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Wireless channels generally exhibit dispersion in both time and frequency domain, known as doubly selective or doubly dispersive channels. To combat the delay spread effect, multicarrier modulation (MCM) such as orthogonal frequency division multiplexing (OFDM) and its universal filtered variant (UF-OFDM) can be employed, leading to a simple per-subcarrier one tap equalization. The time-varying nature of the channel, in particular, the intra-multicarrier-symbol channel variation induces spectral broadening and thus inter-carrier interference (ICI). Most existing works address both effects separately, focusing on the one effect while ignoring the respective other. This paper considers both effects simultaneously for cyclic prefix (CP)-, zero padded (ZP)- and universal filtered (UF)-based OFDM with a simple one tap equalization, assuming doubly dispersive wireless channel model. For this general channel model, we show that the independent (wide sense stationary uncorrelated scatter, WSSUS) selectivity in time and frequency domain starts to intertwine in contrast to the ideal cases with single selectivity. We derive signal-to-interference-plus-noise ratio (SINR) in closed form for arbitrary system settings and channel parameters, e.g., bandwidth, delay- and Doppler-spread. With the SINR analysis, we compare the three MCM schemes under different channel scenarios. [ABSTRACT FROM AUTHOR]

Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) cods, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat-accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT. function of a code to its Helleseth-Kløve-Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual. [ABSTRACT FROM AUTHOR]

Reed–Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a versatile decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) and may use any polar or RM decoder as constituent decoders. We provide extensive error-rate performance simulations for successive cancellation (SC)-, SC-list (SCL)- and belief propagation (BP)-based constituent decoders. We furthermore compare our results to existing decoding schemes and report a near-ML performance for the RM(3,7)-code (e.g., 0.04 dB away from the ML bound at BLER of 10−3) at a competitive computational cost. Moreover, we provide some insights into the automorphism subgroups of RM codes and SC decoding and, thereby, prove the theoretical limitations of this method with respect to polar codes. [ABSTRACT FROM AUTHOR]

We present a new framework for constructing polar codes (i.e., selecting the frozen bit positions) for arbitrary channels, tailored to a given decoding algorithm rather than assuming the (not necessarily optimal) successive cancellation (SC) decoding. The proposed framework is based on the genetic algorithm (GenAlg), where populations (i.e., collections) of information sets evolve via evolutionary transformations based on their individual error-rate performance. These populations converge toward an information set that fits both the decoding behavior and the defined channel. We construct polar codes, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding over both the AWGN channel and the Rayleigh channel, respectively. Furthermore, a proposed belief propagation (BP)-tailored construction approaches the SCL error-rate performance without any modifications in the decoding algorithm itself. The performance gains can be attributed to the significant reduction in the number of low-weight codewords. We show that, when required, the GenAlg can also be set up to find codes that reduce the decoding complexity. This way, the SCL list size or the number of BP iterations can be reduced while maintaining the same error-rate performance. [ABSTRACT FROM AUTHOR]