This paper proposes a "quasi-synchronous" design approach for signal processing circuits, in which timing violations are permitted, but without the need for a hardware compensation mechanism. The case of a low-density parity-check (LDPC) decoder is studied, and a method for accurately modeling the effect of timing violations at a high level of abstraction is presented. The error-correction performance of code ensembles is then evaluated using density evolution while taking into account the effect of timing faults. Following this, several quasi-synchronous LDPC decoder circuits based on the offset min-sum algorithm are optimized, providing a 23%-40% reduction in energy consumption or energy-delay product, while achieving the same performance and occupying the same area as conventional synchronous circuits.