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IEEE International Symposium on Information Theory (ISIT)

UEP non-binary LDPC codes: A promising framework based on group codes

Alban Goupil, David Declercq

Published Jul 1, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1109/isit.2008.4595386

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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.
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, a new construction of quasi-cyclic low-density parity-check (QC-LDPC) codes for unequal error protection (UEP) is proposed. We first give a new class of UEP block codes. QC-LDPC codes with binomial-term parity-check matrices which can avoid girths less than 8 and achieve an enlarged upper bound on the minimum distance are also introduced. An effective UEP scheme based on the proposed UEP block codes and QC-LDPC codes which can provide flexible choice of protection levels is then presented. Simulation results show that the new QC-LDPC codes can achieve good performance and low error floors. The bits with different designed protection levels can indeed have unequal bit-error-rate performance.
Irregular low-density parity check (LDPC) codes are particularly well-suited for transmission schemes that require unequal error protection (UEP) of the transmitted data due to the different connection degrees of its variable nodes. However, this UEP capability is strongly dependent on the connection profile among the protection classes. This paper applies a multi-edge type analysis of LDPC codes for optimizing such connection profile according to the performance requirements of each protection class. This allows the construction of UEP-LDPC codes where the difference between the performance of the protection classes can be adjusted and with an UEP capability that does not vanish as the number of decoding iterations grows.
In this paper, a generalized construction of quasi-cyclic low-density parity-check (QC-LDPC) codes for unequal error protection (UEP) is proposed based on the masking technique. We can obtain UEP QC-LDPC codes as long as the Tanner graph of the masking matrix satisfies a general condition which can include our previous UEP construction as a special case. A sufficient condition to have flexible choice of protection levels is then presented. Simulation results show that the constructed codes can indeed provide codeword bits with different bit-error-rate performance.
In this paper, we explore a novel approach to evaluate the inherent UEP (unequal error protection) properties of irregular LDPC (low-density parity-check) codes over BECs (binary erasure channels). Exploiting the finite-length scaling methodology, suggested by Amraoui et. al., we introduce a scaling approach to approximate the bit erasure rates of variable nodes with different degrees in the waterfall region of the peeling decoder. Comparing the bit erasure rates obtained from Monte Carlo simulation with the proposed scaling approximations, we demonstrate that the scaling approach provides a close approximation for a wide range of code lengths (between 1000 and 8000). In view of the complexity associated with the numerical evaluation of the scaling approximation, we also derive simpler upper and lower bounds.
Irregular low-density parity-check (LDPC) codes are particularly well-suited for transmission schemes that require unequal error protection (UEP) of the transmitted data due to the different connection degrees of its variable nodes. However, this UEP capability is strongly dependent on the connection profile among the protection classes. This paper applies a multi-edge type analysis of LDPC codes for optimizing such a connection profile according to the performance requirements of each protection class. This allows the construction of UEP-LDPC codes where the difference between the performance of the protection classes can be adjusted and with an UEP capability that does not vanish as the number of decoding iterations grows.