Decentralized Decoding Architecture

• Decentralized Decoding Architecture is a distributed system where local nodes perform decoding, reducing communication bottlenecks and enabling scalable processing.
• It employs recursive algorithms such as RLS and SGD to incrementally refine estimates from local observations, achieving near-optimal detection with lower latency.
• The modular design enhances system robustness and efficiency in diverse applications like Massive MIMO, quantum error correction, and industrial control.

A decentralized decoding architecture denotes a system-level approach in which the detection or decoding functions are distributed among multiple spatially separated nodes, rather than consolidated in a single central processor. This paradigm is motivated by bottlenecks in inter-node communication, scalability needs for large-dimensional systems (such as Massive MIMO base stations or distributed sensor networks), and process modularity for efficient resource allocation. The underlying principle is to enable nodes or clusters within the system to locally process their observations and exchange compact intermediate estimates, thereby limiting the transfer of high-throughput raw data and supporting optimal or near-optimal detection/decoding by consensus or recursion.

1. Architectural Design and Data Flow

Decentralized decoding architectures are characterized by their network topology, local processing protocol, and communication pattern. Notable instantiations include the daisy-chain model for Massive MIMO (Sanchez et al., 2018, Sanchez et al., 2019), tree-grid networks for quantum error correction (Liyanage et al., 16 Apr 2025), and two-layer control hierarchies for cyber-physical energy systems (Navidi et al., 2018).

In Massive MIMO applications, antenna clusters are equipped with RF and baseband front-ends, channel estimation, and a detection block. Clusters operate sequentially: each receives an intermediate estimate (a vector of dimension K, the number of users), updates it using its own local CSI and received sample, then forwards the refined estimate. This contrasts with centralized architectures where raw signals and full CSI (scaling with the antenna array size M) are routed to a central node, resulting in throughput bottlenecks and increased latency.

In quantum error correction, decentralized FPGA nodes are arranged in a grid, localizing syndrome/boundary exchanges, with a superimposed tree backbone that minimizes worst-case inter-node latency to $O(\log(n))$ for $n$ nodes (Liyanage et al., 16 Apr 2025). In distributed control, local controllers perform fast, fine-grained optimization steps using local states and sporadic global updates, facilitating privacy and robustness in power and industrial networks (Navidi et al., 2018).

2. Recursive and Local Algorithms for Decoding

The recursive local update formula is foundational in decentralized Massive MIMO. The generic recursion:

$\hat{s}_n = f(\hat{s}_{n-1}, h_n, y_n)$

permits each node (antenna or cluster) to incrementally fuse local observations with a compact intermediate estimate.

Recursive Least Squares (RLS):

• At each node $n$, compute the prediction error ($\epsilon_n = y_n - h_n^T \hat{s}_{n-1}$).
• Update an auxiliary matrix $\Gamma_n$, standing for the inverse Gramian, via:

$$\Gamma_n = \Gamma_{n-1} - \frac{\Gamma_{n-1} h_n^* h_n^T \Gamma_{n-1}}{1 + h_n^T \Gamma_{n-1} h_n^*}$$

• Refine the estimate:

$$\hat{s}_n = \hat{s}_{n-1} + \Gamma_n h_n^* \epsilon_n$$

As $n$ grows, $\hat{s}_M$ converges to the ZF solution.

Stochastic Gradient Descent (SGD) and Averaged SGD (ASGD):

• SGD update: $\hat{s}_n = \hat{s}_{n-1} + \mu_n h_n^* \epsilon_n$
• ASGD: An initial SGD phase is followed by averaging iterates beyond some $n_0$ for robust performance.

In ensemble hybrid decoding (Raviv et al., 2020), the codeword space is partitioned (e.g., by Hamming distance or syndromes), and each partition is mapped to a specialized expert, with a hard-decision decoder gating the selection. Only one expert processes any observation, preserving computational simplicity.

3. Communication Efficiency and Scalability

A central tenet is reduction of inter-node communication load. Rather than transmitting full-size received signals or CSI matrices, only K-dimensional estimates (or syndrome summaries) are exchanged. For Massive MIMO systems, this approach achieves data-rate reductions by a factor of $M/K$, directly supporting systems with hundreds or thousands of antennas (Sanchez et al., 2018).

The daisy-chain and grid/tree architectures are inherently scalable. Modules (antenna clusters or FPGAs) can be added or removed without redesigning the interconnection structure. In quantum decoding, resource growth is $O(l \log l)$ for $l$ logical qubits, while latency increases only $O(\log l)$ (Liyanage et al., 16 Apr 2025). For Massive MIMO, architecture modularity prevents CPU or midhaul bottlenecks as node count expands (Khan et al., 20 Oct 2025).

4. Performance, Numerical Results, and Challenges

Numerical results indicate:

• Asymptotic convergence to centralized optimal solutions (ZF) for RLS and properly tuned SGD/ASGD algorithms.
• Frame Error Rate (FER) gains up to $0.4$ dB in the waterfall region, and $1.25$ dB in the error floor region for BCH codes with deep ensemble decoding (Raviv et al., 2020).
• Spectral efficiency improvements of $5$–$10\%$ and user fairness gains of up to $45\%$ over conventional methods in distributed Massive MIMO (Khan et al., 20 Oct 2025).
• DECONET prototype achieves sub-microsecond average decoding latency for real-time quantum error correction, maintaining zero backlog across logical qubit scaling (Liyanage et al., 16 Apr 2025).

Challenges remain in robust parameter tuning (SGD step-size, initial values), synchronization, and error propagation. In hierarchical and split processing (e.g., Hades (Zhu et al., 2 Feb 2025)), latency-critical decoding must be reliably separated from delay-tolerant tasks, with dynamic scheduler policies (Earliest Deadline First, threshold-based triggers) to maintain QoS across edge and remote clouds.

5. Generalization to Cross-Domain Architectures

Decentralized decoding principles extend beyond radio and error-correction settings. For ensemble/hybrid decoders, partitioning complex decoding into expert domains (per error class or syndrome) maps well to large-scale machine learning, NLP, or cyber-physical control scenarios. In distributed control, two-layer (global+local) strategies balance cost and power quality, with local MPCs optimizing based on intermittently received bounds and profiles (Navidi et al., 2018).

Grid-based collective communication procedures such as all-to-all encode (Wang et al., 27 Aug 2024) serve as universal primitives for distributed encoding/decoding, enabling modular scheduling and inversion in both coding and computation offloading.

6. Practical Applications and Implications

Decentralized decoding architectures are directly relevant to:

• Cellular radio/edge vRAN (elastic workload and FEC decoding assignment across edge/remote clouds) (Zhu et al., 2 Feb 2025).
• Quantum error correction for scalable logical qubit systems requiring lattice surgery operations and dynamic decoder graph reconfiguration (Liyanage et al., 16 Apr 2025).
• Collaborative edge-device inference in LLMs via speculative decoding and distributed split-verification, with measured gains in throughput and communication latency (Ning et al., 16 Jul 2025).
• Energy, control, and industrial automation scenarios needing privacy, data ownership, and resilience against buffering delays (Navidi et al., 2018).

These approaches shift the computational and coordination load away from central bottlenecks, distribute adaptivity and intelligence, and support rapid, robust scaling with minimal performance trade-offs. However, practical deployment demands careful engineering of inter-node scheduling, pipeline synchronization, parameter control, and error-handling mechanisms.

7. Mathematical Frameworks and Key Formulas

Core mathematical expressions unified across architectures include:

• Recursive local update: $\hat{s}_n = f(\hat{s}_{n-1}, h_n, y_n)$
• RLS recursion (see Section 2).
• SGD/ASGD update rules.
• Ensemble expert gating:

$$\mathcal{G}(\ell)_j = 1 \text{ if } \hat{e} \in \mathcal{X}^{(j)}$$

• Collective communication cost: $C = \alpha \cdot C_1 + (\beta \log_2 q) \cdot C_2$
• Grid/tree scaling: resource $O(n \log n)$; latency $O(\log n)$.

These formal structures distinguish decentralized architectures from classic centralized models, underpinning their efficiency, scalability, and modularity in advanced large-scale systems.