This paper considers universal lossless variable-length source coding problem and investigates the Bayes code from viewpoints of the distribution of its codeword lengths. First, we show that the codeword lengths of the Bayes code satisfy the asymptotic normality. This study can be seen as the investigation on the asymptotic shape of the distribution of codeword lengths. Second, we show that the codeword lengths of the Bayes code satisfy the law of the iterated logarithm. This study can be seen as the investigation on the asymptotic end points of the distribution of codeword lengths. Moreover, the overflow probability, which represents the bottom of the distribution of codeword lengths, is studied for the Bayes code. We derive upper and lower bounds of the infimum of a threshold on the overflow probability under the condition that the overflow probability does not exceed ε∈(0,1). We also analyze the necessary and sufficient condition on a threshold for the overflow probability of the Bayes code to approach zero asymptotically.

This paper describes low-power dynamic multiple-input and multiple-output (MIMO) detection for a 4×4 MIMO-orthogonal frequency-division multiplexing (MIMO-OFDM) receiver. MIMO-OFDM systems achieve high-speed and large capacity communications. However, they impose high computational cost in MIMO detection when separating spatially multiplexed signals and they consume vast amounts of power. We propose low-power dynamic MIMO detection that controls detection speed according to wireless environments. The power consumption is reduced by dynamic voltage and frequency scaling (DVFS) that controls the operating voltage and clock frequency in the MIMO detector. We implemented dynamic MIMO detection in a pipelined minimum mean square error (MMSE) MIMO detector that we developed in our previous work. A power saving of 92% was achieved under lowest clock frequency mode conditions.

In this paper, sequential prediction is studied. The typical assumptions about the probabilistic model in sequential prediction are following two cases. One is the case that a certain probabilistic model is given and the parameters are unknown. The other is the case that not a certain probabilistic model but a class of probabilistic models is given and the parameters are unknown. If there exist some parameters and some models such that the distributions that are identified by them equal the source distribution, an assumed model or a class of models can represent the source distribution. This case is called that specifiable condition is satisfied. In this study, the decision based on the Bayesian principle is made for a class of probabilistic models (not for a certain probabilistic model). The case that specifiable condition is not satisfied is studied. Then, the asymptotic behaviors of the cumulative logarithmic loss for individual sequence in the sense of almost sure convergence and the expected loss, i.e. redundancy are analyzed and the constant terms of the asymptotic equations are identified.