Log-Domain Decoding of Quantum LDPC Codes Over Binary Finite Fields

A quantum stabilizer code over GF$(q)$ corresponds to a classical additive GF$(q^2)$ that is self-orthogonal with respect symplectic inner product. We study the decoding of low-density parity-check (LDPC) codes binary finite fields GF$(q=2^l)$ by sum-product algorithm, also known as belief propagation (BP). Conventionally, message in nonbinary BP for GF$(2^l)$ represents probability vector GF$(2^{2l})$, inducing high complexity. In this paper, we explore property product and show scalar messages suffice codes, rather than necessary conventional BP. Consequently, propose algorithm passing so it has low computation The specified log domain using log-likelihood ratios (LLRs) channel statistics have implementation cost. Moreover, techniques such normalization or offset can be naturally applied mitigate effects short cycles improve performance. This important since they may more compared codes. Several computer simulations are provided demonstrate these advantages. scalar-based strategy used linear many cycles.