Source coding using a class of universal hash functions

We consider a source coding scheme in which we use a mapping f is an element of F as an encoder, where F is a class of universal hash functions. It is shown that, if F satisfies a certain condition, for any discrete source there exist an encoder using an f is an element of F and a decoder such that the decoding error probability becomes negligible for sufficiently large blocklength. We also give the error exponent of the minimum-entropy decoder for i.i.d. sources that is not less than the error exponent of linear encoders.