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Huazi Zhang

Publications and source records attributed to Huazi Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Construction and Design of MPAC Codes

This paper proposes modified polarization-adjusted convolutional (MPAC) codes and their hybrid decoding that achieves an improved performance-complexity tradeoff. For MPAC codes, only a subset of the information bits undergo the convolutional transform. The output is then combined with the remaining information bits for the inner polar transform. Correspondingly, the convolutionally transformed bits are recovered by Fano decoding, while the remaining information bits are recovered by the successive cancellation (SC) decoding, constituting the hybrid Fano-successive cancellation (HFSC) decoding. The MPAC codes are further designed by the coset-wise analysis that characterizes the number of minimum weight codewords (MWCs). It is discovered that a partially convolutional transform can improve the codeword through utilizing the row combinations of the frozen set efficiently. This property enables the MPAC codes to outperform their prototype polarization-adjusted convolutional (PAC) codes and cyclic redundancy check (CRC)-polar codes. Furthermore, MPAC codes can be optimized by reducing the number of MWCs. Our numerical results demonstrate that, with a similar decoding complexity budget, the MPAC codes offer competent decoding performance when compared with PAC codes using Fano decoding and CRC-polar codes using SC list (SCL) decoding.

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arXiv2026

GII-Polar Codes for Block Fading Channels

Polar codes are proven to be capacity-achieving codes, being gradually practiced in wireless communications. However, their successive cancellation (SC) and successive cancellation list (SCL) decoding incur latency challenge especially for long codes. This paper proposes the generalized integrated interleaved (GII)-polar codes for block Rayleigh fading channels, yielding both reduced decoding latency and competent decoding performance. Under the GII paradigm, two consecutive polar codewords of length $N$ are virtually coupled through a nested codebook which has a lower dimension, capable of correcting more errors. The component polar codes are known as interleaves of a GII-polar code. If decoding of an interleave fails, it can be projected into the decoding of the nested one, enabling richer error patterns to be corrected by each interleave. Since decoding of the interleaves can be performed in parallel, GII-polar codes yield a reduced decoding latency over a single polar code of length $2N$. Our simulation results validate both the decoding latency and performance merits of the proposed coding scheme under block Rayleigh fading channel.

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arXiv2026

A Path-Survival Analytical Framework for SCL Decoding of Polar Codes

A theoretical analysis of CRC-aided successive cancellation list (CA-SCL) decoding for polar codes remains an open problem, despite its widespread practical adoption. While low-density parity-check (LDPC) codes benefit from mature analytical tools, such as density evolution (DE), for predicting the performance of belief-propagation (BP) decoding, similar techniques are not directly applicable to CA-SCL decoding. This limitation stems from the complex path-pruning mechanism inherent in CA-SCL decoding. In this paper, we propose an analytical framework based on a novel path-survival model that captures the evolution of the correct path's rank during decoding. The proposed framework enables efficient prediction of CA-SCL decoding performance without requiring exhaustive list-specific Monte Carlo simulations. Extensive numerical evaluations demonstrate its effectiveness across a wide range of code lengths, code rates, list sizes, and channel models.

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arXiv2026

Beyond 1$\to$N Decoding: Capacity-Aware Rateless Polar Codes for IR-HARQ

This paper introduces a novel framework for polar codes, designed for flexible Incremental Redundancy Hybrid Automatic Repeat Request (IR-HARQ). By generalizing the decoding order beyond the standard 1$\to$N sequence, we enable a capacity-aware scheduling strategy that prioritizes the decoding of reliable subblocks. The framework integrates nested parity-check polar construction and reverse bit-mapping to support continuous and arbitrary transmission lengths $E \in [N_{\min}, N_{\max}]$. Simulation results show that the proposed rateless codes match the coding gain of independently optimized fixed-rate codes across the entire range of rates and lengths. With a validated hardware implementation, this work provides a practical solution for next-generation wireless data channels.

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arXiv2025

Stitched Polar Codes

In this paper, we introduce stitched polar codes, a novel generalization of Arıkan's regular polar codes. Our core methodology reconfigures the fundamental polarization process by stitching additional structures to enhance the reliability of less reliable information bits in the original code. This approach preserves the polar transformation structure and maintains the same encoding and decoding complexity. Thanks to the flexible configuration, stitched polar codes consistently outperform regular polar codes, effectively solving the performance degradation issue in rate-matched scenarios. Furthermore, we provide theoretical analysis on the weight spectrum and the polarization speed of stitched polar codes to prove their superiority.

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arXiv2025

On the Performance of Low-complexity Decoders of LDPC Codes

Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of the fundamental limits in the above-mentioned scenarios. This study aims to explore the performance of LDPC codes under belief propagation (BP) decoding with complexity constraints. In other words, for a small number of iterations, we present a closed-form lower bound on the bit error rate (BER) of LDPC codes as a function of complexity. Specifically, for the regular LDPC code ensembles, the dominant term in the order of the lower bound we provide matches that of the upper bound given by Lentmaier. Furthermore, for irregular LDPC code ensembles, in addition to adopting the approach used for regular codes, we also propose a method to iteratively obtain the lower bound on the average BER.

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arXiv2025

On the Weight Spectrum of Rate-Compatible Polar Codes

The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes remains elusive. In this paper, we address this gap by presenting the theoretical results for enumerating the number of minimum-weight codewords for quasi-uniform punctured, Wang-Liu shortened, and bit-reversal shortened decreasing polar codes. Additionally, we propose efficient algorithms for computing the average spectrum of random upper-triangular pre-transformed shortened and punctured polar codes. Notably, our algorithms operate with polynomial complexity relative to the code length. Simulation results affirm that our findings yield a precise estimation of the performance of rate-compatible polar codes.

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arXiv2024

Partial Orders in Rate-Matched Polar Codes

In this paper, we establish the partial order (POs) for both the binary erasure channel (BEC) and the binary memoryless symmetric channel (BMSC) under any block rate-matched polar codes. Firstly, we define the POs in the sense of rate-matched polar codes as a sequential block version. Furthermore, we demonstrate the persistence of POs after block rate matching in the BEC. Finally, leveraging the existing POs in the BEC, we obtain more POs in the BMSC under block rate matching. Simulations show that the PW sequence constructed from β-expansion can be improved by the tool of POs. Actually, any fixed reliable sequence in the mother polar codes can be improved by POs for rate matching.

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arXiv2024

Coded Water-Filling for Multi-User Interference Cancellation

In this paper, we study the system-level advantages provided by rateless coding, early termination and power allocation strategy for multiple users distributed across multiple cells. In a multi-cell scenario, the early termination of coded transmission not only reduces finite-length loss akin to the single-user scenario but also yields capacity enhancements due to the cancellation of interference across cells. We term this technique \emph{coded water-filling}, a concept that diverges from traditional water-filling by incorporating variable-length rateless coding and interference cancellation. We formulate a series of analytical models to quantify the gains associated with coded water-filling in multi-user scenarios. First, we analyze the capacity gains from interference cancellation in Additive White Gaussian Noise (AWGN) channels, which arises from the disparity in the number of bits transmitted by distinct users. Building upon this, we broaden our analysis to encompass fading channels to show the robustness of the interference cancellation algorithms. Finally, we address the power allocation problem analogous to the water-filling problem under a multi-user framework, proving that an elevation in the water-filling threshold facilitates overall system capacity enhancement. Our analysis reveals the capacity gains achievable through early termination and power allocation techniques in multi-user settings. These results show that coded water-filling is instrumental for further improving spectral efficiency in crowded spectrums.

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arXiv2024

Achievability Bounds on Unequal Error Protection Codes

Unequal error protection (UEP) codes can facilitate the transmission of messages with different protection levels. In this paper, we study the achievability bounds on UEP by the generalization of Gilbert-Varshamov (GV) bound. For the first time, we show that under certain conditions, UEP enhances the code rate comparing with time-sharing (TS) strategies asymptotically.

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arXiv2024

Adaptive Perturbation Enhanced SCL Decoder for Polar Codes

For polar codes, successive cancellation list (SCL) decoding algorithm significantly improves finite-length performance compared to SC decoding. SCL-flip decoding can further enhance the performance but the gain diminishes as code length increases, due to the difficulty in locating the first error bit position. In this work, we introduce an SCL-perturbation decoding algorithm to address this issue. A basic version of the algorithm introduces small random perturbations to the received symbols before each SCL decoding attempt, and exhibits non-diminishing gain at large block lengths. Its enhanced version adaptively performs random perturbations or directional perturbation on each received symbol according to previous decoding results, and managed to correct more errors with fewer decoding attempts. Extensive simulation results demonstrate stable gains across various code rates, lengths and list sizes. To the best of our knowledge, this is the first SCL enhancement with non-diminishing gains as code length increases, and achieves unprecedented efficiency. With only one additional SCL-$L$ decoding attempt (in total two), the proposed algorithm achieves SCL-$2L$-equivalent performance. Since the gain is obtained without increasing list size, the algorithm is best suited for hardware implementation.

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arXiv2024

Second-Order Identification Capacity of AWGN Channels

In this paper, we establish the second-order randomized identification capacity (RID capacity) of the Additive White Gaussian Noise Channel (AWGNC). On the one hand, we obtain a refined version of Hayashi's theorem to prove the achievability part. On the other, we investigate the relationship between identification and channel resolvability, then we propose a finer quantization method to prove the converse part. Consequently, the second-order RID capacity of the AWGNC has the same form as the second-order transmission capacity. The only difference is that the maximum number of messages in RID scales double exponentially in the blocklength.

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arXiv2024

On the Weight Distribution of Weights Less than $2w_{\min}$ in Polar Codes

The number of low-weight codewords is critical to the performance of error-correcting codes. In 1970, Kasami and Tokura characterized the codewords of Reed-Muller (RM) codes whose weights are less than $2w_{\min}$, where $w_{\min}$ represents the minimum weight. In this paper, we extend their results to decreasing polar codes. We present the closed-form expressions for the number of codewords in decreasing polar codes with weights less than $2w_{\min}$. Moreover, the proposed enumeration algorithm runs in polynomial time with respect to the code length.

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arXiv2024

New Partial Orders of Polar Codes for BMSC

In this paper, we define partial orders (POs) of polar codes based on the Bhattacharyya parameter and the bit-error probability, respectively. These POs are applicable to arbitrary binary memoryless symmetric channel (BMSC). Leveraging the extremal inequalities of polarization transformation, we derive new POs for BMSC based on the corresponding POs observed in the Binary Erasure Channel (BEC). %Additionally, we discover more special POs in the Binary Symmetric Channel (BSC). We provide examples that demonstrate the inability of existing POs to deduce these novel POs. Furthermore, we establish upper bounds for the expansion parameter $β$ if the polar codes constructed by $β$-expansion method obey these POs.

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arXiv2024

Achieving the Fundamental Limit of Lossless Analog Compression via Polarization

In this paper, we study the lossless analog compression for i.i.d. nonsingular signals via the polarization-based framework. We prove that for nonsingular source, the error probability of maximum a posteriori (MAP) estimation polarizes under the Hadamard transform, which extends the polarization phenomenon to analog domain. Building on this insight, we propose partial Hadamard compression and develop the corresponding analog successive cancellation (SC) decoder. The proposed scheme consists of deterministic measurement matrices and non-iterative reconstruction algorithm, providing benefits in both space and computational complexity. Using the polarization of error probability, we prove that our approach achieves the information-theoretical limit for lossless analog compression developed by Wu and Verdu.

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arXiv2023

On the Weight Spectrum Improvement of Pre-transformed Reed-Muller Codes and Polar Codes

Pre-transformation with an upper-triangular matrix (including cyclic redundancy check (CRC), parity-check (PC) and polarization-adjusted convolutional (PAC) codes) improves the weight spectrum of Reed-Muller (RM) codes and polar codes significantly. However, a theoretical analysis to quantify the improvement is missing. In this paper, we provide asymptotic analysis on the number of low-weight codewords of the original and pre-transformed RM codes respectively, and prove that pre-transformation significantly reduces low-weight codewords, even in the order sense. For polar codes, we prove that the average number of minimum-weight codewords does not increase after pre-transformation. Both results confirm the advantages of pre-transformation.

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arXiv2023

Theoretical Bounds for the Size of Elementary Trapping Sets by Graphic Methods

Elementary trapping sets (ETSs) are the main culprits for the performance of LDPC codes in the error floor region. Due to the large quantity, complex structures, and computational difficulties of ETSs, how to eliminate dominant ETSs in designing LDPC codes becomes a pivotal issue to improve the error floor behavior. In practice, researchers commonly address this problem by avoiding some special graph structures to free specific ETSs in Tanner graph. In this paper, we deduce the accurate Turán number of $θ(1,2,2)$ and prove that all $(a,b)$-ETSs in Tanner graph with variable-regular degree $d_L(v)=γ$ must satisfy the bound $b\geq aγ-\frac{1}{2}a^2$, which improves the lower bound obtained by Amirzade when the girth is 6. For the case of girth 8, by limiting the relation between any two 8-cycles in the Tanner graph, we prove a similar inequality $b\geq aγ-\frac{a(\sqrt{8a-7}-1)}{2}$. The simulation results show that the designed codes have good performance with lower error floor over additive white Gaussian noise channels.

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