Conference Paper

A Markov chain model for Edge Memories in stochastic decoding of LDPC codes

Dept. of Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA
DOI: 10.1109/CISS.2011.5766114 Conference: Information Sciences and Systems (CISS), 2011 45th Annual Conference on
Source: IEEE Xplore


Stochastic decoding is a recently proposed method for decoding Low-Density Parity-Check (LDPC) codes. Stochastic decoding is, however, sensitive to the switching activity of stochastic bits, which can result in a latching problem. Using Edge Memories (EMs) has been proposed as a method to counter the latching problem in stochastic decoding. In this paper, we introduce a Markov chain model for EMs and study state transitions over decoding cycles. The proposed method can be used to determine the convergence and the required number of decoding cycles in stochastic decoding. Moreover, it can help to study the behavior of decoding process and to estimate the decoding time.

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Available from: Vincent C. Gaudet, Oct 06, 2015
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    • "Splitting row-modules by partitioning check node operations has been shown to provide substantial gains in the required area and power efficiency [22] [23]. In another prominent line of work, researchers have proposed various stochastic decoding algorithms [10] [35] [33] [34] [24] [19] [20] [31]. They are all based on stochastic representation of the SP messages. "
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    ABSTRACT: Low-density parity-check codes, a class of capacity-approaching linear codes, are particularly recognized for their efficient decoding scheme. The decoding scheme, known as the sum-product, is an iterative algorithm consisting of passing messages between variable and check nodes of the factor graph. The sum-product algorithm is fully parallelizable, owing to the fact that all messages can be update concurrently. However, since it requires extensive number of highly interconnected wires, the fully-parallel implementation of the sum-product on chips is exceedingly challenging. Stochastic decoding algorithms, which exchange binary messages, are of great interest for mitigating this challenge and have been the focus of extensive research over the past decade. They significantly reduce the required wiring and computational complexity of the message-passing algorithm. Even though stochastic decoders have been shown extremely effective in practice, the theoretical aspect and understanding of such algorithms remains limited at large. Our main objective in this paper is to address this issue. We first propose a novel algorithm referred to as the Markov based stochastic decoding. Then, we provide concrete quantitative guarantees on its performance for tree-structured as well as general factor graphs. More specifically, we provide upper-bounds on the first and second moments of the error, illustrating that the proposed algorithm is an asymptotically consistent estimate of the sum-product algorithm. We also validate our theoretical predictions with experimental results, showing we achieve comparable performance to other practical stochastic decoders.
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    ABSTRACT: A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes. The algorithm, called Noisy GDBF (NGDBF) offers improvement in terms of performance by adding a random perturbation at each iteration to escape from undesirable local maxima. Both single-bit and multi-bit flipping versions of the algorithm are proposed and evaluated. The proposed single-bit and multi-bit versions of the algorithm are shown to improve the Bit Error Rate (BER) compared to previous GDBF algorithms of comparable complexity. The multi-bit NGDBF algorithm achieves a 0.5dB coding gain compared to the best GDBF algorithms previously reported. Unlike other multi-bit GDBF algorithms that provide an escape from local maxima, the proposed algorithm does not require computing a global objective function or a sort over all symbol metrics, making it highly efficient in comparison. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.
    IEEE Transactions on Communications 02/2014; 62(10). DOI:10.1109/TCOMM.2014.2356458 · 1.99 Impact Factor