SPARCs and AMP for Unsourced Random Access

Abstract

This paper studies the optimal achievable performance of compressed sensing based unsourced random-access communication over the real AWGN channel. "Unsourced" means, that every user employs the same codebook. This paradigm, recently introduced by Polyanskiy, is a natural consequence of a very large number of potential users of which only a finite number is active in each time slot. The idea behind compressed sensing based schemes is that each user encodes his message into a sparse binary vector and compresses it into a real or complex valued vector using a random linear mapping. When each user employs the same matrix this creates an effective binary inner multiple-access channel. To reduce the complexity to an acceptable level the messages have to be split into blocks. An outer code is used to assign the symbols to individual messages. This division into sparse blocks is analogous to the construction of sparse regression codes (SPARCs), a novel type of channel codes, and we can use concepts from SPARCs to design efficient random-access codes. We analyze the asymptotically optimal performance of the inner code using the recently rigorized replica symmetric formula for the free energy which is achievable with the approximate message passing (AMP) decoder with spatial coupling. An upper bound on the achievable rates of the outer code is derived by classical Shannon theory. Together this establishes a framework to analyse the trade-off between SNR, complexity and achievable rates in the asymptotic infinite blocklength limit. Finite blocklength simulations show that the combination of AMP decoding, with suitable approximations, together with an outer code recently proposed by Amalladinne et. al. outperforms state of the art methods in terms of required energy-per-bit at lower decoding complexity.

Massive Access for Future Wireless Communication Systems

“…Polyanskiys framework has attracted a wide research interest from different aspects recently. For AWGN channel, Calderbank et al [29], Fengler et al [30], and Pradhan [31] use binary chirp code, sparse regression code, and short blocklength LDPC code as inter code in Figure 5 [34]. It is revealed in [34] that by leveraging the inherent randomization introduced by the channel, it is more easily to approach the optimal performance via a practical coding scheme.…”

“…It is revealed in [34] that by leveraging the inherent randomization introduced by the channel, it is more easily to approach the optimal performance via a practical coding scheme. Figure 6 plots the E b /N 0 required by Ordentlich-Polyanskiy scheme, sparse regression code scheme [30], CS-based coding scheme [31], and relevant benchmarks for k = 100 bits per user, n = 30000 channel uses, P e = 0.05 error probability, and different number of active users K a . We observe from Figure 6 that the TIN scheme and the traditional ALOHA scheme result in very poor energy efficiency in the massive access regime whereas Odentlich-Polyanskiy scheme is still effective when K a = 300.…”

Grant-Free Massive Random Access With a Massive MIMO Receiver

“…By choosing the thresholds, we can balance between missed detections and false alarms. Furthermore, we may consider the use of a non-uniform decaying power allocation across the slots as described in [9]. For the simulations in Figure 1 we choose B = 96 bits as payload size for each user, a frame of choose S = 32 slots of L = 100 dimensions per slot, yielding an overall block length n = 3200.…”

Sparse Regression Codes

“…SPARC-based coding schemes have recently been used for unsourced random access communication over the AWGN channel [44]. Since SPARCs are built on the principle of superposition coding, we expect that they will be promising candidates for new variants of multiple-access or broadcast communication involving a large number of nodes.…”