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In this paper, a method to design regular (2, dc)- LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets...
In this paper, we propose a hardware implementation of the EMS decoding algorithm for non-binary LDPC (NB- LDPC) codes, presented in [4]. To the knowledge of the authors this is the first implementation of an GF(q) LDPC decoder for high order fields (q ges 64). The originality of the proposed architecture is that it takes into account the memory problem of the NB-LDPC decoders, together with a significant...
In this paper, we propose a hardware implementation of the EMS decoding algorithm for non-binary LDPC codes, presented in [10]. To the knowledge of the authors this is the first implementation of a GF(q) LDPC decoder for high order fields (q ges 64). The originality of the proposed architecture is that it takes into account the memory problem of the non-binary LDPC decoders, together with a significant...
Unequal error protection is the key to future transport of multimedia data. The paper presents an overview of some new approaches realizing UEP properties in physical transport, especially multicarrier modulation, or with LDPC and turbo codes. For multicarrier modulation, a UEP bit-loading method is described allowing for an arbitrary number of classes, arbitrary SNR margins between the classes and...
In this paper, we develop algebraic properties of regular (2, t r, N) non binary LDPC codes designed using their binary image. First, we characterize the algebraic properties of optimized rows of the parity check matrix H associated with a code, and then we study the algebraic properties of cycles and stopping sets associated with the underlaying Tanner graph
Low-density parity check codes (LDPC) are a class of channel decoding codes used in digital communications. Very high error correcting performances can be reached with such codes but they require both a great computing effort and randomly constructed decoding matrices. LDPC codes are used to perform the channel coding of the satellite television broadcast standard DVB-S2. This paper proposes a way...
In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes hybrid LDPC codes. Although efficient optimization techniques exist for binary LDPC codes and more recently for non-binary LDFC codes, they both exhibit drawbacks due to different reasons. Our goal is to capitalize on the...
In this paper, we develop a generalization of the minsum (MS) algorithm which not only performs additions without the need of channel estimation, but also with the two following objectives: (i) a complexity much lower than O(q2) so that finite fields of large order can be considered; and (ii) a small performance degradation compared with BP decoding. The first objective is achieved by introducing...
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