Computer Science

Polar codes can be decoded with the low-complexity successive-cancellation flip (SCF) algorithm. To improve error-correction performance, the dynamic successive-cancellation flip (DSCF) variant was proposed, where the resulting error-correction performance is similar to that of the successive-cancellation list algorithm with low to moderate list sizes. Regardless of the variant, the SCF algorithm exhibits a variable execution time with a high (worst-case) latency. In this work, we propose an early-stopping metric used to detect codewords that are likely undecodable such that the decoder can be stopped at earlier stages for those codewords. We then propose a modified version of the DSCF algorithm that integrates our early-stopping metric that exploits the specific properties of DSCF. Compared to the original DSCF algorithm, in the region of interest for wireless communications, simulation results show that our proposed modifications can lead to reductions of 22% to the average execution time and of 45% to the execution-time variance at the cost of a minor error-correction loss of approximately 0.05 dB.

This paper considers an information bottleneck problem with the objective of obtaining a most informative representation of a hidden feature subject to a Rényi entropy complexity constraint. The optimal bottleneck trade-off between relevance (measured via Shannon's mutual information) and Rényi entropy cost is defined and an iterative algorithm for finding approximate solutions is provided. We also derive an operational characterization for the optimal trade-off by demonstrating that the optimal Rényi entropy-relevance trade-off is achievable by a simple time-sharing scalar coding scheme and that no coding scheme can provide better performance. Two examples where the optimal Shannon entropy-relevance trade-off can be exactly determined are further given.

This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field GF(q) where q is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant codes. Using these methods, we construct an amount of symmetric self-dual codes over GF(11) , GF(19) , and GF(23) of every length less than 42. We also find 153 {\it new} self-dual codes up to equivalence: they are [32,16,12] , [36,18,13] , and [40,20,14] codes over GF(11) , [36,18,14] and [40,20,15] codes over GF(19) , and [32,16,12] , [36,18,14] , and [40,20,15] codes over GF(23) . They all have new parameters with respect to self-dual codes. Consequently, we improve bounds on the highest minimum distance of self-dual codes, which have not been significantly updated for almost two decades.

In this paper, we focus on the design and analysis of the Analog Fountain Code (AFC) for short packet communications. We first propose a density evolution (DE) based framework, which tracks the evolution of the probability density function of the messages exchanged between variable and check nodes of AFC in the belief propagation decoder. Using the proposed DE framework, we formulate an optimisation problem to find the optimal AFC code parameters, including the weight-set, which minimizes the bit error rate at a given signal-to-noise ratio (SNR). Our results show the superiority of our code design in comparison to existing code designs and thus the validity of the proposed DE framework in the asymptotic block length regime. We then focus on the selection of the precoder to improve the performance of AFC at short block lengths. Simulation results show that lower precoder rates obtain better realised rates over a wide SNR range for short information block length.

This letter investigates the uplink outage performance of intelligent reflecting surface (IRS)-assisted non-orthogonal multiple access (NOMA). We consider the general case where all users have both direct and reflection links, and all links undergo Nakagami-m fading. We approximate the received powers of the NOMA users as Gamma random variables via moments matching. This allows for tractable expressions of the outage under interference cancellation (IC), while being flexible in modeling various propagation environments. Our analysis shows that under certain conditions, the presence of an IRS might degrade the performance of users that have dominant line-of-sight (LOS) to the base station (BS), while users dominated by non-line-of-sight (NLOS) will always benefit from it.

Compressed sensing (CS) involves sampling signals at rates less than their Nyquist rates and attempting to reconstruct them after sample acquisition. Most such algorithms have parameters, for example the regularization parameter in LASSO, which need to be chosen carefully for optimal performance. These parameters can be chosen based on assumptions on the noise level or signal sparsity, but this knowledge may often be unavailable. In such cases, cross validation (CV) can be used to choose these parameters in a purely data-driven fashion. Previous work analysing the use of CV in CS has been based on the ??2 cross-validation error with Gaussian measurement noise. But it is well known that the ??2 error is not robust to impulse noise and provides a poor estimate of the recovery error, failing to choose the best parameter. Here we propose using the ??1 CV error which provides substantial performance benefits given impulse measurement noise. Most importantly, we provide a detailed theoretical analysis and error bounds for the use of ??1 CV error in CS reconstruction. We show that with high probability, choosing the parameter that yields the minimum ??1 CV error is equivalent to choosing the minimum recovery error (which is not observable in practice). To our best knowledge, this is the first paper which theoretically analyzes ??1 -based CV in CS.

Channel estimation is a practical challenge for intelligent reflecting surface (IRS) aided wireless communication. As the number of IRS reflecting elements or IRS-aided users increases, the channel training overhead becomes excessively high, which results in long delay and low throughput in data transmission. To tackle this challenge, we propose in this paper a new anchor-assisted channel estimation approach, where two anchor nodes, namely A1 and A2, are deployed near the IRS for facilitating its aided base station (BS) in acquiring the cascaded BS-IRS-user channels required for data transmission. Specifically, in the first scheme, the partial channel state information (CSI) on the element-wise channel gain square of the common BS-IRS link for all users is first obtained at the BS via the anchor-assisted training and feedback. Then, by leveraging such partial CSI, the cascaded BS-IRS-user channels are efficiently resolved at the BS with additional training by the users. While in the second scheme, the BS-IRS-A1 and A1-IRS-A2 channels are first estimated via the training by A1. Then, with additional training by A2, all users estimate their individual cascaded A2-IRS-user channels simultaneously. Based on the CSI fed back from A2 and all users, the BS resolves the cascaded BS-IRS-user channels efficiently. In both schemes, the quasi-static channels among the fixed BS, IRS, and two anchors are estimated off-line only, which greatly reduces the real-time training overhead. Simulation results demonstrate that our proposed anchor-assisted channel estimation schemes achieve superior performance as compared to existing IRS channel estimation schemes, under various practical setups. In addition, the first proposed scheme outperforms the second one when the number of antennas at the BS is sufficiently large, and vice versa.

Motivated by various data science applications including de-anonymizing user identities in social networks, we consider the graph alignment problem, where the goal is to identify the vertex/user correspondence between two correlated graphs. Existing work mostly recovers the correspondence by exploiting the user-user connections. However, in many real-world applications, additional information about the users, such as user profiles, might be publicly available. In this paper, we introduce the attributed graph alignment problem, where additional user information, referred to as attributes, is incorporated to assist graph alignment. We establish sufficient and necessary conditions for recovering vertex correspondence exactly, where the conditions match for a wide range of practical regimes. Our results recover existing tight information-theoretic limits for models where only the user-user connections are available, spanning the full spectrum between these models and models where only attribute information is available.

We study orbit codes in the field extension F q n . First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not contained in a proper subfield of F q n . We then generalize to orbits under the normalizer of the Singer subgroup. In that situation some exceptional cases arise and some open cases remain. Finally we characterize linear isometries between such codes.

In this paper, the average achievable rate and error probability of a reconfigurable intelligent surface (RIS) aided systems is investigated for the finite blocklength (FBL) regime. The performance loss due to the presence of phase errors arising from limited quantization levels as well as hardware impairments at the RIS elements is also discussed. First, the composite channel containing the direct path plus the product of reflected channels through the RIS is characterized. Then, the distribution of the received signal-to-noise ratio (SNR) is matched to a Gamma random variable whose parameters depend on the total number of RIS elements, phase errors and the channels' path loss. Next, by considering the FBL regime, the achievable rate expression and error probability are identified and the corresponding average rate and average error probability are elaborated based on the proposed SNR distribution. Furthermore, the impact of the presence of phase error due to either limited quantization levels or hardware impairments on the average rate and error probability is discussed. The numerical results show that Monte Carlo simulations conform to matched Gamma distribution to received SNR for sufficiently large number of RIS elements. In addition, the system reliability indicated by the tightness of the SNR distribution increases when RIS is leveraged particularly when only the reflected channel exists. This highlights the advantages of RIS-aided communications for ultra-reliable and low-latency systems. The difference between Shannon capacity and achievable rate in FBL regime is also discussed. Additionally, the required number of RIS elements to achieve a desired error probability in the FBL regime will be significantly reduced when the phase shifts are performed without error.