Apparatus, method, and system for synchronization and a three-dimensional display apparatus using the same are provided. At least 50% in area of the face portion is formed by the unidirectionally rolled plate. When a choice of quantizer is available, the codec efficiently encodes the current quantizer by defining a subset of quantizers and indexes the current quantizer from the set. Soft values, such as log-likelihood values, are then estimated for each of at least one systematic bit and at least one parity bit of the received communications data corresponding to the interval between the first and second times, based on the partial sums. Accordingly, the use of costly metal material can be reduced to lower the production cost, and the decrease of strength and deformation of the fan frame structure due to high temperature can be prevented.