying CPCD to longer codes with higher-order modulation too. Specifically, it is shown that parallel CPCD with two parallel concatenated codes D = 2 achieves 0.3 − 1 dB gain over standard SPA decoding of the LDPC code of length 1944 employed in the WiFi standard with QPSK, 16-QAM or 64- QAM modulation while simultaneously reducing decoding delay by about 50%. It is also shown that the CPCD technique can similarly improve the performance of the LDPC code employed in the 5G NR standard at its highest code rate by about 0.6 dB while reducing the decoding delay by about 50%. In the second part of the dissertation, a novel implicit transmission with bit flipping (ITBF) technique is introduced to transmit a coded stream implicitly while transmitting a coded stream explicitly over a channel. ITBF flips a set of chosen parity bits of the explicitly transmitted stream according to an implicit stream. Numerical results show that the ITBF can transmit an implicit stream at the rate up to 13.19% of the explicit stream without significantly sacrificing performance, or increasing the decoding complexity or the decoding delay. The ITBF is combined with CPCD to form ITCD schemes that can further increase the rate of transmission on the implicit stream. It is demonstrated with the LDPC code in the WiFi standard that ITCD can transmit an implicit stream at up to 25% of the rate of the explicit.