A simpler derivation of the coding theorem

A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information follow naturally in the proof. It may also be applicable to situations where typicality is not natural

End-to-end Learning for OFDM: From Neural Receivers to Pilotless Communication

Previous studies have demonstrated that end-to-end learning enables significant shaping gains over additive white Gaussian noise (AWGN) channels. However, its benefits have not yet been quantified over realistic wireless channel models. This work aims to fill this gap by exploring the gains of end-to-end learning over a frequency- and time-selective fading channel using orthogonal frequency division multiplexing (OFDM). With imperfect channel knowledge at the receiver, the shaping gains observed on AWGN channels vanish. Nonetheless, we identify two other sources of performance improvements. The first comes from a neural network (NN)-based receiver operating over a large number of subcarriers and OFDM symbols which allows to significantly reduce the number of orthogonal pilots without loss of bit error rate (BER). The second comes from entirely eliminating orthognal pilots by jointly learning a neural receiver together with either superimposed pilots (SIPs), linearly combined with conventional quadrature amplitude modulation (QAM), or an optimized constellation geometry. The learned geometry works for a wide range of signal-to-noise ratios (SNRs), Doppler and delay spreads, has zero mean and does hence not contain any form of superimposed pilots. Both schemes achieve the same BER as the pilot-based baseline with around 7% higher throughput. Thus, we believe that a jointly learned transmitter and receiver are a very interesting component for beyond-5G communication systems which could remove the need and associated control overhead for demodulation reference signals (DMRSs)