  We present a practical strategy that aims to attain rate points on the
dominant face of the multiple access channel capacity using a standard low
complexity decoder. This technique is built upon recent theoretical
developments of Zhu and Gastpar on compute-forward multiple access (CFMA) which
achieves the capacity of the multiple access channel using a sequential
decoder. We illustrate this strategy with off-the-shelf LDPC codes. In the
first stage of decoding, the receiver first recovers a linear combination of
the transmitted codewords using the sum-product algorithm (SPA). In the second
stage, by using the recovered sum-of-codewords as side information, the
receiver recovers one of the two codewords using a modified SPA, ultimately
recovering both codewords. The main benefit of recovering the sum-of-codewords
instead of the codeword itself is that it allows to attain points on the
dominant face of the multiple access channel capacity without the need of
rate-splitting or time sharing while maintaining a low complexity in the order
of a standard point-to-point decoder. This property is also shown to be crucial
for some applications, e.g., interference channels. For all the simulations
with single-layer binary codes, our proposed practical strategy is shown to be
within \SI{1.7}{\decibel} of the theoretical limits, without explicit
optimization on the off-the-self LDPC codes.
