LDPC codes are a family of error-correcting codes that are present in most space communication standards. Thanks to their large processing power and their parallelization capabilities, prevailing multicore devices facilitate real-time implementations of digital communication systems, which were previously implemented into dedicated hardware devices. Previous works were done over the last decade on the implementation of Gbps decoders on programmable devices. However, these works focus on the soft input LDPC decoding algorithms. But, hard-input LDPC decoders are also required to design and prototype for instance next optical-based satellite communication systems. These systems should provide high throughput (≥10 Gbps) and low latency (≤1ms) internet links. In this article, the first software-based implementation of a hard-input multi-Gbps LDPC decoder is detailed. Thanks to different parallelization strategies and deeply optimized SIMD codes, throughput up to 7.5 Gbps is achieved when 10 Gallager-E iterations are executed onto an INTEL Xeon device making possible the design of software base station systems providing throughputs of tens of Gbps for optical system evaluation or base station design.