Charly Poulliat

Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images

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 associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes.

Design of cages with a randomized progressive edge-growth algorithm

The progressive edge-growth (PEG) construction is a well known algorithm for constructing bipartite graphs with good girth properties. In this letter, we propose some improvements in the PEG algorithm which greatly improve the girth properties of the resulting graphs: given a graph size, they increase the girth g achievable by the algorithm, and when the girth cannot be increased, our modified algorithm minimizes the number of cycles of length g. As a main illustration, we focus on regular column-weight two graphs (dv = 2), although our algorithm can be applied to any graph connectivity. The class of dv = 2 graphs is often used for non-binary low density parity check codes that can be seen as monopartite graphs: for a given target girth gt, this new instance of the PEG algorithm allows to construct cages, i.e. graphs with the minimal size such that a graph of girth gt exists, which is the best result one might hope for.

Multiplicatively Repeated Nonbinary LDPC Codes

We propose nonbinary LDPC codes concatenated with multiplicative repetition codes. By multiplicatively repeating the (2,3)-regular nonbinary LDPC mother code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9, 1/12,.... Surprisingly, such simple low-rate nonbinary LDPC codes outperform the best low-rate binary LDPC codes so far. Moreover, we propose the decoding algorithm for the proposed codes, which can be decoded with almost the same computational complexity as that of the mother code.

JPEG 2000 backward compatible error protection with Reed-Solomon codes

In this paper, a backward compatible header error protection mechanism is described. It consists of the addition of a dedicated marker segment to a JPEG 2000 codestream, that will contain the error correction data generated by a block error correction code (e.g. a Reed Solomon code). This mechanism allows leaving the original data intact, hence providing backward compatibility with the already standardised JPEG 2000. Neither side information from higher level, nor extra signalling encapsulation is needed, as the required information is directly embedded in the codestream and also protected. Finally, it is shown how this mechanism can be used for perform unequal error protection of the whole JPEG 2000 stream.

Jointly decoded raptor codes: analysis and design for the BIAWGN channel

We are interested in the analysis and optimization of Raptor codes under a joint decoding framework, that is, when the precode and the fountain code exchange soft information iteratively. We develop an analytical asymptotic convergence analysis of the joint decoder, derive an optimization method for the design of efficient output degree distributions, and show that the new optimized distributions outperform the existing ones, both at long and moderate lengths. We also show that jointly decoded Raptor codes are robust to channel variation: they perform reasonably well over a wide range of channel capacities. This robustness property was already known for the erasure channel but not for the Gaussian channel. Finally, we discuss some finite length code design issues. Contrary to what is commonly believed, we show by simulations that using a relatively low rate for the precode, we can improve greatly the error floor performance of the Raptor code.

Analysis and design of raptor codes for joint decoding using Information Content evolution

This paper is eligible for the student paper award. In this paper, we present an analytical analysis of the convergence of raptor codes under joint decoding over the binary input additive white noise channel (BIAWGNC), and derive an optimization method. We use information content evolution under Gaussian approximation, and focus on a new decoding scheme that proves to be more efficient: the joint decoding of the two code components of the raptor code. In our general model, the classical tandem decoding scheme appears to be a sub-case, and thus, the design of LT codes is also possible.

Enhancement of unequal error protection properties of LDPC codes

It has been widely recognized in the literature that irregular low-density parity-check (LDPC) codes exhibit naturally an unequal error protection (UEP) behavior. In this paper, we propose a general method to emphasize and control the UEP properties of LDPC codes. The method is based on a hierarchical optimization of the bit node irregularity profile for each sensitivity class within the codeword by maximizing the average bit node degree while guaranteeing a minimum degree as high as possible. We show that this optimization strategy is efficient, since the codes that we optimize show better UEP capabilities than the codes optimized for the additive white Gaussian noise channel.

Design of non binary LDPC codes using their binary image: algebraic properties

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

Analysis and optimization of irregular LDPC codes for joint source-channel decoding

In this paper, we present a characterization, through its convergence analysis, and an optimisation of a joint source-channel receiver composed of a LDPC decoder and a Soft Input Soft Output (SISO) source decoder. Under Gaussian approximation, assuming the knowledge of the extrinsic mutual information transfer function (EXIT chart) of the source decoder, we derive the Mutual Information evolution equations, that semianalytically describe the convergence of the iterative system behavior and, to complete the study, the stability condition at the convergence fixed point is derived for the joint receiver. From this analysis, a general optimisation method of the irregularity of the LDPC codes is proposed, which can be reduced to a linear programming optimisation problem. Simulation results show improved performance when compared to an AWGN optimized LDPC code.

Optimization of LDPC codes for UEP channels

This paper describes the optimization of LDPC codes for unequal error protection (UEP) transmission schemes. The method is based on a hierarchical optimization of the irregularity for each class within the codeword by maximizing the average data node degree with a given error sensitivity at a finite number of decoding iterations.