Faulty Successive Cancellation Decoding of Polar Codes for the Binary Erasure Channel

In this paper, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under this model, polarization does not happen, meaning that fully reliable communication is not possible at any rate. Furthermore, a lower bound on the frame error rate of polar codes under faulty SC decoding is provided, which is then used, along with a well-known upper bound, in order to choose a blocklength that minimizes the erasure probability under faulty decoding. Finally, an unequal error protection scheme that can re-enable asymptotically erasure-free transmission at a small rate loss and by protecting only a constant fraction of the decoder is proposed. The same scheme is also shown to significantly improve the finite-length performance of the faulty successive cancellation decoder by protecting as little as 1.5% of the decoder.Comment: Accepted for publications in the IEEE Transactions on Communication

MIMO Systems: Principles, Iterative Techniques, and advanced Polarization

International audienceThis chapter considers the principles of multiple-input multiple-output (MIMO) wireless communication systems as well as some recent accomplishments concerning their implementation. By employing multiple antennas at both transmitter and receiver, very high data rates can be achieved under the condition of deployment in a rich-scattering propagation medium. This interesting property of MIMO systems suggests their use in the future high-rate and high-quality wireless communication systems. Several concepts in MIMO systems are reviewed in this chapter. We first consider MIMO channel models and recall the basic principles of MIMO structures and channel modeling. We next study the MIMO channel capacity and present the early developments in these systems concerning the information theory aspect. Iterative signal detection is considered next; it considers iterative techniques for space-time decoding. As the capacity is inversely proportional to the spatial channel correlation, MIMO antennas should be sufficiently separated, usually by several wavelengths. In order to minimize antennas' deployment, we present advanced polarization diversity techniques for MIMO systems and explain how they can help to reduce the spatial correlation in order to achieve high transmission rates. We end the chapter by considering the application of MIMO systems in local area networks, as well as their potential in enhancing range, localization, and power efficiency of sensor networks

Neural Network Equalizers and Successive Interference Cancellation for Bandlimited Channels with a Nonlinearity

Neural networks (NNs) inspired by the forward-backward algorithm (FBA) are used as equalizers for bandlimited channels with a memoryless nonlinearity. The NN-equalizers are combined with successive interference cancellation (SIC) to approach the information rates of joint detection and decoding (JDD) with considerably less complexity than JDD and other existing equalizers. Simulations for short-haul optical fiber links with square-law detection illustrate the gains of NNs as compared to the complexity-limited FBA and Gibbs sampling.Comment: Submitted to IEEE Trans. Commun. on January 11, 2024