Parallel Viterbi Decoders

• Parallel Viterbi decoders are architectures that exploit concurrent execution of add–compare–select operations across trellis graphs for rapid maximum-likelihood sequence estimation.
• They employ methods like fully parallel ACS on FPGAs, group-based state partitioning on GPUs, and custom instruction sets to optimize throughput and energy efficiency.
• Performance evaluations show high throughput improvements and reduced power consumption, making them ideal for wireless communication, speech recognition, and edge applications.

Parallel Viterbi decoders are algorithmic and hardware architectures that exploit concurrency to accelerate maximum-likelihood sequence estimation across trellis graphs, supporting high-throughput, low-latency communications and sequence inference tasks in domains such as wireless systems, speech recognition, and embedded applications. The essential principle is to execute independent computations—over states, branches, or candidate paths—in parallel, leveraging platform capabilities ranging from FPGAs and GPUs to dedicated processor or quantum hardware. Architectural patterns, trade-offs, and performance metrics vary significantly depending on parallelization granularity, memory organization, and target deployment.

1. Architectural Principles of Parallel Viterbi Decoding

Parallel Viterbi decoders depart from the inherently sequential structure of the original dynamic programming algorithm by mapping the add–compare–select (ACS) and survivor path computations onto parallel hardware resources.

• Fully parallel ACS implementation: On FPGAs, such as Xilinx Virtex-II Pro, a massively parallel architecture may dedicate an ACS circuit to every trellis state, enabling simultaneous processing for all state updates within a decoding stage (Shaker et al., 2010). Integration of branch metric computation (BMC) with ACS in unified modular blocks for each trellis "wing" facilitates further concurrency.
• Group-based state partitioning: GPUs exploit fine- and coarse-grained parallelism by grouping trellis states (for instance, by common α values in butterfly structures) and mapping these groups to virtual processors (VPs) that process forward ACS operations simultaneously (Peng et al., 2016). For each trellis stage, group-based computation radically reduces the number of branch metrics required by exploiting generator polynomial properties.
• Custom instruction parallelization: Acceleration on RISC, stack, and soft-core FPGA processors is achieved by implementing custom ISA instructions (e.g., Texpand) that encapsulate the ACS primitive in hardware (Ahmad et al., 2018). These can be instantiated as parallel units within an FPGA fabric or pipeline.
• Beam search and list-based parallelization: Extensions such as the parallel list Viterbi algorithm (PLVA) maintain L candidate paths (list size)—rather than a singleton survivor per state—advancing multiple likely sequences in parallel (Rowshan et al., 2020, Kanaan et al., 3 Mar 2025).
• Quantum-classical integration: Mapping trellis search to quantum circuit evaluation (via the Quantum Approximation Optimization Algorithm) enables quantum parallelism over the entire codeword/path space (Bhattacharyya et al., 2023).

2. Kernel Partitioning, Memory Organization, and Data Flow

Efficient parallel execution demands careful mapping between computation and memory organization.

• GPU kernel decomposition: Block-based Viterbi decoders divide the input stream into parallel blocks handling truncated/decode/traceback operations. Two distinct CUDA kernels (K1 for forward ACS, K2 for trace-back) allow optimal scheduling and resource utilization, though forward path computation is more parallelizable than the inherently sequential traceback (Peng et al., 2016, Mohammadidoost et al., 2020).
• Shared vs. global memory: Unified kernel designs on GPUs merge forward and backward passes, storing survivor paths in shared memory with per-block tiling and bank-conflict avoidance, obviating the latency and bandwidth costs of global memory (Mohammadidoost et al., 2020). Survivor paths and metrics may be bit-packed and bank-aligned for coalesced accesses.
• Tensor core utilization: Matrix multiplications for branch metric and path metric computations are "reshaped" into tensor core operations by mapping butterfly/dragonfly structures in the trellis to matrix blocks (using FP16/FP32 formats as appropriate) (Mohammadidoost et al., 2020). Matrix dimensions are chosen to saturate tensor cores and minimize data redundancy.
• FPGA double buffering and task queues: Hardware accelerator architectures rely on non-recursive task scheduling, FIFO-based subtask queues, and double-buffered memory for intermediate state transfer, supporting hardware-friendly resource allocation and parallel subtask execution (Deng et al., 22 Oct 2025).

Platform	Kernel/Task Partition	Memory Optimization
FPGA	Per-state ACS blocks	Local registers, clock gating
GPU	Grouped VPs, kernels	Shared/global memory, bit packing
FPGA/CPU	Custom instructions	Microcode/microarchitecture
Quantum	Parallel quantum gates	Superposition, shot-based eval

3. Performance Metrics and Comparative Results

Performance benchmarks are crucial for evaluating parallel Viterbi decoders. Key metrics include throughput (Mbps/Gbps), power consumption, memory usage, and error correction quality (e.g., BER, PER, FER).

• Throughput improvements: Massively parallel FPGA designs achieved clock rates of up to 47.4 MHz with power consumption as low as 0.065 W (Shaker et al., 2010). GPU implementations reached 598 Mbps (GTX580) and 1802 Mbps (GTX980) for 64-state codes (Peng et al., 2016); Tensor-core mapped versions achieved up to 22.2 Gb/s (Tesla V100) (Mohammadidoost et al., 2020). Unified kernel approaches further improved throughput and memory efficiency, surpassing previous GPU implementations (Mohammadidoost et al., 2020).
• Energy and power efficiency: Power savings are realized through trace-back methods with clock gating, reduced switching activity in storage blocks, and, for input-distribution-aware decoders, dynamic path count adaptation based on input statistics, achieving up to 17% complexity reduction (Condo et al., 2021).
• Error correction performance: List-decoding variants (LVA/PLVA) enhanced FER/PER compared to classical single-survivor VAs, especially in noisy or collision-prone environments—e.g., a ~3 dB PER gain for satellite AIS with PLVA (P=16) over conventional VA (Kanaan et al., 3 Mar 2025). PAC concatenation improved minimum Hamming distance (Rowshan et al., 2020).
• Speedups in WFST/Speech: GPU-parallel WFST Viterbi decoding in ASR achieved 240× speedup vs CPU and 40× vs previous GPU decoders, supporting large-scale graph inference with bounded memory footprints (Braun et al., 2019).

4. Algorithmic Variants and Dynamic Adaptivity

Parallel Viterbi decoders are highly configurable for diverse channels, code rates, and application constraints.

• Reconfigurability: FPGA VHDL-based decoders support dynamic adaptation to constraint lengths, code rates, and coding schemes, enabling migration between standards and optimization for SDR scenarios (Shaker et al., 2010).
• Input-distribution-aware parallelism: IDA schemes dynamically determine the parallel processing degree by sampling input LLR distribution and applying rules such as

$$P_{used} = \begin{cases} P_{low}, & \text{if } |\tilde{y}_{P_{high}-1}| > \gamma_M \ P_{high}, & \text{otherwise} \end{cases}$$

thereby trading off complexity and latency against error performance (Condo et al., 2021).

• Divide-and-conquer, beam search, and pruning: FLASH Viterbi leverages a non-recursive segmentation with optimality-based pruning at division points, enabling parallel task execution, memory decoupling, and dynamic parameter tuning (parallelism degree $P$, beam width $B$) (Deng et al., 22 Oct 2025). FLASH-BS Viterbi further reduces space complexity by maintaining top-$B$ paths.

5. Practical Applications Across Domains

Parallel Viterbi decoders underpin high-performance communications and data inference.

• Wireless base stations and SDR: Massively parallel FPGA designs and GPU kernels support real-time, high-throughput convolutional code decoding for standards such as WiMAX, LTE, DVB-T/S, and 5G (Shaker et al., 2010, Mohammadidoost et al., 2020).
• AIS satellite detection: PLVA with CRC post-processing enhances packet recovery amid collisions, reducing PER, enabling improved interference cancellation, and increasing throughput under high system loads (Kanaan et al., 3 Mar 2025).
• Speech and structured inference: GPU-parallel WFST Viterbi enables batched/streaming ASR with LLM graphs, scalability to low-power edge and server platforms (Braun et al., 2019).
• Trajectory, recommendation, and edge analytics: FLASH Viterbi FPGA accelerators and software variants operate efficiently under memory and compute constraints, delivering high throughput for modern data systems (Deng et al., 22 Oct 2025).
• Quantum/hybrid decoding: QAOA-based decoders provide a framework for implicit parallel exploration of trellis paths, supporting codeword inference via energy minimization (Bhattacharyya et al., 2023).

6. Trade-offs, Limitations, and Future Directions

Parallel Viterbi decoding raises challenges in hardware resource management, error performance, and adaptability.

• Resource trade-offs: Full parallel ACS instantiation requires high hardware area; shared memory strategies on GPUs are limited by chip architecture. List-based decoding increases memory with list size $L/P$, necessitating careful parameter tuning.
• Complexity vs. error performance: Adaptive reduction in parallel effort via IDA achieves complexity savings with minimal degradation in error correction, but threshold tuning and integration into sequential trellis architectures require careful design (Condo et al., 2021).
• Beam search and pruning risks: Aggressive candidate pruning (as in FLASH Viterbi) may risk loss of diversity if optimal transitions are incorrectly detected, affecting robustness in uncertain environments—a tuning point for edge deployments (Deng et al., 22 Oct 2025).
• Platform-dependent efficiency: Custom instruction sets are effective on programmable hardware but require chip synthesis and ISA support; Tensor core mappings leverage specific GPU matrix sizes, with precision trade-offs affecting accuracy (Mohammadidoost et al., 2020).
• Quantum circuit depth and optimization: QAOA-based hybrid decoders depend on circuit depth and uniform parameter selection for efficiency; barren plateau avoidance is a key design issue for practical deployment (Bhattacharyya et al., 2023).

A plausible implication is that future parallel Viterbi decoders will continue to integrate adaptive, resource-aware scheduling, efficient memory layouts, and hybrid digital/quantum algorithms, dynamically tuning parallelism and error correction trade-offs for emerging wireless, inference, and edge computing domains. The growing set of FPGA/GPU accelerators, input-distribution-aware controllers, and list- or beam-search strategies suggests increasing adaptability and efficiency, but requires rigorous benchmarking across realistic workload and deployment scenarios.