In this work, we investigate the design of the parity-check matrix in the recently introduced Syndrome-Based Neural Decoders, which are powerful neural-network-based channel decoders. We show that the structure of the parity-check matrix has a crucial effect on the decoder’s performance, propose an information-theoretic metric to describe this effect, and suggest an algorithm to construct a parity-check matrix accordingly. The results are illustrated both analytically and numerically, showing a considerable performance gain for the proposed design without any increase in training or decoding complexity.

We consider the transmission of a continuous phase modulated (CPM) signal through a Gaussian channel affected by Doppler shifts. We propose a receiver robust to the Doppler shifts derived from a non-coherent detection criterion. We compare its performance to another non-coherent receiver based on a linear approximation of the CPM signal (Laurent decomposition) on which we add a Doppler compensation. Simulation results show that the first algorithm is robust to low-moderate Doppler shifts, while the second is robust to any one. We finally compare these two algorithms to delay-optimized differential detectors which do not require any Doppler shift estimation. We also provide complexity estimations to guide the possible complexity-performance trade-offs.

The maximum a posteriori (MAP) threshold corresponds to the fundamental limit that one can hope to achieve with the given channel code ensemble. Apart from theoretical interests, finding this limit is also desirable sincespatial-coupledcode ensembles approach this MAP threshold due to phenomenon termed asthreshold saturation. However finding this MAP threshold, in general, is known to be computationally prohibitive. This work proposes a tractable method for estimating the MAP threshold for various families of sparse-graph code ensembles over non-binary complex-input additive white Gaussian noise (AWGN) channel. Towards this, we provide a method to approximate the extended belief propagation generalized extrinsic information transfer (EBP-GEXIT) chart and estimate the MAP threshold by applying theMaxwell constructionto it. To illustrate the validity of our method, we study spatial coupling for serially-concatenated turbo-codes and numerically observe threshold saturation of these codes to the MAP thresholds estimated via our method.

We investigate the problem of estimating the maximum a posteriori (MAP) threshold for serially concatenated turbo codes. First, we provide a method to compute this MAP threshold using a numerical approximation of the EBP-GEXIT chart and the Maxwell construction. Second, we explore where the spatially coupled belief propagation (BP) threshold is located with respect to the previously computed MAP threshold and analyze the saturation phenomenon of such schemes. Simulation results indicate that the BP threshold of the spatially coupled turbo-codes saturates to the MAP threshold obtained using the EBP-GEXIT chart.

In this paper, we provide a general framework for spatially-coupled concatenated systems. We explicit the analogy with spatially-coupled protographs and provide an adapted EXIT chart analysis. By proposing a continuous-valued coupling matrix, we propose a code design procedure for faster convergence. When considering general bit- interleaved coded-modulation scheme, we also conjecture that the spatially-coupled scheme of general detectors saturates to a value very close (lower bound) to the threshold given by the Area theorem.

The spatial coupling is an efficient technique that improves the threshold of Low Density Parity Check (LDPC) codes. In this paper, we investigate the performance of the serial concatenation of Continuous phase modulation (CPM) and LDPC convolutional codes over a memoryless additive white Gaussian noise channel. We show that coupling protographs optimized for CPM improves their performance and helps designing very good `small' protographs. Inspired from convolutional codes and thanks to the inner structure of CPM, we also introduce a new termination without rate loss but that still exhibits a coupling gain and it thus has a very good threshold. We will illustrate the behavior of different LDPC convolutional codes with different termination methods by giving some examples and studying their performance using multidimensional EXIT analysis.

In this paper, we provide a proof for the conjecture made by Abu Surra et al. [1] to simplify the computation of ensemble input output weight enumerators for protograph-based low density parity check (LDPC) codes. Furthermore, we propose a new method to compute more efficiently the ensemble weight enumerator. This approach can be applied particularly to lighten the computations for high rate codes, generalized LDPC codes or spatially coupled LDPC codes.

In this paper, we derive an asymptotic analysis for a capacity approaching design of serially concatenated turbo schemes with low density parity check (LDPC) codes and continuous phase modulation (CPM) based on Laurent decomposition. The proposed design is based on extrinsic mutual information evolution and Gaussian approximation. By inserting partial interleavers between LDPC and CPM and allowing degree-1 variable nodes under a certain constraint we show that designed rates are very close to the maximum achievable rates. Furthermore, we discuss the selection of low complexity receivers that works with the same optimized profiles.

In this paper, we derive an asymptotic analysis and optimization of coded CPM systems using both unstructured and protograph-based LDPC codes ensembles. First, we present a simple yet effective approach to design unstructured LDPC codes : by inserting partial interleavers between LDPC and CPM, and allowing degree-1 and degree-2 variable nodes in a controlled pattern, we show that designed codes perform that can operate very close to the maximum achievable rates. Finally, the extension to protograph based codes is discussed. We provide some simple rules to design good protograph codes with good threshold properties.