We normally hold a lot of confidential information in hard disk drives and solid-state drives. When we want to erase such information to prevent the leakage, we have to overwrite the sequence of information with a sequence of symbols independent of the information. The overwriting is needed only at places where overwritten symbols are different from original symbols. Then, the cost of overwrites such as the number of overwritten symbols to erase information is important. In this paper, we clarify the minimum cost such as the minimum number of overwrites to erase information under weak and strong independence criteria. The former (resp. the latter) criterion represents that the mutual information between the original sequence and the overwritten sequence normalized (resp. not normalized) by the length of the sequences is less than a given desired value.

In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give non-asymptotic inner and outer bounds on pairs of numbers of codewords of two encoders such that each probability that a distortion exceeds a given distortion level is less than a given probability level. We also give a general formula for the rate-distortion region for general sources, where the rate-distortion region is the set of rate pairs of two encoders such that each maximum value of possible distortions is less than a given distortion level.

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Recently the author determined the optimal exponent on the correct probability of decoding have the form similar to that of Dueck and Körner determined. In this paper we give a rigorous proof of the equivalence of the above exponet function of Dueck and Körner to a exponent function which can be regarded as an extention of Arimoto's bound to the case with the cost constraint on the channel input.

We consider fixed-to-variable length coding with a regular cost function by allowing the error probability up to any constantε. We first derive finite-length upper and lower bounds on the average codeword cost, which are used to derive general formulas of two kinds of minimum achievable rates. For a fixed-to-variable length code, we call the set of source sequences that can be decoded without error the dominant set of source sequences. For any two regular cost functions, it is revealed that the dominant set of source sequences for a code attaining the minimum achievable rate under a cost function is also the dominant set for a code attaining the minimum achievable rate under the other cost function. We also give general formulas of the second-order minimum achievable rates.

In this letter, we first introduce a stronger notion of the optimistic achievable coding rate and discuss a coding theorem. Next, we give a necessary and sufficient condition under which the coding rates of all the optimal FF codes asymptotically converge to a constant.

The multiple-access channel (MAC) becomes very popular in various communication systems, because multi-terminal communication systems have been widely used in practical systems, e.g., mobile phones and P2P, etc. For some MACs, it is known that feedback can enlarge the capacity region, where the capacity region is the set of rate pairs such that the error probability can be made arbitrarily small for sufficiently large block length. The capacity region for general MACs, which are not required to satisfy ergodicity and stationarity with perfect feedback was first shown by Tatikonda and Mitter without the proof, where perfect feedback means that the channel output is perfectly fed back to senders. In this paper, we generalize Tatikonda and Mitter's result to the case of deterministic feedback, where the values of deterministic functions of past channel outputs is fed back to senders. We show that the capacity region for general MACs with deterministic feedback can be represented by the information-spectrum formula introduced by Han and Verdu, and directed information introduced by Massey. We also investigate the compound MAC problem, the ε-coding problem, the strong converse property and the cost constraint problem for general MACs with deterministic feedback.

In this paper, Information-Spectrum characterization is derived for the reliable transmission of general correlated sources over the general multiple-access channels. We consider the necessary and sufficient conditions for the transmission of general correlated sources over the general multiple-access channels by using Information-Spectrum methods which are introduced by Han and Verdu.

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.

Wyner and Ziv considered the rate-distortion function for source coding with side information at the decoder (we call the Wyner-Ziv problem). In this paper we show an information-spectrum approach to the Wyner-Ziv problem for general class of nonstationary and/or nonergodic sources with side information at the decoder, where the distortion measure is arbitrary and may be nonadditive. We show that a general formula for the rate-distortion function of the Wyner-Ziv problem for general sources with the maximum distortion criterion under fixed-length coding by using the information spectrum approach.