Simultaneous Code/Error-Trellis Reduction for Convolutional Codes Using Shifted Code/Error-Subsequences

In this paper, we show that the code-trellis and the error-trellis for a convolutional code can be reduced simultaneously, if reduction is possible. Assume that the error-trellis can be reduced using shifted error-subsequences. In this case, if the identical shifts occur in the subsequences of each code path, then the code-trellis can also be reduced. First, we obtain pairs of transformations which generate the identical shifts both in the subsequences of the code-path and in those of the error-path. Next, by applying these transformations to the generator matrix and the parity-check matrix, we show that reduction of these matrices is accomplished simultaneously, if it is possible. Moreover, it is shown that the two associated trellises are also reduced simultaneously.Comment: 5 pages, submitted to the 2011 IEEE International Symposium on Information Theor

Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information

Energetic coherence is indispensable for various operations, including precise measurement of time and acceleration of quantum manipulations. Since energetic coherence is fragile, it is essential to understand the limits in distillation and dilution to restore damage. The resource theory of asymmetry (RTA) provides a rigorous framework to investigate energetic coherence as a resource to break time-translation symmetry. Recently, in the i.i.d. regime where identical copies of a state are converted into identical copies of another state, it has been shown that the convertibility of energetic coherence is governed by a standard measure of energetic coherence, called the quantum Fisher information (QFI). This fact means that QFI in the theory of energetic coherence takes the place of entropy in thermodynamics and entanglement entropy in entanglement theory. However, distillation and dilution in realistic situations take place in regimes beyond i.i.d., where quantum states often have complex correlations. Unlike entanglement theory, the conversion theory of energetic coherence in pure states in the non-i.i.d. regime has been an open problem. In this Letter, we solve this problem by introducing a new technique: an information-spectrum method for QFI. Two fundamental quantities, coherence cost and distillable coherence, are shown to be equal to the spectral QFI rates for arbitrary sequences of pure states. As a consequence, we find that both entanglement theory and RTA in the non-i.i.d. regime are understood in the information-spectrum method, while they are based on different quantities, i.e., entropy and QFI, respectively.Comment: 25 pages, 3 figure

Smooth Metric Adjusted Skew Information Rates

Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an asymptotic discontinuity. We here introduce a new class of asymmetry measures with the smoothing technique, which we term smooth metric adjusted skew information. We prove that its asymptotic sup- and inf-rates are valid asymptotic measures in the resource theory of asymmetry. Furthermore, it is proven that the smooth metric adjusted skew information rates provide a lower bound for the coherence cost and an upper bound for the distillable coherence.Comment: 21 page

Effects of the Zero-Mode Landau Level on Inter-Layer Magnetoresistance in Multilayer Massless Dirac Fermion Systems

We report on the experimental results of interlayer magnetoresistance in multilayer massless Dirac fermion system $\alpha$-(BEDT-TTF)$_2$I$_3$ under hydrostatic pressure and its interpretation. We succeeded in detecting the zero-mode Landau level (n=0 Landau level) that is epected to appear at the contact points of Dirac cones in the magnetic field normal to the two-dimensional plane. The characteristic feature of zero-mode Landau carriers including the Zeeman effect is clearly seen in the interlayer magnetoresistance.Comment: 2 pages, 2 figure

Learning strategies adopted in 5 : 3 polyrhythmic tapping

Recently, bimanual coordination tasks with temporal constraints, such as polyrhythmic tapping, have been approached from two theoretically distinguished viewpoints. These are cognitive and dynamical approaches. However, there are situations that can not be explained by only one of the two approaches. The purposes of this study were to identify learning strategies adopted by subjects in the production of 5 : 3 polyrhythm, and to clarify the timing mechanisms of coordinating two hands by integrating the two approaches. Ten out of twenty subjects could learn 5 : 3 polyrhythmic tapping in a synchronized task and reproduce it in a test task. Learning strategies adopted by subjects were identified by deviations of observed interresponse intervals (IRIs) from expected IRIs and correlations between the adjacent IRIs. Results showed that an integrated chained organization was adopted in the first half of one cycle, whereas an integrated hierarchical organization was adopted in the last half of the same cycle. This indicated that one cycle of polyrhythm was separated into two units, and was performed with the two different strategies. These strategies were discussed in terms of a cognitive attentional perspective and a dynamical entrainment property of coupled nonlinear oscillators

Personal tempo and pattern formation in polyrhythmic tapping

Personal tempos in our rhythmic movements have been studied with various tasks. However, no studies have examined the personal tempo in bimanual coordination with interference between the right and left hand movements, because the previous studies used auditory or visual stimuli in acquisition. For the same reason, a formation of the bimanual coordination pattern could not be examined. Therefore, the purposes of this study were to compare personal tempos produced by a single-rhythmic tapping and a 3 : 2 polyrhythmic tapping, and to clarify a mechanism of the 3 : 2 polyrhythmic pattern formation from a viewpoint of entrainment. Intertap intervals (ITIs) of each rhythmic tapping by ten subjects were analyzed. Results showed that the single-rhythmic tapping produced ITIs which were similar to ITIs of 3-beat sequence in the 3 : 2 polyrhythmic tapping. This suggests that there exist consistency between the single-rhythmic tapping and polyrhythmic tapping with a personal tempo. Another result showed that 2 : 1 and 1 : 1 patterns were emerged before the formation of 3 : 2 pattern. Such a shift is expressed in Farey tree that shows frequency rations at entrainment. We found that the complicated pattern was formed through the formation of more stable patterns formed by entrainment