— In this paper, we propose a semi-analytical method to compute error floors of LDPC codes on the binary symmetric channel decoded iteratively using the Gallager B algorithm. The error events of the decoder are characterized using combinatorial objects called trapping sets, originally defined by Richardson. In general, trapping sets are characteristic of… (More)
— We discuss error floor asympotics and present a method for improving the performance of low-density parity check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets from the original code. The advantages of the method are that it is universal, as it can be applied to any LDPC… (More)
—In this paper, we develop a theoretical framework for the analysis and design of fault-tolerant memory architectures. Our approach is a modification of the method developed by Taylor and refined by Kuznetsov. Taylor and Kuznetsov (TK) showed that memory systems have nonzero computational (storage) capacity, i.e., the redundancy necessary to ensure… (More)
In this paper, we investigate the error correction capability of column-weight-three LDPC codes when decoded using the Gallager A algorithm. We prove that the necessary condition for a code to correct k ≥ 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, we show that given any α > 0, ∃N such that ∀n > N ,… (More)
— In this paper, we provide necessary and sufficient conditions for a column-weight-three LDPC code to correct three errors when decoded using Gallager A algorithm. We then provide a construction technique which results in a code satisfying the above conditions. We also provide numerical assessment of code performance via simulation results.
— In this paper we propose an analytical method to evaluate the performance of one step majority logic decoders constructed from faulty gates. We analyze the decoder under the assumption that the gates fail independently. We calculate the average bit error probability of such a decoder and apply the method to the special case of projective geometry codes.… (More)
—In this paper, a novel approach for suppressing the intrachannel nonlinear effects using pseudoternary constrained codes is proposed. A significant Q-factor improvement of up to 9.75 dB is obtained. The eye opening penalty (EOP) is also significantly improved by more than 10.24 dB.
—We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly… (More)
— The failures of iterative decoders for low-density parity-check (LDPC) codes on the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC) can be understood in terms of combinatorial objects known as trapping sets. In this paper, we derive a systematic method to identify the most relevant trapping sets for decoding over the… (More)