Design of Implicit Partial Product-LDPC Codes and Low Complexity Decoding Algorithm

In this letter, we are concerned with a recently proposed class of product codes, called implicit partial product low-density parity-check (IP-LDPC) codes, which consist of LDPC codes for rows and Bose-Chaudhuri-Hocquenghem (BCH) codes for columns. Distinguished from the conventional product codes, only partial columns are doubly-protected and the column checks are transmitted implicitly rather than explicitly. For any given LDPC code, we present three heuristic rules to design an IP-LDPC code with the same code rate, showing how to select the number of doubly-protected columns and the BCH code (for columns). The stringent constraint is that the product of the number of doubly-protected columns and the length of syndrome per column must be less than or equal to the product of the number of the rows and the length of extra bits that can be carried reliably and implicitly per row (LDPC codeword). We also propose a simple bit-flipping algorithm for the column decoding in the case when the number of unsuccessfully decoded rows is relatively small, which occurs often especially when the iterative decoding is implemented. The simulation results show that IP-LDPC codes can lower down the word error rate (WER) of a (3,6)-regular LDPC code with length 1024 from 10
⁻²
to 10
⁻⁶
at the SNR around 2.0 dB but without any code rate loss.