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This article introduces a novel concatenated coding scheme called sparse regression LDPC (SR-LDPC) codes. An SR-LDPC code consists of an outer non-binary LDPC code and an inner sparse regression code (SPARC), whose respective field size and section sizes are equal. For such codes, an efficient decoding algorithm is proposed based on approximate message passing (AMP) that dynamically shares soft information between inner and outer decoders. This dynamic exchange of information is facilitated by a denoiser that runs belief propagation (BP) on the factor graph of the outer LDPC code within each AMP iteration. It is shown that this BP denoiser falls within the framework of non-separable denoising functions and subsequently, that state evolution holds for the proposed AMP-BP algorithm. Leveraging the rich structure of SR-LDPC codes, this article proposes an efficient low-dimensional approximate state evolution recursion that can be used for efficient hyperparameter tuning, thus paving the way for future work on optimal code design. Finally, numerical simulations demonstrate that SR-LDPC codes outperform contemporary codes over the AWGN channel for parameters of practical interest. SR-LDPC codes are shown to be viable means for obtaining shaping gains over the AWGN channel. 

Novel sparse regression LDPC (SR-LDPC) codes exhibit excellent performance over additive white Gaussian noise (AWGN) channels in part due to their natural provision of shaping gains. Though SR-LDPC-like codes have been considered within the context of single-user error correction and massive random access, they are yet to be examined as candidates for coordinated multi-user communication scenarios. This article explores this gap in the literature and demonstrates that SR-LDPC codes, when combined with coded demixing techniques, offer a new framework for efficient non-orthogonal multiple access (NOMA) in the context of coordinated multi-user communication channels. The ensuing communication scheme is referred to as MU-SR-LDPC coding. Empirical evidence suggests that MU-SR-LDPC coding can increase the sum-rate for a fixed Eb/N0 when compared to orthogonal multiple access (OMA) techniques such as time division multiple access (TDMA) or frequency division multiple access (FDMA). Importantly, MU-SR-LDPC coding enables a pragmatic solution path for user-centric cell-free communication systems with (local) joint decoding. Results are supported by numerical simulations. 

In [1], the linked loop code (LLC) is presented as a promising code for the unsourced A-channel with erasures (UACE). The UACE is an unsourced multiple access channel in which active users’ transmitted symbols are erased with a given probability and the channel output is obtained as the union of the non-erased symbols. In this paper, we extend the UACE channel model to the unsourced B-channel with erasures (UBCE). The UBCE differs from the UACE in that the channel output is the multiset union – or bag union– of the non-erased input symbols. In other words, the UBCE preserves the symbol multiplicity of the channel output while the UACE does not. Both the UACE and UBCE find applications in modeling aspects of unsourced random access. The LLC from [1] is enhanced and shown to outperform the tree code over the UBCE. Findings are supported by numerical simulations. 

The A -channel is a noiseless multiple access channel in which users simultaneously transmit Q-ary symbols and the receiver observes the set of transmitted symbols, but not their multiplicities. An A-channel is said to be unsourced if, additionally, users' transmissions are encoded across time using a common codebook and decoding of the transmitted messages is done without regard to the identities of the active users. An interesting variant of the unsourced A -channel is the unsourced A-channel with erasures (UACE), in which transmitted symbols are erased with a given independent and identically distributed probability. In this paper, we focus on designing a code that enables a list of transmitted codewords to be recovered despite the erasures of some of the transmitted symbols. To this end, we propose the linked-loop code (LLC), which uses parity bits to link each symbol to the previous M symbols in a tail-biting manner, i.e., the first symbols of the transmission are linked to the last ones. The decoding process occurs in two phases: the first phase decodes the codewords that do not suffer from any erasures, and the second phase attempts to recover the erased symbols using the available parities. We compare the performance of the LLC over the UACE with other codes in the literature and argue for the effectiveness of the construction. Our motivation for studying the UACE comes from its relevance in machine-type communication and coded compressed sensing. 

Iterative decoding of graph-based codes and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces sparse regression LDPC codes (SR-LDPC codes) and their decoding. Sparse regression codes (SPARCs) are a class of error correcting codes that build on ideas from compressed sensing and can be decoded using AMP. In certain settings, SPARCs are known to achieve capacity; yet, their performance suffers at finite block lengths. Likewise, low-density parity-check (LDPC) codes can be decoded efficiently using belief propagation and can also be capacity achieving. This article introduces a novel concatenated coding structure that combines an LDPC outer code with a SPARC-inspired inner code. Efficient decoding for such a code can be achieved using AMP with a denoiser that performs belief propagation on the factor graph of the outer LDPC code. The proposed framework exhibits performance improvements over SPARCs and standard LDPC codes for finite block lengths and results in a steep waterfall in error performance, a phenomenon not observed in uncoded SPARCs. 

Unsourced random access emerged as a novel wireless paradigm enabling massive device connectivity on the uplink. We consider quasi-static Rayleigh fading wherein the access point has multiple receive antennas and every mobile device a single transmit antenna. The objective is to construct a coding scheme that minimizes the energy-per-bit subject to a maximum probability of error given a fixed message length and a prescribed number of channel uses. Every message is partitioned into two parts: the first determines pilot values and spreading sequences; the remaining bits are encoded using a polar code. The transmitted signal contains two distinct sections. The first features pilots and the second is composed of spread modulated symbols. The receiver has three modules: an energy detector, tasked with recovering the set of active pilot sequences; a bank of Minimum Mean Square Error (MMSE) estimators acting on measurements at the receiver; and a polar list-decoder, which seeks to retrieve the coded information bits. A successive cancellation step is applied to subtract recovered codewords, before the residual signal is fed back to the decoder. Empirical evidence suggests that an appropriate combination of these ideas can outperform state-of-the-art coding techniques when the number of active users exceeds one hundred. 

We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ∼30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing. 

Unsourced random access (URA) has emerged as a candidate paradigm for massive machine-type communication (mMTC) in next-generation wireless networks. While many excellent uplink schemes have been developed for URA, these schemes do not specify a mechanism for providing feedback regarding whether a user’s message was successfully decoded. While this may be acceptable in some mMTC scenarios, the lack of feedback is inadequate for applications that demand a high level of reliability. However, the problem of providing feedback to active users is complicated by the fact that the base station does not know the identities of the active users. In this paper, a novel downlink beamforming scheme called HashBeam is presented that enables the base station to provide feedback to the active users within URA, despite not knowing their identities. The key idea of this scheme is that the users’ channels and hashes of their messages may be used as proxies for their true identities. The proposed scheme may be adapted to any number of antennas at the base station and it is shown that the required number of channel uses is linear in the number of users to acknowledge. 

This article considers the massive MIMO unsourced random access problem on a quasi-static Rayleigh fading channel. Given a fixed message length and a prescribed number of channel uses, the objective is to construct a coding scheme that minimizes the energy-per-bit subject to a fixed probability of error. The proposed scheme differs from other state-of-the-art schemes in that it blends activity detection, single-user coding, pilot-aided and temporary decisions-aided iterative channel estimation and decoding, minimum-mean squared error (MMSE) estimation, and successive interference cancellation (SIC). We show that an appropriate combination of these ideas can substantially outperform state-of-the-art coding schemes when the number of active users is more than 100, making this the best performing scheme known for this regime.