The complexity of deterministic source encoding with a fidelity criterion

Block encoding of discrete, memoryless sources with equiprobable outputs subject to a fidelity criterion is discussed. The encoder is assumed to be deterministic and a lower bound is derived on the amount of computational work required to encode such sources as a function of the code rate and fidelity of the encoding. An example is given to show that the bound cannot be substantially improved. These bounds apply primarily to sources and distortion measures which are such that the minimum distortion given by the rate-distortion bound is not achievable with a finite block length, deterministic encoder.