Low Complexity Decoding for Higher Order Punctured Trellis-Coded Modulation Over Intersymbol Interference Channels

Trellis-coded modulation (TCM) is a power and bandwidth efficient digital transmission scheme which offers very low structural delay of the data stream. Classical TCM uses a signal constellation of twice the cardinality compared to an uncoded transmission with one bit of redundancy per PAM symbol, i.e., application of codes with rates $\frac{n-1}{n}$ when $2^{n}$ denotes the cardinality of the signal constellation. Recently published work allows rate adjustment for TCM by means of puncturing the convolutional code (CC) on which a TCM scheme is based on. In this paper it is shown how punctured TCM-signals transmitted over intersymbol interference (ISI) channels can favorably be decoded. Significant complexity reductions at only minor performance loss can be achieved by means of reduced state sequence estimation.Comment: 4 pages, 5 figures, 3 algorithms, accepted and published at 6th International Symposium on Communications, Control, and Signal Processing (ISCCSP 2014

An efficient length- and rate-preserving concatenation of polar and repetition codes

We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known successive decoding algorithms for polar codes. Overall rate and block length remain unchanged, the decoding complexity is at most doubled. A comparison to related methods for performance improvement of polar codes is drawn.Comment: to be presented at International Zurich Seminar (IZS) 201

Low Complexity Decoding for Punctured Trellis-Coded Modulation Over Intersymbol Interference Channels

Classical trellis-coded modulation (TCM) as introduced by Ungerboeck in 1976/1983 uses a signal constellation of twice the cardinality compared to an uncoded transmission with one bit of redundancy per PAM symbol, i.e., application of codes with rates $\frac{n-1}{n}$ when $2^{n}$ denotes the cardinality of the signal constellation. The original approach therefore only comprises integer transmission rates, i.e., $R=\left\{ 2,\,3,\,4\,\ldots \right\}$, additionally, when transmitting over an intersymbol interference (ISI) channel an optimum decoding scheme would perform equalization and decoding of the channel code jointly. In this paper, we allow rate adjustment for TCM by means of puncturing the convolutional code (CC) on which a TCM scheme is based on. In this case a nontrivial mapping of the output symbols of the CC to signal points results in a time-variant trellis. We propose an efficient technique to integrate an ISI-channel into this trellis and show that the computational complexity can be significantly reduced by means of a reduced state sequence estimation (RSSE) algorithm for time-variant trellises.Comment: 4 pages, 7 pictured, accepted for 2014 International Zurich Seminar on Communication

The Postwar West German Economic Transition: From Ordoliberalism to Keynesianism

The Federal Republic of Germany has experienced a fundamental shift in economic philosophy from Ordoliberalism to Keynesianism. This paper elucidates the main tenets of both schools of thought and their eventual influences on economic policy from 1945 through the late 1960s. West Germany’s transition to Keynesianism follows a relatively cohesive narrative, as the complexities of event history resonate to similar effect in academic and political spheres. By the end of this investigation, intellectual quagmires surrounding economic successes of the postwar period appear as the logical consequences of an academic community that underestimates the importance of normative economic philosophy for policy implementation and society writ large. Reconnecting historical narrative with economic philosophy thus serves in a dual capacity, clarifying a particularly controversial period in economic historiography while also illuminating the underlying problems of our present circumstance.Economic History, Ordoliberalism, Keynesianism, German Economic Reform

Observing spin fractionalization in the Kitaev spin liquid via temperature evolution of indirect resonant inelastic x-ray scattering

Motivated by the ongoing effort to search for high-resolution signatures of quantum spin liquids, we investigate the temperature dependence of the indirect resonant inelastic x-ray scattering (RIXS) response for the Kitaev honeycomb model. We find that, as a result of spin fractionalization, the RIXS response changes qualitatively at two well-separated temperature scales, $T_L$ and $T_H$, which correspond to the characteristic energies of the two kinds of fractionalized excitations, $\mathbb{Z}_2$ gauge fluxes and Majorana fermions, respectively. While thermally excited $\mathbb{Z}_2$ gauge fluxes at temperature $T_L$ lead to a general broadening and softening of the response, the thermal proliferation of Majorana fermions at temperature $T_H \sim 10 \, T_L$ results in a significant shift of the spectral weight, both in terms of energy and momentum. Due to its exclusively indirect nature, the RIXS process we consider gives rise to a universal magnetic response and, from an experimental perspective, it directly corresponds to the $K$-edge of Ru$^{3+}$ in the Kitaev candidate material $\alpha$-RuCl$_3$.Comment: 8 pages, 5 figures, published version with infinitesimal change

Punctured Trellis-Coded Modulation

In classic trellis-coded modulation (TCM) signal constellations of twice the cardinality are applied when compared to an uncoded transmission enabling transmission of one bit of redundancy per PAM-symbol, i.e., rates of $\frac{K}{K+1}$ when $2^{K+1}$ denotes the cardinality of the signal constellation. In order to support different rates, multi-dimensional (i.e., $\mathcal{D}$-dimensional) constellations had been proposed by means of combining subsequent one- or two-dimensional modulation steps, resulting in TCM-schemes with $\frac{1}{\mathcal{D}}$ bit redundancy per real dimension. In contrast, in this paper we propose to perform rate adjustment for TCM by means of puncturing the convolutional code (CC) on which a TCM-scheme is based on. It is shown, that due to the nontrivial mapping of the output symbols of the CC to signal points in the case of puncturing, a modification of the corresponding Viterbi-decoder algorithm and an optimization of the CC and the puncturing scheme are necessary.Comment: 5 pages, 10 figures, submitted to IEEE International Symposium on Information Theory 2013 (ISIT