Comparison of Simplified Gradient Descent Algorithms for Decoding Ldpc Codes

In this paper it is shown that multi GDBF algorithm exhibits much faster convergence as compared to the single GDBF algorithm. The multi GDBF algorithm require less iterations when compared to the single GDBF algorithm for the search point to closely approach the local maximum point taking into consideration the gradient descent bit flipping (GDBF) algorithms exhibiting better decoding performance than known BF algorithms. A novel class of bit-flipping (BF) algorithm for decoding low-density parity-check (LDPC) codes is presented. The behaviour of the proposed algorithms can be explained from the view point of optimization of the objective function. The GDBF algorithm with escape process performance very well compare with known BF algorithms, such as weighted BF (WBF) algorithms. A natural relationship between weighted bit-flipping (WBF) decoding and message-passing decoding is explored. This understanding can help us develop a dual WBF decoding algorithm from one type of message-passing decoding algorithm and vice versa. The GDBF algorithms can be regarded as a maximization process of the object function using the bit-flipping gradient descent method (i.e., bit-flipping dynamics, which minimizes the energy. The dynamics of the decoder is naturally derived by differentiating the energy function, and the gradient descent formulation introduces an energy landscape of the state-space of the BF-decoder. Keyword: GDBF, BF, MWBF, LDPC Code.