Lowering Error Floor of Irregular LDPC Codes by CRC and OSD Algorithm

Satoshi GOUNAI
Tomoaki OHTSUKI

Publication
IEICE TRANSACTIONS on Communications   Vol.E89-B    No.1    pp.1-10
Publication Date: 2006/01/01
Online ISSN: 1745-1345
DOI: 10.1093/ietcom/e89-b.1.1
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Fundamental Theories for Communications
Keyword: 
irregular low-density parity-check code,  log-likelihood ratio belief propagation,  ordered statistic decoding,  CRC,  error floor,  maximum likelihood decoding,  

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Summary: 
Irregular Low-Density Parity-Check (LDPC) codes generally achieve better performance than regular LDPC codes at low Eb/N0 values. They have, however, higher error floors than regular LDPC codes. With respect to the construction of the irregular LDPC code, it can achieve the trade-off between the performance degradation of low Eb/N0 region and lowering error floor. It is known that a decoding algorithm can achieve very good performance if it combines the Ordered Statistic Decoding (OSD) algorithm and the Log Likelihood Ratio-Belief Propagation (LLR-BP) decoding algorithm. Unfortunately, all the codewords obtained by the OSD algorithm satisfy the parity check equation of the LDPC code. While we can not use the parity check equation of the LDPC code to stop the decoding process, the wrong codeword that satisfies the parity check equation raises the error floor. Once a codeword that satisfies the parity check equation is generated by the LLR-BP decoding algorithm, we regard that codeword as the final estimate and halt decoding; the OSD algorithm is not performed. In this paper, we propose a new encoding/decoding scheme to lower the error floor created by irregular LDPC codes. The proposed encoding scheme encodes information bits by Cyclic Redundancy Check (CRC) and LDPC code. The proposed decoding scheme, which consists of the LLR-BP decoding, CRC check, and OSD decoding, detects errors in the codewords obtained by the LLR-BP decoding algorithm and the OSD decoding algorithm using the parity check equations of LDPC codes and CRC. Computer simulations show that the proposed encoding/decoding scheme can lower the error floor of irregular LDPC codes.