© 2015 IEEE. The focus of this article is on low-complexity capacity-achieving coding schemes for write-once memory (WOM) systems. The construction is based on spatially-coupled compound LDGM/LDPC codes. Both noiseless systems and systems with read errors are considered. Compound LDGM/LDPC codes are known to achieve capacity under MAP decoding for the closely related Gelfand-Pinsker problem and their coset decomposition provides an elegant way to encode the messages while simultaneously providing error protection. The application of compound codes to the WOM system is new. The main result is that spatial coupling enables these codes to achieve the capacity region of the 2-write WOM system with low-complexity message-passing encoding and decoding algorithms.