The problem of maximum likelihood decoding with a neural decoder for
error-correcting code is considered. It is shown that the neural decoder can be
improved with two novel loss terms on the node's activations. The first loss
term imposes a sparse constraint on the node's activations. Whereas, the second
loss term tried to mimic the node's activations from a teacher decoder which
has better performance. The proposed method has the same run time complexity
and model size as the neural Belief Propagation decoder, while improving the
decoding performance by up to $1.1dB$ on BCH codes.

研究了神经解码器的最大似然解码问题，通过在节点的激活上使用两个新的损失项，实现了神经解码器的改进；这个改进方法的运行时间和模型大小与 BP 神经解码器相同，但在 BCH 码上将解码性能提高了 1.1dB。

优化节点激活的神经解码

Neural Decoding with Optimization of Node Activations

The idea of counting the number of satisfying truth assignments (models) of a
formula by adding random parity constraints can be traced back to the seminal
work of Valiant and Vazirani, showing that NP is as easy as detecting unique
solutions. While theoretically sound, the random parity constraints in that
construction have the following drawback: each constraint, on average, involves
half of all variables. As a result, the branching factor associated with
searching for models that also satisfy the parity constraints quickly gets out
of hand. In this work we prove that one can work with much shorter parity
constraints and still get rigorous mathematical guarantees, especially when the
number of models is large so that many constraints need to be added. Our work
is based on the realization that the essential feature for random systems of
parity constraints to be useful in probabilistic model counting is that the
geometry of their set of solutions resembles an error-correcting code.

该研究论文探讨了如何通过增加短的随机奇偶约束来计算公式满足的真实赋值（模型），实现 NP 问题的计数，尤其是当需要添加多个约束时，随机奇偶约束的集合解的几何结构类似于纠错编码，得到了严格的数学保证。