This article presents a novel transmission scheme for the unsourced, uncoordinated Gaussian multiple access problem. The proposed scheme leverages notions from single-user coding, random spreading, minimum-mean squared error (MMSE) estimation, and successive interference cancellation. Specifically, every message is split into two parts: the first fragment serves as the argument to an injective function that determines which spreading sequence should be employed, whereas the second component of the message is encoded using a polar code. The latter coded bits are then spread using the sequence determined during the first step. The ensuing signal is transmitted through a Gaussian multiple-access channel (GMAC). On the receiver side, active sequences are detected using a correlation-based energy detector, thereby simultaneously recovering individual signature sequences and their generating information bits in the form of preimages of the sequence selection function. Using the set of detected active spreading sequences, an MMSE estimator is employed to produce log-likelihood ratios (LLRs) for the second part of the messages corresponding to these detected users. The LLRs associated with each detected user are then passed to a list decoder of the polar code, which performs single-user decoding to decode the second portion of the message. This decoding operation proceeds iteratively by subtracting the interference due to the successfully decoded messages from the received signal, and repeating the above steps on the residual signal. At this stage, the proposed algorithm outperforms alternate existing lowcomplexity schemes when the number of active uses is below 225.

Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced random access with coded compressed sensing (CCS), as first demonstrated by Fengler, Jung, and Caire. Specifically, their approach employs a concatenated coding framework with an inner AMP decoder followed by an outer tree decoder. In their original implementation, these two components work independently of each other, with the tree decoder acting on the static output of the AMP decoder. This article introduces a novel framework where the inner AMP decoder and the outer tree decoder operate in tandem, dynamically passing information back and forth to take full advantage of the underlying CCS structure. This scheme necessitates the redesign of the tree code as to enable belief propagation in a computationally tractable manner. The enhanced architecture exhibits significant performance benefits over a range of system parameters. The error performance of the proposed scheme can be accurately predicted through a set of equations, known as state evolution of AMP. These findings are supported both analytically and through numerical methods.

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We consider the problem of learning an episodic safe control policy that minimizes an objective function, while satisfying necessary safety constraints -both during learning and deployment. We formulate this safety constrained reinforcement learning (RL) problem using the framework of a finite-horizon Constrained Markov Decision Process (CMDP) with an unknown transition probability function. Here, we model the safety requirements as constraints on the expected cumulative costs that must be satisfied during all episodes of learning. We propose a model-based safe RL algorithm that we call the Optimistic-Pessimistic Safe Reinforcement Learning (OPSRL) algorithm, and show that it achieves an Õ(S 2 √ AH 7 K/( C − Cb )) cumulative regret without violating the safety constraints during learning, where S is the number of states, A is the number of actions, H is the horizon length, K is the number of learning episodes, and ( C − Cb ) is the safety gap, i.e., the difference between the constraint value and the cost of a known safe baseline policy. The scaling as Õ( √ K) is the same as the traditional approach where constraints may be violated during learning, which means that our algorithm suffers no additional regret in spite of providing a safety guarantee. Our key idea is to use an optimistic exploration approach with pessimistic constraint enforcement for learning the policy. This approach simultaneously incentivizes the exploration of unknown states while imposing a penalty for visiting states that are likely to cause violation of safety constraints. We validate our algorithm by evaluating its performance on benchmark problems against conventional approaches.