The achievability part of the rate-distortion theorem is proved by showing existence of good codes. For i.i.d. sources, two methods showing existence are known; random coding and non-random coding. For general sources, however, no proof in which good codes are constructed with non-random coding is found. In this paper, with a non-random method of code construction, we prove the achievability part of the rate-distortion theorem for general sources. Moreover, we also prove a stochastic variation of the rate-distortion theorem with the same method.

This letter deals with the Slepian-Wolf coding problem for general sources. The second-order achievable rate region is derived using quantity which is related to the smooth max-entropy and the conditional smooth max-entropy. Moreover, we show the relationship of the functions which characterize the second-order achievable rate region in our study and previous study.

In this paper we consider fixed-to-fixed length (FF) coding of a general source X with vanishing error probability and define two kinds of optimalities with respect to the coding rate and the redundancy, where the redundancy is defined as the difference between the coding rate and the symbolwise ideal codeword length. We first show that the infimum achievable redundancy coincides with the asymptotic width W(X) of the entropy spectrum. Next, we consider the two sets $mCH(X)$ and $mCW(X)$ and investigate relationships between them, where $mCH(X)$ and $mCW(X)$ denote the sets of all the optimal FF codes with respect to the coding rate and the redundancy, respectively. We give two necessary and sufficient conditions corresponding to $mCH(X) subseteq mCW(X)$ and $mCW(X) subseteq mCH(X)$, respectively. We can also show the existence of an FF code that is optimal with respect to both the redundancy and the coding rate.

This paper clarifies a necessary condition and a sufficient condition for transmissibility for a given set of general sources and a given general broadcast channel. The approach is based on the information-spectrum methods introduced by Han and Verdu. Moreover, we consider the capacity region of the general broadcast channel with arbitrarily fixed error probabilities if we send independent private and common messages over the channel. Furthermore, we treat the capacity region for mixed broadcast channel.

Slepian, Wolf and Wyner proved famous source coding theorems for correlated i.i.d. sources. On the other hand recently Han and Verdú have shown the source and channel coding theorems on general sources and channels whose statistics can be arbitrary, that is, no assumption such as stationarity or ergodicity is imposed. We prove source coding theorems on correlated general sources by using the method which Han and Verdú developed to prove their theorems. Also, through an example, we show some new results which are essentially different from those already obtained for the i.i.d. source cases.