Channel Polarization on q-ary Discrete Memoryless Channels by Arbitrary Kernels

A method of channel polarization, proposed by Arikan, allows us to construct efficient capacity-achieving channel codes. In the original work, binary input discrete memoryless channels are considered. A special case of $q$-ary channel polarization is considered by Sasoglu, Telatar, and Arikan. In this paper, we consider more general channel polarization on $q$-ary channels. We further show explicit constructions using Reed-Solomon codes, on which asymptotically fast channel polarization is induced.Comment: 5 pages, a final version of a manuscript for ISIT201

Source and Channel Polarization over Finite Fields and Reed-Solomon Matrices

Polarization phenomenon over any finite field $\mathbb{F}_{q}$ with size $q$ being a power of a prime is considered. This problem is a generalization of the original proposal of channel polarization by Arikan for the binary field, as well as its extension to a prime field by Sasoglu, Telatar, and Arikan. In this paper, a necessary and sufficient condition of a matrix over a finite field $\mathbb{F}_q$ is shown under which any source and channel are polarized. Furthermore, the result of the speed of polarization for the binary alphabet obtained by Arikan and Telatar is generalized to arbitrary finite field. It is also shown that the asymptotic error probability of polar codes is improved by using the Reed-Solomon matrix, which can be regarded as a natural generalization of the $2\times 2$ binary matrix used in the original proposal by Arikan.Comment: 17 pages, 3 figures, accepted for publication in the IEEE Transactions on Information Theor

Effects of Single-Cycle Structure on Iterative Decoding for Low-Density Parity-Check Codes

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as blocklength tends to infinity, and the limit is obtained via density evolution. On the other hand, the difference between the bit error probability of codes with blocklength $n$ and that in the large blocklength limit is asymptotically $\alpha(\epsilon,t)/n + \Theta(n^{-2})$ where $\alpha(\epsilon,t)$ denotes a specific constant determined by the code ensemble considered, the number $t$ of iterations, and the erasure probability $\epsilon$ of the BEC. In this paper, we derive a set of recursive formulas which allows evaluation of the constant $\alpha(\epsilon,t)$ for standard irregular ensembles. The dominant difference $\alpha(\epsilon,t)/n$ can be considered as effects of cycle-free and single-cycle structures of local graphs. Furthermore, it is confirmed via numerical simulations that estimation of the bit error probability using $\alpha(\epsilon,t)$ is accurate even for small blocklengths.Comment: 16 pages, 7 figures, submitted to IEEE Transactions on Information Theor

Firm Heterogeneity and the Choice of Internationalization Modes: Statistical Evidence from Japanese Firm-level Data

This paper examines how productivity heterogeneity affects the sorting of export and foreign direct investment (FDI) of Japanese firms in North America and Europe. The statistical analysis based on the firm-level data of 12,000 Japanese firms presents new and interesting results: the ranking of productivity corresponds to the mode of internationalization from export to FDI; the productivity of Japanese firms with exports to North America is similar to the productivity of firms with exports to Europe, and the productivity of Japanese FDI firms in North America is also similar to the productivity of FDI firms in Europe; and further the productivity of firms internationalizing in both North America and Europe is remarkably higher than that of firms internationalizing in either North America or Europe, regardless the modes of internationalization, export or FDI. These results conclude that the internationalization modes of Japanese firms in North America and Europe are completely consistent with the theoretical prediction of the HMY model and the fixed costs are critical for determining their choice of internationalization modes.

Firm Heterogeneity and Different Modes of Internationalization: Evidence from Japanese Firms

This paper examines how differently productivity heterogeneity of firms sorts their export and foreign direct investment (FDI) between North and South as well as between single and multiple destinations. The empirical examinations based on 12,000 Japanese firm-level data present new findings; the rank of productivity differently sorts the internationalization modes between North (North America and Europe) and South (East Asia); the productivity of firms internationalizing in both North America and Europe is remarkably higher than that of firms internationalizing in either North America or Europe, regardless the modes of internationalization, export or FDI, even if the productivity of firms internationalizing in North America is similar to the productivity of firms in Europe. This paper confirms that the difference in wage rate or fixed costs causes different modes of internationalization from the standard theoretical prediction based on the Helpman-Melitz-Yeaple model.productivity-cutoff, export, FDI, North, South, East Asia

How Do Exporters Respond to Exogenous Shocks: Evidence from Japanese Firm-Level Data

This study investigates how exporters respond to an exogenous shock, using the 2012 customer boycott of Japanese products in China that occurred after political conflict over the islands in the East China Sea. By using Japanese firm-level data for 2011-2013 and employing the difference-in-differences method, we conduct an assessment of the boycott. We find that Japanese firms faced a large decrease in exports to China after the 2012 boycott and that the decrease in exports was more pronounced for arm's length exports than intra-firm exports. In addition, the estimation results provide evidence that Japanese firms exporting to China responded to the exogenous trade shock by reducing their number of temporary workers. This finding suggests that trade shocks due to international conflict hit the most insecure workers