Decoding of Non-Binary LDPC Codes Using the Information Bottleneck Method
This work addresses decoding efficiency for non-binary LDPC codes, which is an incremental improvement in communication systems.
The paper tackled the problem of decoding non-binary LDPC codes by extending a lookup table-based method from binary to non-binary domains, requiring sophisticated design for Galois field arithmetic. The result shows that the proposed scheme outperforms log-max decoding and operates close to sum-product decoding in bit error rate simulations.
Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension, but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.