The design of optimal linear block codes capable of being efficiently decoded
is of major concern, especially for short block lengths. As near
capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess
several advantages over other families of codes, the most notable being its
efficient decoding via Belief Propagation. While many LDPC code design methods
exist, the development of efficient sparse codes that meet the constraints of
modern short code lengths and accommodate new channel models remains a
challenge. In this work, we propose for the first time a data-driven approach
for the design of sparse codes. We develop locally optimal codes with respect
to Belief Propagation decoding via the learning on the Factor graph (also
called the Tanner graph) under channel noise simulations. This is performed via
a novel tensor representation of the Belief Propagation algorithm, optimized
over finite fields via backpropagation coupled with an efficient line-search
method. The proposed approach is shown to outperform the decoding performance
of existing popular codes by orders of magnitude and demonstrates the power of
data-driven approaches for code design.

使用数据驱动方法，通过利用因子图（也称为 Tanner 图）上的学习，在信道噪声模拟下开发满足现代短码长度约束并适应新的信道模型的局部最优稀疏码，以提高信念传播解码的性能。该方法通过使用信念传播算法的新型张量表示，在有限域上利用反向传播和高效的线性搜索方法进行优化，在解码性能上比现有流行码优越数个数量级，展示了数据驱动方法在码设计中的优势。