Constant Block Length Research Articles

Multiple-rate error-correcting coding scheme

Error-correcting codes that can effectively encode and decode messages of distinct lengths while maintaining a constant blocklength are considered. It is known conventionally that a k-dimensional block code of length n defined over $$\texttt {GF}(q^{n})$$ is designed to encode a k-symbol user data in to an n-length codeword, resulting in a fixed-rate coding. In contrast, considering $$q=p^{\lambda }$$, this paper proposes two coding procedures (for the cases of $$\lambda =k$$ and $$\lambda =n$$) each deriving a multiple-rate code from existing channel codes defined over a composite field $$\texttt {GF}(q^{n})$$. Formally, the proposed coding schemes employ $$\lambda$$ codes $${\mathcal {C}}_{1}(\lambda , 1), {\mathcal {C}}_{2}(\lambda , 2), \ldots , {\mathcal {C}}_{\lambda }(\lambda , \lambda )$$ defined over $$\texttt {GF}(q)$$ to encode user messages of distinct lengths and incorporate variable-rate feature. Unlike traditional block codes, the derived multiple-rate codes of fixed blocklength n can be used to encode and decode user messages $$\mathbf{m}$$ of distinct lengths $$|\mathbf{m}| = 1, 2, \ldots , k, k+1, \ldots , kn$$, thereby supporting a range of information rates—inclusive of the code rates $$1/n^{2}, 2/n^{2},\ldots , k/n^{2}$$ and $$1/n, 2/n, \ldots , k/n$$ ! A simple decoding procedure to the derived multiple-rate code is also given; in that, orthogonal projectors are employed for the identification of encoded user messages of variable length.

CE and asymmetrical flow-field flow fractionation studies of polymer interactions with surfaces and solutes reveal conformation changes of polymers.

Amphiphilic diblock copolymers consisting of a hydrophobic core containing a polymerized ionic liquid and an outer shell composed of poly(N-isoprolylacrylamide) were investigated by capillary electrophoresis and asymmetrical flow-field flow fractionation. The polymerized ionic liquid comprised poly(2-(1-butylimidazolium-3-yl)ethyl methacrylate tetrafluoroborate) with a constant block length (n=24), while the length of the poly(N-isoprolylacrylamide) block varied (n=14; 26; 59; 88). Possible adsorption of the block copolymer on the fused silica capillary, due to alterations in the polymeric conformation upon a change in the temperature (25 and 45°C), was initially studied. For comparison, the effect of temperature on the copolymer conformation/hydrodynamic size was determined with the aid of asymmetrical flow-field flow fractionation and light scattering. To get more information about the hydrophilic/hydrophobic properties of the synthesized block copolymers, they were used as a pseudostationary phase in electrokinetic chromatography for the separation of some model compounds, that is, benzoates and steroids. Of particular interest was to find out whether a change in the length or concentration of the poly(N-isoprolylacrylamide) block would affect the separation of the model compounds. Overall, our results show that capillary electrophoresis and asymmetrical flow-field flow fractionation are suitable methods for characterizing conformational changes of such diblock copolymers.

Thermal properties of the multi-stereo block poly(lactic acid)s with various block lengths

Multi-sb-PLAs with molecular weights of approximately 60,000 (MSB-60) and 130,000 (MSB-130) with various block lengths were synthesized. These have a structure in which di-block copolymers consisting of L- and D-blocks with the same length are connected with 1,12-dodecanediol (DMG), an initiator and hexamethylene diisocyanate (HMDI), a chain extender alternately. DSC analyses revealed that Tg increases with the increase in the block length and the multi-sb-PLA with a lower molecular weight has higher Tg at a constant block length. These are attributable to the higher concentration of DMG and HMDI in the multi-sb-PLA. Tm increases with the increase in the block length and the molecular weight of multi-sb-PLA and those of MSB-60 and MSB-130 get close to a constant value at higher block length. The variation of Tm seems to be attributable to change in the lateral dimension of lamella rather than that of the thickness. Tc in the heating process from the amorphous solid decreases and that in the cooling process from the melt increases with the increase in the block length, indicating that the multi-sb-PLA with a long block has a wider temperature range of the crystallization.

Modified poly(butyl methacrylate- b -glycidyl methacrylate) dispersant for solvent-based paint by Reverse Atom Transfer Radical Polymerization

Block copolymers of butyl methacrylate (BMA) and glycidyl methacrylate (GMA) were synthesized using reverse atom transfer radical polymerization. Azobisisobutyronitrile/copper (II) bromide/pentamethyldiethylenetriamine was used as a precursor. These copolymers had a constant block length but variable molecular weights of 7500, 10,000, and 15,000, respectively. The copolymers were further reacted with methyl ethanol amine to form dispersible modified poly(BMA-b-GMA) (MPBGA). The synthesized block copolymers were structurally evaluated by gel permeation chromatography, Fourier transform infrared spectroscopy, differential scanning calorimetry, and nuclear magnetic resonance. The ability of additives to function as wetting and dispersing agents was evaluated by analyzing their mechanical, optical, chemical, and rheological properties in solvent-based paints at different pigment volume concentrations. The effects of the chain length of copolymers on dispersibilty and optical properties were studied. The optical properties of paints suggested that the dispersibilty of MPBGA increased with an increase in the molecular weight of the copolymer.

Morphology control of giant vesicles by manipulating hydrophobic-hydrophilic balance of amphiphilic random block copolymers through polymerization-induced self-assembly

The morphology of giant vesicles composed of amphiphilic poly(methacrylic acid)-block-poly(methyl methacrylate-random-methacrylic acid) random block copolymers, PMAA-b-P(MMA-r-MAA), was effectively controlled by manipulating the hydrophobic-hydrophilic balance of the P(MMA-r-MAA) blocks through the self-assembly induced by the nitroxide-mediated photo-controlled/living radical polymerization in an aqueous methanol solution. The morphology was transformed from spherical vesicles into fibers and finally into membranes as the molar ratio of the MAA units in the hydrophobic P(MMA-r-MAA) block increased at a constant block length. The membrane morphology reverted to spherical vesicles by exchanging the MMA units with more hydrophobic isopropyl methacrylate units at a constant MAA ratio. These morphology transitions were accounted for by the change in the critical packing shape of the random block copolymers based on the variation in the extent of the hydrophobic block chains.

Multiple-rate low-density parity-check codes with constant blocklength

This paper describes and analyzes low-density parity-check code families that support variety of different rates while maintaining the same fundamental decoder architecture. Such families facilitate the decoding hardware design and implementation for applications that require communication at different rates, for example to adapt to changing channel conditions. Combining rows of the lowest-rate parity-check matrix produces the parity-check matrices for higher rates. An important advantage of this approach is that all effective code rates have the same blocklength. This approach is compatible with well known techniques that allow low-complexity encoding and parallel decoding of these LDPC codes. This technique also allows the design of programmable analog LDPC decoders. The proposed design method maintains good graphical properties and hence low error floors for all rates.

Phase behavior of linear polystyrene-block-poly(2-vinylpyridine)-block-poly(tert-butyl methacrylate) triblock terpolymers

Using sequential living anionic polymerization we synthesized well-defined linear ABC triblock terpolymers from polystyrene (PS), poly(2-vinylpyridine) (P2VP), and poly(tert-butyl methacrylate) (PtBMA). The length of the PtBMA block was systematically increased at constant block length ratios of the PS and P2VP blocks. The microdomain structures were characterized by transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS). With increasing PtBMA block size we observe a systematic change in the bulk structure of the block copolymers.

Synthesis and characterization of amphiphilic diblock copolymers of methyl tri(ethylene glycol) vinyl ether and isobutyl vinyl ether

Water-soluble diblock copolymers of methyl tri(ethylene glycol) vinyl ether (hydrophilic block) and isobutyl vinyl ether (hydrophobic block) of different molecular weights and composition were synthesized by living cationic polymerization. The molecular weight and comonomer composition of these copolymers were determined by GPC and 1H NMR spectroscopy, respectively. Aqueous solutions of the copolymers were characterized in terms of their micellar behavior using dynamic light scattering, aqueous GPC, and dye solubilization. All the copolymers formed aggregates with the exception of a diblock copolymer with only two hydrophobic monomer units. The micellar hydrodynamic size scaled with the 0.61 power of the number of hydrophobic units, in good agreement with a theoretical exponent of 0.73. An increase in the length of the hydrophobic block at constant hydrophilic block length or an increase in the overall polymer size at constant block length ratio both resulted in lower critical micelle concentrations (cmcs). The cloud points of 1% w/w aqueous solutions of the polymers were determined by turbidimetry. An increase in the length of the hydrophobic block at constant hydrophilic block length caused a decrease in the cloud points of the copolymers. However, an increase in the overall polymer size at constant block length ratio led to an increase in the cloud point. © 1996 John Wiley & Sons, Inc.