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

The Functional Domain of GCS1-Based Gamete Fusion Resides in the Amino Terminus in Plant and Parasite Species

Fertilization is one of the most important processes in all organisms utilizing sexual reproduction. In a previous study, we succeeded in identifying a novel male gametic transmembrane protein GCS1 (GENERATIVE CELL SPECIFIC 1), also called HAP2 (HAPLESS 2) in the male-sterile Arabidopsis thaliana mutants, as a factor critical to gamete fusion in flowering plants. Interestingly, GCS1 is highly conserved among various eukaryotes covering plants, protists and invertebrates. Of these organisms, Chlamydomonas (green alga) and Plasmodium (malaria parasite) GCS1s similarly show male gametic expression and gamete fusion function. Since it is generally believed that protein factors controlling gamete fusion have rapidly evolved and different organisms utilize species-specific gamete fusion factors, GCS1 may be an ancient fertilization factor derived from the common ancestor of those organisms above. And therefore, its molecular structure and function are important to understanding the common molecular mechanics of eukaryotic fertilization. In this study, we tried to detect the central functional domain(s) of GCS1, using complementation assay of ArabidopsisGCS1 mutant lines expressing modified GCS1. As a result, the positively-charged C-terminal sequence of this protein is dispensable for gamete fusion, while the highly conserved N-terminal domain is critical to GCS1 function. In addition, in vitro fertilization assay of Plasmodium berghei (mouse malaria parasite) knock-in lines expressing partly truncated GCS1 showed similar results. Those findings above indicate that the extracellular N-terminus alone is sufficient for GCS1-based gamete fusion

A Plant Germline-Specific Integrator of Sperm Specification and Cell Cycle Progression

The unique double fertilisation mechanism in flowering plants depends upon a pair of functional sperm cells. During male gametogenesis, each haploid microspore undergoes an asymmetric division to produce a large, non-germline vegetative cell and a single germ cell that divides once to produce the sperm cell pair. Despite the importance of sperm cells in plant reproduction, relatively little is known about the molecular mechanisms controlling germ cell proliferation and specification. Here, we investigate the role of the Arabidopsis male germline-specific Myb protein DUO POLLEN1, DUO1, as a positive regulator of male germline development. We show that DUO1 is required for correct male germ cell differentiation including the expression of key genes required for fertilisation. DUO1 is also necessary for male germ cell division, and we show that DUO1 is required for the germline expression of the G2/M regulator AtCycB1;1 and that AtCycB1:1 can partially rescue defective germ cell division in duo1. We further show that the male germline-restricted expression of DUO1 depends upon positive promoter elements and not upon a proposed repressor binding site. Thus, DUO1 is a key regulator in the production of functional sperm cells in flowering plants that has a novel integrative role linking gametic cell specification and cell cycle progression

Trinucleotide cassettes increase diversity of T7 phage-displayed peptide library

<p>Abstract</p> <p>Background</p> <p>Amino acid sequence diversity is introduced into a phage-displayed peptide library by randomizing library oligonucleotide DNA. We recently evaluated the diversity of peptide libraries displayed on T7 lytic phage and M13 filamentous phage and showed that T7 phage can display a more diverse amino acid sequence repertoire due to differing processes of viral morphogenesis.</p> <p>Methods</p> <p>In this study, we evaluated and compared the diversity of a 12-mer T7 phage-displayed peptide library randomized using codon-corrected trinucleotide cassettes with a T7 and an M13 12-mer phage-displayed peptide library constructed using the degenerate codon randomization method.</p> <p>Results</p> <p>We herein demonstrate that the combination of trinucleotide cassette amino acid codon randomization and T7 phage display construction methods resulted in a significant enhancement to the functional diversity of a 12-mer peptide library. This novel library exhibited superior amino acid uniformity and order-of-magnitude increases in amino acid sequence diversity as compared to degenerate codon randomized peptide libraries. Comparative analyses of the biophysical characteristics of the 12-mer peptide libraries revealed the trinucleotide cassette-randomized library to be a unique resource.</p> <p>Conclusion</p> <p>The combination of T7 phage display and trinucleotide cassette randomization resulted in a novel resource for the potential isolation of binding peptides for new and previously studied molecular targets.</p