A-posteriori symbol probabilities and log-likelihood ratios for coherently detected π/4-DE-QPSK

In this letter, coherent detection of p/4-DE-QPSK is considered, but our analysis also holds for common DE-QPSK. It is shown that maximum a-posteriori (MAP) sequence detection can be regarded as an approximation, based on selecting dominant exponentials, of MAP symbol detection. A better approximation, relying on piecewise-linear fitting of the logarithm of the hyperbolic cosine, is proposed. This approximation results in a performance very close to optimal symbol detection. For the case where the symbols are produced by convolutional encoding and Gray mapping, the log-likelihood ratios are investigated. Again a simple approximation based on selecting dominant exponentials and an improved approximation relying on piecewise-linear fits, are discussed. As in the uncoded case the improved approximation gives a performance quite close to ideal. While the particular examples considered show modest gains in performance, this letter provides a way of improving performance when needed

On constellation shaping for short block lengths

Gaussian channel inputs are required to achieve the capacity of additive white Gaussian noise (AWGN) channels. Equivalently, the n-dimensional constellation boundary must be an n-sphere. In this work, constellation shaping is discussed for short block lengths. Two different approaches are considered: Sphere shaping and constant composition distribution matching (CCDM). It is shown that both achieve the maximum rate and generate Maxwell-Boltzmann (MB) distributed inputs. However sphere shaping achieves this maximum faster than CCDM and performs more efficiently in the short block length regime. This is shown by computing the finite-length rate losses. Then the analysis is justified by numerical simulations employing low-density parity-check (LDPC) codes of the IEEE 802.11 standard

A system dynamics and participatory action research approach to promote healthy living and a healthy weight among 10–14-year-old adolescents in Amsterdam: The LIKE programme

This paper describes the design of the LIKE programme, which aims to tackle the complex problem of childhood overweight and obesity in 10–14-year-old adolescents using a systems dynamics and participatory approach. The LIKE programme focuses on the transition period from 10-years-old to teenager and was implemented in collaboration with the Amsterdam Healthy Weight Programme (AHWP) in Amsterdam-East, the Netherlands. The aim is to develop, implement and evaluate an integrated action programme at the levels of family, school, neighbourhood, health care and city. Following the principles of Participatory Action Research (PAR), we worked with our population and societal stakeholders as co-creators. Applying a system lens, we first obtained a dynamic picture of the pre-existing systems that shape adolescents’ behaviour relating to diet, physical activity, sleep an

A-posteriori symbol probabilities and log-likelihood ratios for coherently detected π/4-DE-QPSK

In this letter, coherent detection of p/4-DE-QPSK is considered, but our analysis also holds for common DE-QPSK. It is shown that maximum a-posteriori (MAP) sequence detection can be regarded as an approximation, based on selecting dominant exponentials, of MAP symbol detection. A better approximation, relying on piecewise-linear fitting of the logarithm of the hyperbolic cosine, is proposed. This approximation results in a performance very close to optimal symbol detection. For the case where the symbols are produced by convolutional encoding and Gray mapping, the log-likelihood ratios are investigated. Again a simple approximation based on selecting dominant exponentials and an improved approximation relying on piecewise-linear fits, are discussed. As in the uncoded case the improved approximation gives a performance quite close to ideal. While the particular examples considered show modest gains in performance, this letter provides a way of improving performance when needed

Complexity reduction for non-coherent iteratively detected differentially encoded quaternary phase shift keying based on trellis decomposition

In this letter, we investigate complexity reduction for non-coherent iterative detection of differentially encoded quadrature phase shift keying applied to digital audio broadcast receivers. We use 2D blocks in an orthogonal frequency division multiplexing scheme and trellis decomposition to calculate, iteratively, the a posteriori probabilities of the information symbols. Furthermore, the trellis decomposition method allows us to estimate the unknown channel phase efficiently. This phase is related to sub-trellises of which we can determine the a posteriori probabilities. In our first approach, we investigate a method that is based on finding, at the start of each new iteration, the dominant sub-trellis first and then do the forward- backward processing for demodulation only in this dominant sub-trellis. This method reduces the number of multiplications by a factor of 3, the normalizations by a factor 8 and, after five iterations, introducing ≈ 0.05 dB loss in performance on the COST-207 TU-6 channel. Our second approach involves choosing the dominant sub-trellis only once, before starting with the iterations. This results in reducing the number of multiplications and normalizations by a factor of 8 and introduces ≈ 0.5 dB loss in performance

Constellation shaping for IEEE 802.11

A constellation shaping scheme is proposed. The motivation is to decrease the required transmit power for a specified spectral efficiency. Instead of imposing a non-uniform distribution on the constellation or using nonuniformly spaced symbols, a sphere constraint is employed on the n-dimensional signal space. An efficient algorithm called enumerative amplitude shaping is given to find and index all signal points in the sphere. A comparison with a prominent probabilistic shaping algorithm is provided. The enumerative approach achieves the target rate more efficiently for small block lengths. To introduce error correction, the convolutional encoder used in IEEE Std 802.11 is combined with the shaper in a novel way. Instead of utilizing a larger constellation in combination with shaping, a higher code rate is used by puncturing. Gains up to 1.61 dB are observed for the rates 3 to 6 bits/2-D with 64- and 256-QAM schemes in AWGN channels. The contribution of puncturing in these gains is discussed

Approximate enumerative sphere shaping

Enumerative sphere shaping of N-dimensional constellations is discussed. It is proven that a finite-precision number representation is suitable for use in two enumerative indexing algorithms: Enumerative sphere shaping and Divide Conquer (DC) shaping. This representation decreases the storage complexities of these methods significantly. DC is the basis of the well-known shell mapping algorithm and thus our approximations also apply there

Low SAR 31P (multi-echo) spectroscopic imaging using an integrated whole-body transmit coil at 7T

Phosphorus (31P) MRSI provides opportunities to monitor potential biomarkers. However, current applications of 31P MRS are generally restricted to relatively small volumes as small coils are used. Conventional surface coils require high energy adiabatic RF pulses to achieve flip angle homogeneity, leading to high specific absorption rates (SARs), and occupy space within the MRI bore. A birdcage coil behind the bore cover can potentially reduce the SAR constraints massively by use of conventional amplitude modulated pulses without sacrificing patient space. Here, we demonstrate that the integrated 31P birdcage coil setup with a high power RF amplifier at 7 T allows for low flip angle excitations with short repetition time (TR) for fast 3D chemical shift imaging (CSI) and 3D T1-weighted CSI as well as high flip angle multi-refocusing pulses, enabling multi-echo CSI that can measure metabolite T2, over a large field of view in the body. B1 + calibration showed a variation of only 30% in maximum B1 in four volunteers. High signal-to-noise ratio (SNR) MRSI was obtained in the gluteal muscle using two fast in vivo 3D spectroscopic imaging protocols, with low and high flip angles, and with multi-echo MRSI without exceeding SAR levels. In addition, full liver MRSI was achieved within SAR constraints. The integrated 31P body coil allowed for fast spectroscopic imaging and successful implementation of the multi-echo method in the body at 7 T. Moreover, no additional enclosing hardware was needed for 31P excitation, paving the way to include larger subjects and more space for receiver arrays. The increase in possible number of RF excitations per scan time, due to the improved B1 + homogeneity and low SAR, allows SNR to be exchanged for spatial resolution in CSI and/or T1 weighting by simply manipulating TR and/or flip angle to detect and quantify ratios from different molecular species