Shashi Kiran Chilappagari

Learn More
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 the(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)
We present a method to construct low-density parity-check (LDPC) codes with low error floors on the binary symmetric channel. Codes are constructed so that their Tanner graphs are free of certain small trapping sets. These trapping sets are selected from the trapping set ontology for the Gallager A/B decoder. They are selected based on their relative(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 , no(More)
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)
In this paper, we study state transitions, induced by low-density parity-check codes, of the Gallager B algorithm in order to characterize failures of the decoder. The failures of the decoder depend on the properties of the underlying graph of the code. Two classes of sets, namely trapping sets and propagating sets, of variables of the code are defined to(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 compare performance of three classes of forward error correction schemes for 40-Gb/s optical transmission systems. The first class is based on the concatenation of Reed–Solomon codes and this is employed in the state-of-theart fiber-optics communication systems. The second class is the turbo product codes with Bose–Chaudhuri–Hocquenghen(More)
The relation between the girth and the guaranteed error correction capability of <i>¿</i> -left-regular low-density parity-check (LDPC) codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least <i>3 ¿/4</i> is found based on the Moore(More)
We consider linear programming (LP) decoding of a fixed low-density parity-check (LDPC) code over the binary symmetric channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not equal to the transmitted codeword. We design an efficient algorithm termed the Instanton Search Algorithm (ISA) which generates an error vector called the(More)