Rate and Performance Enhancement of LDPC Codes Using Collection of Punctured Codes Decoding (CPCD)

Abstract

Background: Low-Density Parity-Check (LDPC) codes have received significant interest in a variety of communication systems due to their superior performance and reasonable decoding complexity. Methods: 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 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. Results: 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. Conclusion: Numerical results demonstrate that CPCD can either significantly improve the performance, or significantly increase the code rate of LDPC codes.