Compute-Forward Multiple Access (CFMA): Practical Implementations

• Published in: IEEE transactions on communications 2019-02, Vol.67 (2), p.1133-1147
• Main Authors: Sula, Erixhen, Zhu, Jingge, Pastore, Adriano, Lim, Sung Hoon, Gastpar, Michael
• Format: Article
• Language: English
• Subjects: Algorithms; Binary codes; Binary system; Channel capacity; Codes; Complexity; Complexity theory; Computer simulation; Compute–forward multiple access (CFMA); Decoding; Face; Interference channels; Low density parity check codes; low density parity check codes (LDPC); Multiple access; multiple access channel; Parity check codes; Receivers; sequential decoding; Strategy; sum-product algorithm; Time sharing
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2018.2874240

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 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 1.7 dB of the theoretical limits, without explicit optimization on the off-the-self LDPC codes.