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International Conference on Computer and Communication Systems (ICCCS)

An Unequal Error Protection of Quasi-Cyclic Low Density Parity Check (QC-LDPC) Codes Based on Combinatorial Designs

Bijaya Paudel, Sina Vafi

Published Feb 1, 2019• 4 citations
Publisher

Abstract

This paper presents a novel method for constructing high performance unequal error protection (UEP) quasicyclic low-density parity-check (QC-LDPC) codes. These codes are highly efficient and designed with flexible rates, lengths and number of protection levels. The given QC-LDPC codes are based on the combinatorial design. Each circulant constituting the parity check matrix of the UEP code is determined from subsets with the distinct difference between elements. Simulation results indicate that proposed UEP codes have equivalent performance to UEP codes constructed with the higher girth and lower rate, while achieving superior performance than the codes constructed by conventional equal error protection (EEP) techniques.

DOI
10.1109/ccoms.2019.8821723

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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.
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.
This paper presents new half rate Quasi Cyclic Low Density Parity Check (QC- LDPC) codes formed on the basis of combinatorial designs. In these codes, circulant matrices of the parity check matrix are formed on the basis of subsets in which the difference between any two elements of a subset is unique with all differences obtained from the same or different subsets. This structure of circulant matrices guarantees non-existence of cycle-4 in the Tanner graph of QC-LDPC codes. First, an irregular code with girth 6 constituted by two rows of circulant matrices is proposed. Then, more criteria will be considered on the structure of subsets with the mentioned feature aiming to represent a new scheme of regular QC-LPDC codes with girth at least 8. From simulations, it is confirmed that codes have similar to or better performance than other well-known half rate codes, while require lower complexity in their design.
This paper presents a novel regular Quasi-Cyclic (QC) Low Density Parity Check (LDPC) codes with column-weight three and girth at least eight. These are designed on the basis of combinatorial design in which subsets applied for the construction of circulant matrices are determined by a particular subset. Considering the non-existence of cycles four and six in the structure of the parity check matrix, a bound for their minimum weight is proposed. The simulations conducted confirm that without applying a masking technique, the newly implemented codes have a performance similar to or better than other well-known codes. This is evident in the waterfall region, while their error floor at very low Bit Error Rate (BER) is expected.