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IEEE Transactions on Information Theory

On decoding unequal error protection product codes

P.C. Stevens

Published Jul 1, 1990• 3 citations
Publisher

Abstract

The decoding of unequal error protection product codes, which are a combination of linear unequal error protection (UEP) codes and product codes, is addressed. A nonconstructive proof of the existence of a good error-erasure-decoding algorithm is presented; however, obtaining the decoding procedure is still an open research problem. A particular subclass of UEP product codes is considered, including a decoding algorithm that is an extension of the Blokh-Zyablov decoding algorithm for product codes. For this particular subclass the decoding problem is solved.>

DOI
10.1109/18.53753

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The decoding of unequal error protection product codes, which are a combination of linear unequal error protection (UEP) codes and product codes, is addressed. A nonconstructive proof of the existence of a good error-erasure-decoding algorithm is presented; however, obtaining the decoding procedure is still an open research problem. A particular subclass of UEP product codes is considered, including a decoding algorithm that is an extension of the Blokh-Zyablov decoding algorithm for product codes. For this particular subclass the decoding problem is solved.>
In coding theory, it is important to find upper bounds for the code size given a code length and minimum distance. The Hamming bounds and Linear Programming (LP) bounds were proposed in previous works. On the other hand, Masnick et al. proposed Unequal Error Protection (UEP) codes and modified Hamming bounds as upper bounds for the code size of UEP codes. In our previous work, we defined 2-level UEP codes as a subclass of UEP codes, and derived LP bounds for 2-level UEP codes. In this paper, we define multi-level UEP codes by extending 2-level UEP codes, and derive LP bounds for multi-level UEP codes. Moreover, we show that LP bounds for UEP codes are tighter upper bound than modified Hamming bounds.
A family of unequal error-protection (UEP) low-density parity-check (LDPC) codes, based on Plotkin-type constructions, is introduced. The codes are decoded in multiple stages in such a manner that the order of decoding determines the level of error protection. The level of UEP among the code bits can be further increased by properly combining structured and random-like LDPC component codes with carefully chosen properties, and by using some new reliability features. The proposed scheme also offers a good trade-off between code performance on the one hand and encoding/decoding and storage complexity on the other. To the best of our knowledge, the proposed approach represents the first iterative UEP method with analytically provable properties.
In this paper, we address the problem of providing unequal error protection (UEP) with LDPC codes built on finite sets of order strictly greater than 2 (nonbinary codes). The main interest of providing UEP with nonbinary LDPC codes is that future standards are likely to prefer nonbinary coding schemes because of their better robustness to the codeword length and the modulation size. However, the problem of giving UEP properties with nonbinary LDPC codes is much more difficult than with binary LDPC codes. We present a first attempt to solve this difficult problem, based on LDPC codes built on finite groups. The framework and the basis about group LDPC codes are first presented in details, and the framework is used to give examples of UEP nonbinary LDPC codes that actually achieve different UEP properties at the bit level while the symbol error properties are kept equally protected.
Algebraic constructions of quasi-cyclic (QC) low-density parity-check (LDPC) codes with unequal error protection (UEP) capabilities have recently been proposed, which can provide different error-correcting capabilities for different parts of the coded bits. However, conventional decoding algorithms are not designed for LDPC codes with UEP. In this paper, we propose three decoding schemes for UEP QC-LDPC codes extended from existing scheduling strategies, tailored to the special structures of the parity-check matrices. Simulation results show that the proposed schemes can provide improved error rate performance especially for coded bits on low protection levels. The decoding convergence can also be accelerated, thereby reducing the computational complexity.
A lower bound on the length of binary self-orthogonal unequal error protection (UEP) codes is derived, and two design procedures for constructing optimal self-orthogonal UEP codes are proposed. With this lower bound, known self-orthogonal UEP codes can be evaluated. It is pointed out that, for given values of minimum distance and code rate, the self-orthogonal codes must be relatively long, so optimal self-orthogonal codes are not optimal in general. But self-orthogonal codes can be implemented simply, and they have error-correcting capabilities beyond those guaranteed by their minimum distance. These properties can be viewed as a partial compensation for using self-orthogonal codes.>
In coding theory, it is important to find upper bounds for the code size given a code length and minimum distance. The Hamming bounds and Linear Programming (LP) bounds were proposed in previous works. On the other hand, Masnick et al. proposed Unequal Error Protection (UEP) codes and modified Hamming bounds as upper bounds for the code size of UEP codes. In our previous work, we defined 2-level UEP codes as a subclass of UEP codes, and derived LP bounds for 2-level UEP codes. In this paper, we define multi-level UEP codes by extending 2-level UEP codes, and derive LP bounds for multi-level UEP codes. Moreover, we show that LP bounds for UEP codes are tighter upper bound than modified Hamming bounds.