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We introduce a novel approach to error correction decoding in the presence of additive alpha-stable noise, which serves as a model of interference-limited wireless systems. In the absence of modifications to decoding algorithms, treating alpha-stable distributions as Gaussian results in significant performance loss. Building on Guessing Random Additive Noise Decoding (GRAND), we consider two approaches. The first accounts for alpha-stable noise in the evaluation of log-likelihood ratios (LLRs) that serve as input to Ordered Reliability Bits GRAND (ORBGRAND). The second builds on an ORBGRAND variant that was originally designed to account for jamming that treats outlying LLRs as erasures. This results in a hybrid error and erasure correcting decoder that corrects errors via ORBGRAND and corrects erasures via Gaussian elimination. The block error rate (BLER) performance of both approaches are similar. Both outperform decoding assuming that the LLRs originated from Gaussian noise by ∼2 to ∼3 dB for [128,112] 5G NR CA-Polar and CRC codes. 

While many communication systems experience extraneous noise that is well-modelled as Gaussian, experimental studies have shown that large values are more common when noise is impulsive and the Laplace distribution has been proposed as a more appropriate statistical model in that setting. Guessing Random Additive Noise Decoding is a class of forward error correction decoders that can avail of channel knowledge to improve decoding. Here we introduce a GRAND decoder that is specifically tailored to impulsive noise, which we call Laplace Ordered Reliability Bits GRAND (LORBGRAND). By adapting GRAND to the characteristics of Laplace noise we find an improvement of the order of ~1dB in block error rate, highlighting the benefits of noise-specific decoding strategies. Additionally, we extend the algorithm to provide soft output to indicate the probability estimation of correct decoding, which can be used to identify unreliable decoded signals. 

We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $$(\epsilon,\delta)$$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $$(\epsilon,\delta)$$-DP, improving upon previous results that only apply to at most three colors and for $$\epsilon$$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism. 

In this work, we discuss time-shift coding and GRAND ZigZag decoding for uncoordinated multiple access channels (MACs). Time-shift coding relies on the delay difference of the received packets to prevent fully overlapped collisions. Users transmit with different time-shifts in designated time slots until the receiver successfully decodes all messages. At the receiver side, ZigZag decoding is employed to separate packets with linear complexity in noiseless scenarios. For cases with noise, a guessing random additive noise decoding (GRAND)-based algorithm is utilized to identify the most probable noise vector in conjunction with ZigZag decoding. Simulation results demonstrate that time-shift coding significantly reduces collision probabilities, thereby enhancing system throughput in noiseless scenarios. In the context of Gaussian MAC, the GRAND ZigZag decoding method outperforms successive interference cancellation (SIC)-based schemes in high signal-to-noise ratio (SNR) regimes.