bch decoder implementation

This work addresses the challenge of achieving high-throughput, low-latency hardware implementations of BCH decoders that simultaneously support flexible error-correction capabilities and arbitrary code lengths. The authors propose two novel architectures: a conventional decoder based on the Berlekamp–Massey algorithm and Chien search, which accommodates any error-correction capability and code length, and a pioneering direct decoder that efficiently computes the roots of the error-locator polynomial, supporting up to t = 4 errors. Both architectures are optimized for Xilinx Ultrascale+ FPGAs and 16 nm FinFET technology. In 16 nm implementation, the (256,239) and (256,223) codes achieve single-cycle decoding with throughputs of 239 Gb/s and 223 Gb/s, respectively, and latencies of only 2–8 ns, substantially improving area efficiency and throughput performance.

BCH short-code decoding suffers from high undetected error rates, slow iterative convergence, and rigid algebraic structure limiting performance. Method: This paper proposes a low-complexity, high-robustness belief propagation (BP) decoding framework. Its core innovations are: (1) a heuristic sparsification method—binary summation combined with cyclic shifts—to construct a low-density, quasi-regular parity-check matrix with few short cycles; and the first systematic quantification of the relationship among frame error rate, dual-code minimum-weight codeword rank deficiency, and row redundancy; (2) integration of three types of random automorphism injections and iterative message aggregation to enhance error-pattern diversity and suppress undetected errors. Results: At comparable throughput, the proposed decoder achieves 1–2 dB BER gain over parallel algebraic decoders, reduces average iteration count by two orders of magnitude, and significantly improves decoding reliability and real-time performance for short BCH codes.

This work addresses the inefficiency in test pattern set design for soft-input decoding of high-rate BCH codes by proposing a novel algorithm based on high-probability error pattern coverage. Leveraging order statistics, probabilistic modeling of the coverage space, and Monte Carlo simulations, the study systematically evaluates the performance of both structured and unstructured test pattern sets and constructs an optimized set accordingly. Implemented within a Chase-II decoding framework, the proposed method significantly enhances decoding performance, achieving up to a 0.2 dB gain over conventional approaches for high-rate BCH codes, thereby demonstrating its effectiveness and superiority.

This work addresses the challenge of accurately modeling the decoding failure probability of binary BCH codes under joint error-erasure decoding—a long-standing open problem. Method: Leveraging algebraic coding theory and exact probabilistic analysis, we derive closed-form expressions for the decoding failure probability under multiple decoding strategies, including standard bounded-distance decoding and its error-erasure variants—thereby overcoming the conservatism inherent in conventional Hamming-bound-based performance evaluation. Contribution/Results: The theoretical expressions are rigorously validated via numerical simulations, exhibiting negligible error. Furthermore, we apply the framework to analyze concatenated coding systems, achieving significantly improved accuracy in end-to-end bit-error-rate prediction. To the best of our knowledge, this is the first analytically tractable, high-precision performance evaluation tool for BCH codes operating under mixed channel impairments (errors and erasures), enabling reliable code design and optimization in practical communication scenarios.

In fault-tolerant quantum computing (FTQC), classical decoders for quantum error correction (QEC) face severe resource demand fluctuations—peak loads can exceed idle-period requirements by several orders of magnitude—rendering static hardware allocation inefficient (causing underutilization or real-time violations). Method: We propose the first workload-aware decoder virtualization framework and latency-aware dynamic scheduling strategy, enabling elastic, on-demand allocation of hardware decoder resources. Our approach integrates fine-grained syndrome processing modeling, reusable customized decoder designs, and cross-logical-qubit task coordination. Contribution/Results: Evaluated at the 100–1,000 logical qubit scale, our method reduces hardware decoder resource requirements by 10× while strictly guaranteeing real-time decoding latency and fault-tolerance reliability. This breakthrough overcomes a critical scalability bottleneck in the classical processing layer of QEC, providing essential infrastructure for practical FTQC deployment.

This work addresses the high decoding complexity and suboptimal performance of conventional belief propagation (BP) decoding for BCH codes compared to LDPC codes. The authors propose a quasi-BP decoding framework that integrates code automorphism structures with an optimized redundant parity-check matrix and, for the first time, embeds a lightweight convolutional neural network into check nodes to replace the computationally intensive tanh and inverse-tanh operations. A triple-constraint loss function is designed to enforce non-negativity and order consistency in the outputs, enabling seamless concatenation with ordered statistics decoding. Experiments on three BCH codes demonstrate that the proposed method achieves performance within approximately 0.25 dB of the maximum-likelihood bound—comparable to LDPC codes of similar blocklength—while the neural-network-based variant incurs negligible performance loss, supporting efficient hardware implementation.

This work addresses the high computational complexity of Chase decoding for BCH codes by proposing a low-complexity Ordered Reliability Bits Chase (ORB-Chase) decoding algorithm. The method replaces conventional reliability metrics with logically weighted test error patterns and incorporates an integer-based early termination criterion to eliminate redundant computations. Integrated within the Chase framework and leveraging the Berlekamp–Massey decoder, the proposed algorithm achieves near-maximum-likelihood performance on both (127,113,5) BCH and (256,239,6) eBCH codes while reducing the number of Berlekamp–Massey decoder invocations by up to 98.1%, thereby significantly enhancing decoding efficiency.

This work addresses the challenge of elevating bit-level capacity-achieving coding schemes to block-level reliability. It proposes a product code construction that combines low-error-probability row codes with high-rate column codes: the channel output is first cleaned via row decoding, and the remaining sparse errors are then corrected using column codes. Through rigorous theoretical analysis employing bounded-distance decoding, binomial large-deviation estimates, and union bound techniques, the paper establishes—for the first time—that block error probability can be driven to zero while achieving the capacity of any fixed binary memoryless symmetric (BMS) channel. The proposed family of RM–BCH product codes provides a concrete and practical instantiation of this approach.

Fault-tolerant quantum computing demands real-time surface code decoders with low latency and high throughput to bridge the gap between room-temperature control systems and cryogenic hardware. This work presents the first implementation and validation of the Snowflake streaming decoder on a commercial FPGA under cryogenic conditions, demonstrating its practical feasibility. The authors introduce a locality-aware 2D sliced parallel architecture to enable scalable deployment across large code distances and integrate a lightweight confidence scoring mechanism with near-zero overhead. Experimental results show that the design achieves high-throughput decoding at small code distances, with extrapolated performance sufficient for larger distances. Critically, the added latency and resource consumption from the confidence scoring module are negligible, preserving the decoder’s efficiency while providing valuable reliability metrics.