An asynchronous$\mathrm{K}_{\mathrm{a}}$-active-user unsourced multiple access channel (AUMAC) is a key model for uncoordinated massive access in future networks. We focus on a scenario where each transmission is subject to the maximal delay constraint ($\mathbf{D}_{\mathbf{m}}$), yet the precise delay of each user is unknown at the receiver. The combined effects of asynchronicity and uncertain delays require analysis over all possible delay-codeword combinations, making the complexity of the analysis grow with$\mathbf{D}_{\mathbf{m}}$and$\mathrm{K}_{\mathrm{a}}$exponentially. To overcome the complexity, we employ a wrap-decoder for the AUMAC and derive a uniform upper bound on the per-user probability of error (PUPE). Numerical results illuminate the trade-off between energy per bit and the number of active users under various delay constraints. Furthermore, in our considered AUMAC, decoding without explicit delay information is shown to achieve nearly the same energy efficiency as decoding with perfect delay knowledge.

In this paper, we derive the second-order coding rates for message identification via simple-dispersion discrete memoryless channels (DMCs) with noiseless feedback, both for deterministic and randomized encoding. Identification via channels, originally introduced by Ahlswede and Dueck, differs fundamentally from traditional message transmission: instead of decoding a specific message from multiple possibilities, the receiver seeks only to determine if a particular message was sent. Previous research established that feedback significantly enhances identification capacity, a stark contrast to the message transmission scenario. While second-order expansions are extensively studied for transmission, analogous results for identification remain largely unexplored. Our results generalize classical identification proofs by carefully modifying the standard two-phase codebook construction, previously reliant on typical sequences, thus making it suitable for second-order analysis. Additionally, we generalize the established converse argument and use martingale-based methods to obtain a tight second-order converse.

This work considers an asynchronous$\mathrm{K}_{\mathrm{a}}$-active-user unsourced multiple access channel (AUMAC) with the worst-case asynchronicity. The transmitted messages must be decoded within$n$channel uses, while some codewords are not completely received due to asynchronicities. We consider a constraint of the largest allowed delay of the transmission. The AUMAC lacks the permutation-invariant property of the synchronous UMAC since different permutations of the same codewords with a fixed asynchronicity are distinguishable. Hence, the analyses require calculating all$2^{\mathrm{K}_{\mathrm{a}}}-1$combinations of erroneously decoded messages. Moreover, transmitters cannot adapt the corresponding codebooks according to asynchronicity due to a lack of information on asynchronicities. To overcome this challenge, a uniform bound of the per-user probability of error (PUPE) is derived by investigating the worst-case of the asynchronous patterns with the delay constraint. Numerical results show the trade-off between the energy-per-bit and the number of active users for different delay constraints. In addition, although the asynchronous transmission reduces interference, the required energy-per-bit increases as the receiver decodes with incompletely received codewords, compared to the synchronous case.

Future wireless access networks aim to simultaneously support a large number of devices with heterogeneous service requirements, including data rates, error rates, and latencies. While achievable rate and capacity results exist for Gaussian broadcast channels in the asymptotic blocklength regime, the characterization of second-order achievable rate regions for heterogeneous blocklength constraints is not available. Therefore, we investigate a two-user Gaussian broadcast channel (GBC) with heterogeneous blocklength constraints, specified according to users’ channel output signal-to-noise ratios (SNRs). We assume that the user with higher output SNR has a shorter blocklength constraint. We show that with sufficiently large output SNR, the stronger user can perform the early decoding (ED) technique to decode and subtract the interference via successive interference cancellation (SIC). To achieve this goal, we derive an explicit lower bound on the necessary number of received symbols for a successful ED, using an independent and identically distributed Gaussian input. The second-order rate region is also derived. Numerical results show that ED can outperform the hybrid non-orthogonal multiple access scheme when the stronger channel is sufficiently better than the weaker one. Under the considered setting, about 7-dB SNR gain can be achieved compared to treating interference as noise. These results show that ED with SIC is a promising technique for future wireless networks.

We investigate the Gaussian broadcast channel with heterogeneous finite blocklength constraints (HB-GBC), which models different latency requirements for different users. To derive an outer bound on the rate region, we introduce a novel way of applying a Sato-type outer bound in the finite blocklength regime, since Sato’s classical outer bound is not directly applicable. To derive the achievable rate region, we present a way to useshell codes, which are second-order optimal for the single-user case, in the HB-GBC. We apply our technique to a hybrid TDMA/NOMA approach as well asearly decoding, which is a technique that performs successive interference cancellation with an incompletely received interference codeword. Our numerical results show that the range of power allocations where early decoding is feasible is significantly enlarged compared to the state-of-the-art, leading to considerably improved rates in the regime where rate fairness between users is the goal. This makes early decoding a promising technique to increase the rates and fairness when strict latency constraints have to be met.

We investigate early decoding in a Gaussian broadcast channel with heterogeneous blocklength constraints when shell codes are used. By shell codes, we refer to non-i.i.d. codes that fulfill the power constraint with equality. Early decoding is a technique where one user can perform successive interference cancellation with an interference codeword that is not yet fully received. By decoding the interfering shell codeword earlier, it loses the shell property, making the statistical error analysis more challenging. We address this by using composite shell codes in combination with change of measure techniques and the Berry-Esseen Theorem for functions. We derive a bound on the minimum number of symbols that is required to successfully early decode the interference and we characterize the rate region when shell codewords are used. Numerical results show a latency reduction that is at least doubled compared to the state of the art as well as a much broader range of feasible input powers, leading to a significantly improved rate region compared to previous results on early decoding.

Future wireless access networks will simultaneously support a large number of devices with heterogeneous service requirements. These include data rates, error rates, and latencies. While capacity results exist for Gaussian broadcast channels in the asymptotic regime, the characterization of second-order achievable rate region for different blocklength constraints is not available. Therefore, we investigate a two-user Gaussian broadcast channel (GBC) with heterogeneous blocklength constraints, specified according to users’ channel output signal to noise ratios (SNRs) under a maximal input power constraint and an average error probability constraint. We show that with sufficiently large output SNR, the stronger user can invoke the technique named early decoding (ED) to decode the interference. Then the successive interference cancellation (SIC) is performed. We derive the rate region of the considered setting with individual and also sum power constraints and compare with the hybrid non-orthogonal multiple access (HNOMA) scheme. Numerical results show that under sum power constraint, ED has a larger rate region than HNOMA at the region where the weaker user’s rate is sufficiently large, when the gain of the better channel is sufficiently larger than the weaker one. The above observation makes ED with SIC a promising technique for future wireless networks.