Low-density parity check codes and iterative decoding for long-haul optical communication systems

Abstract

A forward-error correction)FEC) scheme based on low-density parity check (LDPC) codes and iterative decoding using belief propagation in code graphs is presented in this paper. We show that LDPC codes provide a significant system performance improvement with respect to the state-of-the-art FEC schemes employed in optical communications systems. We present a class of structured codes based on mutually orthogonal Latin rectangles. Such codes have high rates and can lend themselves to very low-complexity encoder/decoder implementations. The system performance is further improved by a code design that eliminates short cycles in a graph employed in iterative decoding. Index Terms-Balanced incomplete block designs (BIBDs), belief propagation algorithm, forward-error correction (FEC), long-haul transmission, low-density parity check(LDPC) codes, optical communications.

Projective-Plane Iteratively Decodable Block Codes for WDM High-Speed Long-Haul Transmission Systems

“…(The derivation of the expressions (4) and (5) is given in our previous paper [20].) The autocorrelation function of the optical filter output noise can be expressed as (6) where is the optical filter autocorrelation function. Notice that the photodiode output noise process is not stationary (the mean values and the standard deviation are functions of time).…”

“…Ait Sab proposed a concatenated scheme with two Reed-Solomon (RS) codes and another scheme with block turbo codes (BTCs) [3]- [5]. In a series of recent articles, we showed that error performance and decoder hardware complexity offered by turbo codes can be greatly improved by using other types of iteratively decodable coding schemes, in particular low-density parity-check (LDPC) codes [2], [6]. The LDPC codes have been shown to perform approximately within 0.005 dB of the Shannon limit on an additive white Gaussian noise (AWGN) channel (rate 1/2, codeword size of ) [7], breaking the record previously set by turbo codes.…”

“…For example, Agere Systems have reportedly built an optical networking interface device with four parallel RS codecs, each operating at 2.5 Gb/s [28]. Several well-known systematic construction methods for LDPC codes [2], [6], [17], [25] provide parity-check matrices with cyclic or quasi-cyclic structures, thereby reducing the hardware complexity of LDPC encoders and decoders.…”

“…In [2], [6], and [25], we presented systematic LDPC code constructions based on rectangular lattices, mutually orthogonal Latin squares, and projective geometry (PG), respectively. These codes have many favorable features, namely high code rate and large minimum distance, and they support simple encoders, realized using shift registers, and simple iterative decoding algorithms.…”

Beyond 240 Gb/s per Wavelength Optical Transmission Using Coded Hybrid Subcarrier/Amplitude/Phase/Polarization Modulation

“…At any symbol rate and code rate, H-SAPP is capable of achieving the aggregate rate of the individual HAPP systems it is composed of, without introducing any bit-error-ratio (BER) performance degradation, as long as the orthogonality among subcarriers is preserved. In this letter, coding is done using structured low-density parity-check (LDPC) codes [1]. Structured LDPC codes are chosen for this scheme to allow easier iterative exchange of the extrinsic soft bit reliabilities between the equalizer and the LDPC decoder, and to reduce the encoding complexity in comparison to the random codes, as encoding is done using linear shift register circuitry.…”