The explicit construction of a universal source code for correlated sources is presented. The construction is based on a technique of simulated random coding algorithms [5]. The proposed algorithm simulates the random generation of linear codes. For every pair of correlated sources whose achievable rate region includes a given pair of encoding rates, the decoding error rate of the proposed algorithm goes to zero almost surely as the block length goes to infinity.

We propose source coding algorithms that use the randomness of a past sequence. The proposed algorithms solve the problems of multi-terminal source coding, rate-distortion source coding, and source coding with partial side information at the decoder. We analyze the encoding rate and the decoding error rate in terms of almost-sure convergence.

Recently, Muramatsu proposed source coding algorithms that use the randomness of a past sequence. The technique of his source coding algorithms is one method of constructing codes from the technique of random coding. By using his technique, we propose a channel coding algorithm with random numbers which can be observed by both the encoder and the decoder where the random numbers are independent of the messages to be transmitted. Then the proposed coding algorithm can transmit messages over a discrete memoryless channel up to the channel capacity with an arbitrarily small decoding error rate and arbitrarily small bits of random numbers per message transmission asymptotically.