We compare the performance of a selection of short-length and very short-length linear binary error-correcting codes on the binary-input Gaussian noise channel, and on the fast and quasi-static flat Rayleigh fading channel. We use the probabilistic Ordered Statistics Decoder, that is universal to any code construction. As such we compare codes and not decoders. The word error rate versus the signal-to-noise ratio is found for LDPC, Reed-Muller, Polar, Turbo, Golay, random, and BCH codes at length 20, 32 and 256 bits. BCH and random codes outperform other codes in absence of a cyclic redundancy check concatenation. Under joint decoding, the concatenation of a cyclic redundancy check makes all codes perform very close to optimal lower bounds. Optimizations of the Ordered Statistics Decoder are discussed and revealed to bring near-ML performance with a notable complexity reduction, making the decoding complexity at very short length affordable.

Motivated by scenario requirements for 5G cellular networks, we study one of the candidate protocols for massive random access: the family of random access methods known as Coded Slotted ALOHA (CSA). A recent trend in research has explored aspects of such methods in various contexts, but one aspect has not been fully taken into account: the impact of path loss, which is a major design constraint in long-range wireless networks. In this article, we explore the behavior of CSA, by focusing on the path loss component correlated to the distance to the base station. Path loss provides opportunities for capture, improving the performance of CSA. We revise methods for estimating CSA behavior, provide bounds of performance, and then, focusing on the achievable throughput, we extensively explore the key parameters, and their associated gain (experimentally). Our results shed light on the behavior of the optimal distribution of repetitions in actual wireless networks.

Ultra Reliable and Low Latency Communications (URLLC) is deemed to be an essential service in 5G systems and beyond (also called 6G) to accommodate a wide range of emerging applications with stringent latency and reliability requirements. Coexistence of URLLC alongside other service categories calls for developing spectrally efficient multiplexing techniques. Specifically, coupling URLLC and conventional enhanced Mobile BroadBand (eMBB) through superposition/puncturing naturally arises as a promising option due to the tolerance of the latter in terms of latency and reliability. The idea here is to transmit URLLC packets (typically sporadic and of short size) over resources occupied by ongoing eMBB transmissions while minimizing the impact on the eMBB transmissions. In this paper, we propose a novel downlink URLLC-eMBB multiplexing technique that exploits possible similarities among URLLC and eMBB symbols, with the objective of reducing the size of the punctured eMBB symbols. We propose that the base station (BS) scans the eMBB traffic' symbol sequences and punctures those that have the highest symbol similarity with that of the URLLC users to be served. As the eMBB and URLLC may use different constellation sizes, we introduce the concept of symbol region similarity to accommodate the different constellations. We assess the performance of the proposed scheme analytically, where we derive closed-form expressions for the symbol error rate (SER) of the eMBB and URLLC services. We also derive an expression for the eMBB loss function due to puncturing in terms of the eMBB SER. We demonstrate through numerical and simulation results the efficacy of the proposed scheme where we show that 1) the eMBB spectral efficiency is improved by puncturing fewer symbols, 2) the SER and reliability performance of eMBB are improved, and 3) the URLLC data is accommodated within the specified delay constraint while maintaining its reliability, 4) and the proposed strategy has polynomial time complexity making it an efficient solution to be used in practice.

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One to Many communications are expected to be among the killer applications for the currently discussed 5G standard. The usage of coding mechanisms is impacting broadcasting standard quality, as coding is involved at several levels of the stack, and more specifically at the application layer where Rateless, LDPC, Reed Slomon codes and network coding schemes have been extensively studied, optimized and standardized in the past. Beyond reusing, extending or adapting existing application layer packet coding mechanisms based on previous schemes and designed for the foregoing LTE or other broadcasting standards; our purpose is to investigate the use of Generalized Reed Muller codes and the value of their locality property in their progressive decoding for Broadcast/Multicast communication schemes with real time video delivery. Our results are meant to bring insight into the use of locally decodable codes in Broadcasting.