This paper presents new FEC codes for the erasure channel, LDPC-Band, that have been designed so as to optimize a hybrid iterative-Maximum Likelihood (ML) decoding. Indeed, these codes feature simultaneously a sparse parity check matrix, which allows an efficient use of iterative LDPC decoding, and a generator matrix with a band structure, which allows fast ML decoding on the erasure channel. The combination of these two decoding algorithms leads to erasure codes achieving a very good trade-off between complexity and erasure correction capability.
The idea of window based encoding in LDPC codes has been proposed by Haken, Luby and al. in patent @cite_8 . However, the goal of this patent is only to minimize memory access during encoding, by localizing the access in a window that slides over the input file. Independantly of whether our proposal falls into the scope of this patent or not, we see that, from a purely scientific point of view, the goal of @cite_8 completely departs from the approach discussed in the current paper, as well as the theoretic tools we introduce to achieve our goals.
@cite_8
2949560198 2062063921 2326109306 2114793420
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman succeeds in correcting a constant fraction of errors with high probability. The fraction of correctable errors guaranteed by our analysis surpasses previous nonasymptotic results for LDPC codes, and in particular, exceeds the best previous finite-length result on LP decoding by a factor greater than ten. This improvement stems in part from our analysis of probabilistic bit-flipping channels, as opposed to adversarial channels. At the core of our analysis is a novel combinatorial characterization of LP decoding success, based on the notion of a flow on the Tanner graph of the code. An interesting by-product of our analysis is to establish the existence of ldquoprobabilistic expansionrdquo in random bipartite graphs, in which one requires only that almost every (as opposed to every) set of a certain size expands, for sets much larger than in the classical worst case setting. In this paper, we provide the performance analysis of unequal error protection (UEP) random linear coding (RLC) strategies designed for transmission of source messages containing packets of different importance over lossy packet erasure links. By introducing the probabilistic encoding framework, we first derive the general performance limits for the packet-level UEP coding strategies that encode the packets of each importance class of the source message independently (non-overlapping windowing strategy) or jointly (expanding windowing strategy). Then, we demonstrate that the general performance limits of both strategies are achievable by the probabilistic encoding over non-overlapping and expanding windows based on RLC and the Gaussian Elimination (GE) decoding. Throughout the paper, we present a number of examples that investigate the performance and optimization of code design parameters of the expanding window RLC strategy and compare it with the non-overlapping RLC strategy selected as a reference. In this letter, we propose an adaptive forward error correction scheme based on low-density parity-check (LDPC) codes to efficiently adjust dimming values in visible light communication (VLC) systems. The proposed code is a quasi-cyclic LDPC code, in which extension and puncturing methods are used to maintain dimming control. The significant advantages of the proposed method are due to the lower number of codes required to support codes with different coding rate and the relatively small performance degradation for dimming control. Simulation results show that our proposed method efficiently maintains the dimming control in VLC systems with LDPC codes. A decode-and-forward LDPC-based coding and decoding scheme is proposed and applied to the BAWGN single-relay channel. The source broadcasts information to both the relay and the destination. The relay is able to simultaneously receive and transmit. Both the relay and the destination apply successive iterative decoding using belief propagation. In the proposed scheme, the LDPC code used by the source and the LDPC code used by the relay are designed independently of each other. Optimality properties of this approach are established via information-theoretic upper and lower bounds. Asymptotic analysis shows that the performance of the proposed scheme can be as close as 0.02 dB away from the theoretical limit for any decode-and-forward scheme, and simulation results show that its performance for a block code of length 214 can be within 0.65 dB away from the same limit with a corresponding bit error probability of 10?6.