Sundararajan Sankaranarayanan

Error Floors of LDPC Codes on the Binary Symmetric Channel

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 graphical representation of a code. We study the structure of trapping sets and explore their relation to graph parameters such as girth and vertex degrees. Using the proposed method, we compute error floors of regular structured and random LDPC codes with column weight three.

Low-density parity-check codes for 40-gb/s optical transmission systems

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 component codes. The application of these codes in optical communication systems was extensively studied by Sab and Lemarie, and Mizuochi The third class is the low-density parity-check (LDPC) codes that have attracted much attention over the past decade. We present enhanced decoding algorithms for Turbo product codes and LDPC codes that use probability density function of output sequences instead of calculating initial likelihood ratios assuming (inaccurate) Gaussian or chi-square approximation. The analysis in this paper shows that the LDPC codes perform better than the other codes in the waterfall region at bit error rates as low as 10-9. We also presented error floors results obtained by analyzing decoding failures of hard-decision iterative decoders

Projective-plane iteratively decodable block codes for WDM high-speed long-haul transmission systems

Low-density parity-check (LDPC) codes are excellent candidates for optical network applications due to their inherent low complexity of both encoders and decoders. A cyclic or quasi-cyclic form of finite geometry LDPC codes simplifies the encoding procedure. In addition, the complexity of an iterative decoder for such codes, namely the min-sum algorithm, is lower than the complexity of a turbo or Reed-Solomon decoder. In fact, simple hard-decoding algorithms such as the bit-flipping algorithm perform very well on codes from projective planes. In this paper, the authors consider LDPC codes from affine planes, projective planes, oval designs, and unitals. The bit-error-rate (BER) performance of these codes is significantly better than that of any other known foward-error correction techniques for optical communications. A coding gain of 9-10 dB at a BER of 10/sup -9/, depending on the code rate, demonstrated here is the best result reported so far. In order to assess the performance of the proposed coding schemes, a very realistic simulation model is used that takes into account in a natural way all major impairments in long-haul optical transmission such as amplified spontaneous emission noise, pulse distortion due to fiber nonlinearities, chromatic dispersion, crosstalk effects, and intersymbol interference. This approach gives a much better estimate of the codes performance than the commonly used additive white Gaussian noise channel model.

Iterative decoding of linear block codes: a parity-check orthogonalization approach

It is widely accepted that short cycles in Tanner graphs deteriorate the performance of message-passing algorithms. This discourages the use of these algorithms on Tanner graphs (TGs) of well-known algebraic codes such as Hamming codes, Bose-Chaudhuri-Hocquenghem codes, and Reed-Solomon codes. Yedidia et al. presented a method to generate code representations suitable for message-passing algorithms. This method does not guarantee a representation free of four-cycles. In this correspondence, we present an algorithm to convert an arbitrary linear block into a code with orthogonal parity-check equations. A combinatorial argument is used to prove that the algorithm guarantees a four-cycle free representation for any linear code. The effects of removing four-cycles on the performance of a belief propagation decoder for the binary erasure channel are studied in detail by analyzing the structures in different representations. Finally, we present bit-error rate (BER) and block-error rate (BLER) performance curves of linear block codes under belief propagation algorithms for the binary erasure channel and the additive white Gaussian noise (AWGN) channel in order to demonstrate the improvement in performance achieved with the help of the proposed algorithm.

Improved data acquisition system for digital flow cytometry

Digital flow cytometry offers the flexibility to explore novel feature extraction and classification schemes for efficient sorting of biological cells. A prototype of a second-generation digital data acquisition system (DDAPS-2) - a mixed-signal design operating at 40 MHz - was built to interface to a commercial flow cytometer. The DDAPS-2 intercepts the analog signal from the photomultiplier tube and preamp, performs analog-to-digital conversion, extracts various features and then feeds these extracted features into one of the several pattern classification algorithms. This paper describes the design and operation of the various sub-systems that constitute the DDAPS-2. The novelty of the DDAPS-2 is the use of dual-buffering FIFO memories to acquire digital samples of the pulse voltage signal. Experimental results demonstrate the improvement in the pulse capture performance of DDAPS-2 over DDAPS-1, which used a single-buffering FIFO memory.

Irregular low-density parity-check codes for long-haul optical communications

A novel forward error correction (FEC) scheme for long-haul optical communication systems based on irregular low-density parity check codes and iterative decoding is proposed. The proposed FEC scheme for long-haul optical transmission significantly outperforms all previously reported FEC schemes, and it has a potential for achieving theoretical limits on reliable transmission through an optical communication channel.

Iteratively decodable codes on m flats for WDM high-speed long-haul transmission

In an earlier paper, we reported that the low-density parity-check (LDPC) codes from finite planes outperform any other known forward error-correction (FEC) scheme for optical communications. However, the number of different LDPC codes of code rate above 0.8 is rather small. As a natural extension of the prior work, in this paper, we consider LDPC codes on m flats derived from projective and affine geometries, which outperform codes from finite planes. The codes on m flats also provide a greater selection of structured LDPC codes of rate 0.8 or higher. The performance of the codes in a long-haul optical-communication system was assessed using an advanced simulator able to capture all important transmission impairments. Specifically, they achieve a coding gain of 10 dB at a bit error rate (BER) of 10/sup -9/, outperforming, therefore, the best turbo product codes proposed for optical communications. In addition, the simulator implements a fixed-point (FP) iterative decoder that allows control of the precision of the soft information used in the decoder. Such quantization is required to facilitate hardware implementations of the iterative decoder, and the high-speed operations for long-haul optical transmission systems. The loss in performance due to reduced precision of the soft information can be as low as 0.2 dB.

Adaptive error protection low-density parity-check codes for joint source-channel coding schemes

Abstruct: We propose a class of unequal error protection (UEP) low-density parity check (LDPC) codes based on cyclic difference families. The proposed code structures enable efficient adaptation of bit protection levels and are suitable for joint sourcechannel coding. I. INTRODUCTtON We consider a joint source-channel coding scheme in which a source signal is compressed by a variable length code, and then protected by an UEP channel code so that the bit error protection level depends on the content of the compressed data. Since the bit “importance distribution” varies from source codeword to source codeword, an adaptability of the channel code UEP profile is required. In this paper we propose to facilitate the UEP and adaptive error protection by using low-density parity check (LDPC) codes. We introduce a class of UEP codes with orthogonal parity checks. Such codes have been studied by Kilgus et al. [3], Mandelbaum [2] Chen, Fan and Jin [4] and Shiozaki [5], among others. Our scheme is based on irregular LDPC codes obtained from orbits of cyclic difference families (CDF).

Irregular low-density parity-check codes: construction and performance on perpendicular magnetic recording channels

In this paper, we propose an algorithm to design an irregular low-density parity-check code (LDPC), with a given degree distribution pair, from a random regular LDPC code. The proposed algorithm splits columns and rows of the regular code in order to achieve the desired degree distribution pair. Kou, Lin, and Fossorier have used column splitting to increase code rate. However, we use the splitting technique to achieve a given degree distribution pair in the bipartite graph of the resultant irregular code. The bit-error rate (BER) performance of high-rate irregular LDPC codes, constructed using this algorithm, were simulated on equalized perpendicular magnetic recording channels. In addition, this paper compares the performance of these irregular codes with that of random regular LDPC codes.

A systematic construction of irregular low-density parity-check codes from combinatorial designs

In this paper, we propose an algorithm to design an irregular low-density parity-check (LDPC) code, with a given degree distribution pair, from a combinatorially constructed regular LDPC code. Richardson et al., (2001) showed that long LDPC codes from irregular bipartite graphs with carefully chosen degree distribution pair performed very close to the Shannon capacity limit. It is known that the cyclic or quasicyclic property of regular LDPC codes, constructed from combinatorial designs Colbourn, J et al., (1996), helps to simplify their encoding procedure and also facilitates a memory-efficient storage of the codes. The proposed algorithm involves splitting columns and rows of a regular LDPC code systematically in order to achieve an irregular code with a given distribution pair. Also, this algorithm is a useful alternative to random generation of irregular codes because it enables to exploit the structural properties of the regular code in efficiently storing the resultant irregular code.