this paper addresses the problem of design of variable length codes (VLC) that would allow to exploit higher-order source statistics while still being resilient to transmission errors. The codes introduced extend and generalize the family of codes called multiplexed codes, referred to as stationary multiplexed codes. The design principle consists in creating fixed length codes (FLCs) for high priority information and in using the inherent redundancy to describe low priority data, hence the name «multiplexed codes». The FLC codebooks are partitioned into equivalence classes according to high priority source statistics, focusing here on first-order statistics. The key aspect to limit error propagation inherent to the use of conditional probabilities relies on the choice of some appropriate partitions (or index assignment) of the set of codewords. Several index assignment methods are described. A crossed-Index Assignment method leads to the construction of a kernel made of codewords offering synchronization properties. The decoder re-synchronization capability can be further increased by periodic use of stationary multiplexed codes. Soft decoding algorithms using MAP, MPM and MMSE criteria are also described. Theoretical and practical performances in terms of error resilience and compression efficiency are analyzed.