This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without requiring any other pre-constructed information (such as trellis diagrams or error-pattern lists), and it can also be customized by exploiting the algebraic properties of the code. We formally define error-building blocks, and derive a recursive theorem that allows efficient construction of larger locally optimal blocks from smaller ones, thereby effectively searching for the block associated with the most likely error pattern. The EBD framework is further optimized for extended Hamming codes as an example, through offline and online exclusion mechanisms, leading to a substantial complexity reduction without loss of ML performance. Complexity analysis shows that, for extended Hamming codes of lengths 64, 128, and 256, the fully optimized EBD requires approximately an order of magnitude fewer floating-point operations on average than minimum-edge trellis Viterbi decoding at a frame error rate of $10^{-3}$.

翻译：本文提出了一种新颖的线性分组码最大似然软判决译码框架，称为误差构建译码。完整的译码过程可以仅使用校验矩阵完成，无需任何其他预构建信息（如网格图或错误模式列表），并且可以通过利用码的代数特性进行定制。我们正式定义了误差构建块，并推导了一个递归定理，该定理允许从较小的块高效地构建更大的局部最优块，从而有效地搜索与最可能错误模式相关联的块。作为示例，该EBD框架针对扩展汉明码通过离线和在线排除机制进行了进一步优化，在不损失ML性能的前提下实现了显著的复杂度降低。复杂度分析表明，对于长度为64、128和256的扩展汉明码，在误帧率为$10^{-3}$时，完全优化的EBD平均所需的浮点运算量比最小边网格维特比译码大约少一个数量级。