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(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 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-the-art fiber-optics communication systems. The second class is the turbo product codes with Bose–Chaudhuri–Hocquenghen(More)
At the heart of modern coding theory lies the fact that low-density parity-check (LDPC) codes can be efficiently decoded by belief propagation (BP). The BP is an inference algorithm which operates on a graphical model of a code, and lends itself to low-complexity and high-speed implementations, making it the algorithm of choice in many applications. It has(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 propose a new class of quantized message-passing decoders for LDPC codes over the BSC. The messages take values (or levels) from a finite set. The update rules do not mimic belief propagation but instead are derived using the knowledge of trapping sets. We show that the update rules can be derived to correct certain error patterns that are(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)