Grant-Free Coded Random Access

• Grant-Free Coded Random Access (CRA) is a protocol that uses graph-coded redundancy and iterative SIC to recover collisions, significantly enhancing uplink throughput over traditional ALOHA schemes.
• It employs structured replica transmission with prescribed degree distributions analyzed via sparse-graph tools, enabling scalable and efficient uncoordinated access.
• Recent advancements integrate realistic massive MIMO models, pilot-domain strategies, and adaptive interference cancellation to address channel estimation errors and heterogeneous user activity.

Searching arXiv for recent and foundational papers on grant-free coded random access. Grant-free coded random access (CRA) is a class of uplink random-access protocols for massive uncoordinated access in which active devices transmit without prior scheduling or resource grants, while the receiver exploits structured redundancy across slots or resources and performs successive interference cancellation (SIC) to recover packets from collisions that legacy slotted ALOHA would discard (Paolini et al., 2014). In the classical sense, CRA is graph-coded slotted random access: active users send multiple replicas or coded packet segments according to a prescribed distribution, the base station stores all received slots, singleton observations seed iterative recovery, and the access process can be analyzed through sparse-graph tools such as density evolution, EXIT charts, and threshold analysis (Paolini et al., 2014). In the broader grant-free literature, the CRA label is also used more loosely for adjacent schemes based on pilot mixtures, signature-domain sparse recovery, covariance-based activity detection, unsourced access, or heterogeneous slot-selection adaptation; these are not all CRA in the strict IRSA/CSA sense, but they address the same core problem of scalable uncoordinated uplink access under sparse activity, imperfect receiver knowledge, and limited control signaling (Jeannerot et al., 2024).

1. Concept, scope, and analytical foundation

Classical CRA begins from the observation that the collision model underlying slotted ALOHA is unnecessarily restrictive. In slotted ALOHA and framed slotted ALOHA, only singleton slots are useful, and the classical maximum throughput is

$T_{\max} = \frac{1}{e} \approx 0.37 .$

CRA changes the decoding model by allowing the receiver to store collided slots and use them later in a transmission recovery process based on SIC, so collisions become latent information rather than waste (Paolini et al., 2014).

The canonical representation is a bipartite graph with user nodes and slot nodes. An edge connects user $i$ to slot $j$ if user $i$ transmits a replica in slot $j$. For repetition-based coded slotted ALOHA, the user-node degree is the repetition rate $d$, while the slot-node degree is the number of packets transmitted in that slot. Under idealized assumptions—slot synchronization, perfect singleton decoding, perfect slot-state discrimination, and ideal interference cancellation—the SIC process is exactly the iterative peeling decoder known from sparse-graph erasure codes (Paolini et al., 2014).

The main asymptotic control parameter is the logical load

$$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$

with $\bar N_{\mathsf a}=p_{\mathsf a}N$ the mean number of active users in a contention period of $M$ slots. With average repetition $\bar d$, the physical load is

$i$0

and the repetition-based protocol rate is

$i$1

In generalized CSA based on packet segmentation and component codes, the rate becomes

$i$2

The central asymptotic object is the threshold $i$3: if $i$4, SIC succeeds with high probability asymptotically, whereas if $i$5, a nonzero fraction remains unresolved (Paolini et al., 2014).

This coding-theoretic reformulation gives CRA its distinctive design language. Degree distributions, thresholds, and threshold upper bounds become protocol-level design objects. For fixed rate $i$6, the threshold $i$7 is upper bounded by the unique positive real solution of

$i$8

The same framework explains why CRDSA already improves asymptotic throughput to about $i$9, and why optimized CSA can approach $j$0 packet/slot in the asymptotic idealized limit (Paolini et al., 2014).

2. Protocol families and graph-coded mechanisms

The best-known CRA family is repetition-based coded slotted ALOHA, often associated with CRDSA and IRSA. Each active user chooses a repetition degree $j$1 from a prescribed distribution and places $j$2 replicas uniformly at random across the frame. Once one replica is decoded, the packet reveals the locations of its other replicas; the receiver then re-encodes and re-modulates the recovered packet and subtracts its contribution from the other slots, potentially turning collisions into new singleton slots and initiating an iterative chain reaction (Paolini et al., 2014).

High-rate CSA generalizes pure repetition. A user splits its packet into $j$3 segments, encodes them using a randomly selected linear block code, and transmits $j$4 encoded segments in randomly chosen slots. SIC still operates across slots, but each user node can also perform local erasure decoding of its component code. This extends CRA beyond repetition overhead and supports any $j$5 (Paolini et al., 2014).

Two structurally important variants are spatially coupled CSA and frameless CSA. In spatially coupled CSA, a user active in one contention period sends one replica immediately and distributes the remaining $j$6 replicas over subsequent periods. The resulting chain of coupled frames creates a wave-like SIC process, and the iterative threshold reaches the block-scheme upper-bound threshold under optimal MAP decoding on the graph. Frameless CSA removes the fixed frame length and lets users transmit on a slot-by-slot basis with slot access probabilities, while the contention period is terminated adaptively by the base station; in the version discussed in the tutorial paper, the access strategy is memoryless and uniform over users and slots, and the reported best-throughput example uses slot access probability

$j$7

For low to moderate active population sizes $j$8 in the range $j$9–$i$0, frameless CSA is reported to yield the best throughputs among the surveyed variants (Paolini et al., 2014).

These families establish the classical CRA design tradeoff. More replicas lower the protocol rate and raise physical load and user energy expenditure, but they also increase the probability that SIC can start and continue. Irregular repetition distributions are useful because they create enough singleton slots to bootstrap peeling while preserving redundancy for later iterations. This design logic remains the reference point against which later grant-free CRA variants are typically compared (Paolini et al., 2014).

A common misconception is that any grant-free random access scheme using randomized slot selection is automatically CRA. Strictly, CRA in the classical sense requires code-like redundancy across slots or segments together with iterative collision resolution. Degree-one heterogeneous slotted ALOHA, signature-based sparse access, or blind grant-free detectors may be closely related and highly relevant, but they are not graph-coded CRA unless they explicitly use repetition or coded placement plus SIC (Jeannerot et al., 2024).

3. PHY-aware grant-free CRA with massive MIMO

A major development in grant-free CRA is the move from collision-channel abstractions to realistic massive-MIMO PHY models. In these systems, each replica occupies a slot and a randomly selected orthogonal pilot, so the effective contention resource is a slot-pilot pair. The base station correlates the received pilot matrix with each pilot to obtain

$i$1

forms

$i$2

and attempts payload decoding. This departs sharply from ideal CRA because even nominal singleton resources can fail under channel estimation errors, pilot collisions, and residual cross-user terms (Valentini et al., 2022).

Two papers make this point especially sharply. The first shows that conventional squared-norm-based or channel-hardening-based subtraction is fragile because it removes only a coarse dominant term and fails to mitigate interference toward other pilots in the same slot; the proposed payload-aided subtraction estimates replica-slot channels from known payloads and subtracts the full user contribution from the raw received pilot and payload matrices. In the reported baseline with $i$3, $i$4, $i$5, BCH $i$6, and $i$7 ms, at target $i$8, the earlier subtraction method supports about $i$9 active users, whereas payload-aided subtraction supports about $j$0 (Valentini et al., 2022). The second paper extends this line and shows that payload-aided SIC plus instantaneous cancellation scheduling can raise support from about $j$1 users for the state-of-the-art SIC baseline to about $j$2 users at $j$3, while the no-SIC logical baseline is around $j$4 users under the representative setting discussed there (Valentini et al., 2023).

A complementary development is fully joint PHY/MAC analysis. Rather than optimizing CRA degree distributions on a collision channel, one can embed random orthogonal pilot selection, Rayleigh block fading, MRC-like combining, BCH decoding, and slot-dependent packet failure probabilities directly into density evolution. In that framework, the classical irregular distribution

$j$5

becomes suboptimal under realistic massive-MIMO grant-free access, while the concentrated distribution

$j$6

performs better; for $j$7 antennas and $j$8, the reported threshold is $j$9 for $d$0, versus $d$1 for the classical irregular design (Valentini et al., 2022). This is an important correction to a widespread intuition: collision-channel-optimal CRA degree distributions need not remain optimal once pilot contamination and realistic packet failure are included.

Pilot-domain enhancements also change the slot-node decoder. In pilot-mixture CRA, each packet superposes $d$2 orthogonal pilots rather than using exactly one pilot, and the receiver performs an inner SIC inside each slot before the usual outer CRA SIC across slots. In the framed system with $d$3, $d$4, and target $d$5, the no-SIC benchmark reaches only about $d$6 active users per frame, inner SIC raises this to roughly $d$7, ACK-based early stopping to about $d$8, and full nested SIC to about $d$9 (Valentini et al., 2023). Conceptually, this upgrades the slot decoder from a singleton detector into a more capable multi-packet-resolution component.

The broader significance is that modern grant-free CRA is no longer well described by graph peeling alone. The slot-node rule depends on pilot assignment, array size, channel statistics, interference subtraction quality, and sometimes intra-slot multiuser detection. As later work repeatedly shows, massive MIMO is beneficial, but only if SIC is implemented as accurate signal subtraction with realistic channel estimation rather than as an idealized peeling abstraction (Valentini et al., 2022).

4. Signature-, pilot-, and unsourced extensions

Outside the strict IRSA/CSA lineage, a broad family of grant-free access schemes shares CRA’s sparsity, collision-resolution, and SIC concerns while replacing slot-graph redundancy with signature, pilot, or tensor structure. These schemes are often adjacent to CRA rather than classical CRA, but they matter because practical grant-free systems increasingly combine both styles.

One branch is signature-domain compressive random access. In layered CRA with Gaussian spreading, each device has a unique non-orthogonal spreading sequence, active users are sparse, and power-domain NOMA creates $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$0 power layers decoded by SIC. For $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$1, $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$2, $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$3, and $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$4, the average total MD/FA count drops from $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$5 for $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$6 to $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$7 for $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$8 and $$G = \frac{\bar N_{\mathsf a}}{M} = p_{\mathsf a}\frac{N}{M},$$9 for $\bar N_{\mathsf a}=p_{\mathsf a}N$0 (Choi, 2018). Multi-sequence spreading random access replaces one fixed spreading sequence per user with an ordered set of $\bar N_{\mathsf a}=p_{\mathsf a}N$1 sequences, yielding a block-sparse MMV problem with reduced average Babel mutual coherence; in the wideband setup reported, the scheme reaches the collision lower bound up to $\bar N_{\mathsf a}=p_{\mathsf a}N$2, whereas the single-sequence baseline does so only up to $\bar N_{\mathsf a}=p_{\mathsf a}N$3, which the paper summarizes as about an $\bar N_{\mathsf a}=p_{\mathsf a}N$4 increase in supported active users or RR utilization (Abebe et al., 2021).

Another branch focuses on activity detection and blind recovery. In cell-free massive MIMO, covariance-based maximum-likelihood activity detection with pre-assigned non-orthogonal signatures and centralized CPU processing provides an activity-detection front end for grant-free access; the paper’s contribution is the ML formulation and a coordinate-descent algorithm of complexity $\bar N_{\mathsf a}=p_{\mathsf a}N$5 for the cell-free setting (Ganesan et al., 2021). In mmWave MIMO, blind grant-free random access can be formulated as a constrained composite matrix factorization

$\bar N_{\mathsf a}=p_{\mathsf a}N$6

with sparse beamspace channels and finite-alphabet data; the proposed UAMP-MF-based Bayesian receiver performs joint user activity detection, channel estimation, and signal detection without pilots (Yuan et al., 2023). These are not CRA in the graph-coded sense, but they solve the same sparse grant-free inverse problem that practical CRA receivers confront.

Unsourced random access provides a further extension. In the tensor-based and coherent modulation scheme, the message is split into an unsourced TBM part and a coherent NOMA part, with iterative FEC decoding and SIC. For equal received powers, $\bar N_{\mathsf a}=p_{\mathsf a}N$7, $\bar N_{\mathsf a}=p_{\mathsf a}N$8, and $\bar N_{\mathsf a}=p_{\mathsf a}N$9, the reported minimum $M$0 for $M$1 is $M$2 dB at $M$3 and $M$4 dB at $M$5 for the TBMC design, outperforming the original TBM baseline across the tested range (Rech et al., 2023). This suggests that the CRA design space has expanded well beyond repetition-only slotted ALOHA toward more general coded grant-free access at the PHY layer.

A useful clarification follows from the survey literature: grant-free access in cellular systems may combine orthogonal or non-orthogonal preambles, preamble hopping across a frame, repeated packet transmission, massive-MIMO spatial multiplexing, SIC, compressed sensing, and NOMA. The paper explicitly notes multi-slot repeated transmission with SIC as a coded random access mechanism, but it also shows that non-orthogonal preambles or larger signature pools are not automatically better, because cross-correlation can contaminate channel estimation and harm payload decoding (Choi et al., 2020). This is one reason practical grant-free CRA increasingly mixes graph-coded redundancy with carefully structured pilot or signature design.

5. Heterogeneity, imperfect activity knowledge, and adaptive access

A separate but increasingly important line of work concerns grant-free access under user heterogeneity and noisy receiver knowledge. In the degree-one heterogeneous frame-slotted system studied in "Exploiting Device Heterogeneity in Grant-Free Random Access: A Data-Driven Approach," each active device transmits in exactly one slot per frame, with user-specific slot-selection probabilities collected in an allocation matrix

$M$6

subject to row-simplex constraints $M$7. The throughput objective is the expected number of collision-free transmissions per frame,

$M$8

and the optimization is nonconvex (Jeannerot et al., 2024).

Although this model is not classical CRA—there is no irregular repetition, no coded segments, and no SIC graph peeling—it is highly relevant to grant-free CRA because it isolates a core design issue: receiver adaptation based on noisy activity estimates. The paper shows that replacing the true activity vector $M$9 with an erroneous estimate $\bar d$0 in stochastic gradient ascent generally produces a biased gradient. To correct this, it introduces importance weighting,

$\bar d$1

yielding the projected update

$\bar d$2

Under Robbins–Monro step-size conditions and finite weights, the corrected method converges almost surely to a stationary point of the true throughput objective (Jeannerot et al., 2024).

The practical findings are also explicit. In moderate-size systems with $\bar d$3 users and $\bar d$4 slots, simulations over $\bar d$5 frames with 20 repetitions show gains up to $\bar d$6, $\bar d$7, and $\bar d$8 under symmetric bit flipping, asymmetric miss-detection, and GAMP-induced activity-estimation errors, respectively, relative to the error-unaware heterogeneous-allocation method (Jeannerot et al., 2024). The important transfer to CRA is not the degree-one access model itself, but the methodological lesson: in grant-free access, activity-estimation errors do not merely reduce detection performance; they can also bias the adaptation law used to optimize slot distributions, repetition probabilities, or other access parameters. A plausible implication is that SIC-aware CRA optimization under noisy user-state information should incorporate analogous uncertainty corrections rather than treating detected activity as ground truth.

This line of work also sharpens a broader misconception. Heterogeneity in user activity is not a nuisance to be averaged away; it is exploitable structure. Device-specific or class-specific access probabilities can outperform uniform allocation, but only if the receiver accounts for the fact that practical grant-free activity detectors—whether pilot-based, AMP/GAMP-based, or data-aided—are imperfect (Jeannerot et al., 2024).

6. Emerging channel regimes, implementation limits, and research directions

Two recent directions illustrate how grant-free CRA is being reworked for channel regimes that classical slotted ALOHA analyses did not anticipate. The first is doubly selective high-mobility channels. In Zak-OTFS-based CRA, users still send $\bar d$9 packet replicas in randomly selected slots and the base station performs SIC, but modulation is carried out in the delay-Doppler domain. The key advantage is that the effective DD-domain channel is predictable across slots, enabling reliable cross-slot replica reconstruction and cancellation in regimes where OFDM-based CRA suffers from unreliable inter-slot channel prediction. In the reported frame-level simulation with $i$00, $i$01, $i$02, $i$03 kHz, SNR $i$04 dB, and $i$05, the Gaussian-pulse Zak-OTFS design supports approximately $i$06 active users while maintaining $i$07 (Mirri et al., 29 Jul 2025).

The second is the near-field regime of extremely large arrays. Coded spatial random access extends repetition-based grant-free CRA so that replicas are sent over different near-field spatial directions rather than only across time/frequency slots. The access point uses energy detection across antenna elements, clusters contiguous illuminated regions for each pilot, combines within clusters by MRC, decodes locally, and then applies SIC over all affected array elements. In the 60 GHz factory-line setting with a 20 m ELAA, $i$08, $i$09 mW, BCH $i$10, QPSK, and packet length $i$11 symbols, the paper reports, for example, that at $i$12 active users and $i$13 replicas, PLR drops from about $i$14 without SIC to about $i$15 with SIC (Testi et al., 21 Aug 2025). This suggests that in the near field, the notion of a CRA resource node can be extended from a slot to a pilot-labeled spatial cluster.

These new regimes do not remove long-standing limitations. The classical tutorial itself assumes perfect slot-state discrimination, error-free singleton decoding, ideal channel estimation, and ideal SIC (Paolini et al., 2014). Later practical work adds pilot collisions, realistic payload decoding, imperfect subtraction, and detector errors, but many issues remain open: explicit density evolution for nested inner/outer SIC architectures, scalable class-based or cluster-based heterogeneity models, correlated rather than independent user activity, finite-length error floors under realistic PHY, and robust operation under synchronization errors, power imbalance, or deployment constraints (Valentini et al., 2022). A plausible implication is that future grant-free CRA will increasingly be a joint PHY/MAC design problem in which waveform choice, pilot structure, array processing, activity inference, and replica/coding policies are optimized together rather than in isolation.

Grant-free CRA therefore denotes both a mature coding-theoretic paradigm and an active research frontier. In its classical form, it is the graph-coded redesign of random access around SIC, sparse-graph analysis, and redundancy over slots. In its contemporary form, it also encompasses PHY-aware slot decoding, pilot-domain diversity, signature-domain sparse recovery, uncertainty-aware adaptation, and new propagation regimes such as near field and delay-Doppler modulation. Across these variants, the defining principle remains stable: collisions are not treated as terminal failures, but as structured observations that can be exploited by receiver-side iteration and carefully designed grant-free redundancy (Paolini et al., 2014).