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IEEE Information Theory Workshop (ITW)

Multi-edge type unequal error protecting low-density parity-check codes

H. V. Beltrão Neto, Werner Henkel, Valdemar C. da Rocha

Published Oct 1, 2011• 6 citations
Publisher

Abstract

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.

DOI
10.1109/itw.2011.6089474

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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.
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.
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 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 many optimization techniques of LDPC codes, the check node irregularity is usually considered as being fixed because the profile must contain only two consecutive degrees in order to maximize the overall convergence speed of the code. We show in this paper that it is possible to construct bit-regular codes with more than two different degrees at check nodes side to speed up the convergence of some parts of the codeword, even if we may decrease a little the global convergence. Then, we take advantage of the check irregularity to create unequal error protection (UEP) codes, and present a very flexible method to achieve it. This method is based on pruning a mother code, thereby creating different subcodes with different UEP properties, but decoded with the same decoder. 1
This letter addresses the effect of threshold offset on the average performance and UEP capability of higher order constellation (HOC) unequal error protection low density parity check (UEP-LDPC) codes. We optimize the variable node degree distribution for an HOC UEP-LDPC code at a minimum threshold, with a fixed check node degree distribution and code rate. The average performance and the UEP capability of the ensemble code for a marginal offset in the threshold value were investigated. The simulation results show that the average performance and UEP capability can be enhanced by a slight offset in the threshold value. We looked into the connectivity between protection classes due to the threshold offset for a possible answer to the performance gain.
In this paper, the algebraic constructions of quasi-cyclic low-density parity-check (QC-LDPC) codes with the unequal error protection (UEP) property are considered. A criterion for constructing such codes via the masking technique is proposed, based on which explicit conditions on the base parity-check matrices and masking matrices to achieve UEP are provided. We also give three specific constructions of UEP QC-LDPC codes. Furthermore, a sufficient condition to ensure strict UEP is presented. Simulation results demonstrate the superiority of our constructed codes over time-sharing schemes. The constructed codes also have competitive error performance against randomly constructed equal-error-protection LDPC codes and irregular UEP LDPC codes designed based on the degree distribution.