This paper presents an efficient lossy compression method based on sparse coding for received noisy signals (RX) in satellite communication systems. The emergence of ground station as a service (GSaaS) and centralized radio access net- works (C-RAN) requires efficient data transfers between ground stations and datacenters. Our approach employs sparse coding to compress baseband signals via offline trained dictionaries. We analyze the loss introduced by compression and its impact on common modulation schemes across a Gaussian channel using the Bit Error Rate (BER) measurement. Additionally, the proposed method is compared to lossless linear prediction coding (LPC) and uniform quantization. Our study highlights the potential of lossy sparse coding to reduce bandwidth requirements while preserving signal integrity by offering a potential compression ratio of up to 8% higher than existing methods for the same degradation.