Gallager’s decoding algorithms ${B}$ (GDB) and ${E}$ (GDE) for low-density parity-check codes have much lower computational complexity and much less required memory size than the sum-product algorithm (SPA). This is because GDB and GDE only use binary or integer operations, while the SPA requires real operations and a look-up table. However, they are hardly used in commercial communication systems since they have a worse performance than the SPA. Layered-division multiplexing (LDM) is considered in ATSC 3.0 in order to deliver multiple broadcasting streams with distinct robustness in a single radio frequency channel. Due to the unique characteristic of the LDM, we propose to use GDB or GDE rather than the SPA for decoding the core layer signal at fixed receivers. Numerical results show that the computational complexity and the required memory size can be reduced without any performance loss by about 50 percent and 80 percent, respectively, when GDB and GDE are employed.