Rate-Adaptive Protograph LDPC Codes for Multi-Level-Cell NAND Flash Memory

The multi-level-cell (MLC) NAND flash memory exhibits a diversity of the raw bit error rate (BER) over different program/erase (P/E) cycles and different types of bits within a memory cell. In this letter, we first apply a protograph-based extrinsic information transfer chart analysis to the MLC flash channel and design novel rate-adaptive protograph low-density parity-check (RAP-LDPC) codes by using a code extension approach. The proposed RAP-LDPC code has multiple code rates, which can be adapted dynamically to different P/E cycles. To mitigate the unbalanced raw BERs between different types of bits within a memory cell, we further propose an optimum mapping between the variable nodes of the protograph and different types of bits of the memory cell. Since the proposed RAP-LDPC codes are based on the same parity-check matrix with specific structure, a single protograph encoder/decoder is sufficient to handle all the code rates. Simulation results demonstrate that the proposed RAP-LDPC codes with optimum mapping outperform the irregular LDPC codes for all the code rates with a faster decoding convergence speed for the MLC flash channel.