Unequal Error Protection Raptor Codes

We design Unequal Error Protection (UEP) Raptor codes with the UEP property provided by the precode part of Raptor codes which is usually a Low Density Parity Check (LDPC) code. Existing UEP Raptor codes apply the UEP property on the Luby transform (LT) code part of Raptor codes. This approach lowers the bit erasure rate (BER) of the more important bits (MIB) of the data decoded by the LT part of the decoder of Raptor code at the expense of degrading the BER performance of Less Important Bits (LIB), and hence the overall BER of the data passed from the LT part to the LDPC part of the decoder is higher compared to the case of using an Equal Error Protection (EEP) LT code. The proposed UEP Raptor code design has the structure of UEP LDPC code and EEP LT code so that it has the advantage of passing data blocks with lower BER from the LT code part to the LDPC code part of the decoder. This advantage is translated into improved performance in terms of required overhead and achieved BER on both the MIB bits and LIB bits of the decoded data compared to UEP Raptor codes applying the UEP property on the LT part. We propose two design schemes. The first combines a partially regular LDPC code which has UEP properties with an EEP LT code, and the second scheme uses two LDPC codes with different code rates in the precode part such that the MIB bits are encoded using the LDPC code with lower rate and the LT part is EEP. Simulations of both designs exhibit improved BER performance on both the MIB bits and LIB bits while consuming smaller overheads. The second design can be used to provide unequal protection for cases where the MIB bits comprise a fraction of more than 0.4 of the source data which is a case where UEP Raptor codes with UEP LT codes perform poorly

Low-density parity-check codes for asymmetric distributed source coding

The research work is partially funded by the Strategic Educational Pathways Scholarship Scheme (STEPS-Malta). This scholarship is partly financed by the European Union - European Social Fund (ESF 1.25).Low-Density Parity-Check (LDPC) codes achieve good performance, tending towards the Slepian-Wolf bound, when used as channel codes in Distributed Source Coding (DSC). Most LDPC codes found in literature are designed assuming random distribution of transmission errors. However, certain DSC applications can predict the error location within a certain level of accuracy. This feature can be exploited in order to design application specific LDPC codes to enhance the performance of traditional LDPC codes. This paper proposes a novel architecture for asymmetric DSC where the encoder is able to estimate the location of the errors within the side information. It then interleaves the bits having a high probability of error to the beginning of the codeword. The LDPC codes are designed to provide a higher level of protection to the front bits. Simulation results show that correct localization of errors pushes the performance of the system on average 13.3% closer to the Slepian-Wolf bound, compared to the randomly constructed LDPC codes. If the error localization prediction fails, such that the errors are randomly distributed, the performance is still in line with that of the traditional DSC architecture.peer-reviewe

Degree-degree Correlated Low-density Parity-check Codes Over a Binary Erasure Channel

Most existing works on analyzing the performance of a random ensemble of low-density parity-check (LDPC) codes assume that the degree distributions of the two ends of a randomly selected edge are independent. In the paper, we take one step further and consider ensembles of LDPC codes with degree-degree correlations. For this, we propose two methods to construct an ensemble of degree-degree correlated LDPC codes. We then derive a system of density evolution equations for such degree-degree correlated LDPC codes over a binary erasure channel (BEC). By conducting extensive numerical experiments, we show how the degree-degree correlation affects the performance of LDPC codes. Our numerical results show that LDPC codes with negative degree-degree correlation could improve the maximum tolerable erasure probability. Moreover, increasing the negative degree-degree correlation could lead to better unequal error protection (UEP) design.Comment: accepted by the 2023 IEEE International Symposium on Information Theory (ISIT