6G demands an evolution of the current 5G New Radio (NR) channel codes. For eMBB+ scenarios, block lengths defined in 5G become inefficient for extremely high data rates, and a larger transport block size is thus desirable. At the same time for URLLC+ scenarios, short code block lengths are preferred for low latency, but then achieving a target frame error rate below 10−5poses a significant challenge for short-length low-density parity-check (LDPC) codes. In this work, we propose a universal LDPC (Uni-LDPC) matrix that supports both short-length and long-length codes. By using a concept of flexible coupling, the proposed Uni-LDPC code integrates the benefits of block codes and coupled codes. This unified design enables a single LDPC matrix to perform effectively across both eMBB+ and URLLC+ scenarios. Simulation results demonstrate that Uni-LDPC codes outperform 5G-NR LDPC codes over a wide range of code rates at a short block length (a few hundred information bits) with a high number of decoding iterations. Meanwhile, thanks to coupling, Uni-LDPC codes can also surpass 5G-NR LDPC codes at long code lengths (tens of thousands of information bits) with a low number of iterations.