We propose parallel rate-variable punctured convolutional coded PPM in photon communication to achieve high energy information efficiency Ie for desired bit error rate (BER) and transmission bandwidth. We theoretically show the BER performance, bandwidth expansion factor β and necessary Ie to achieve BER=10-6 of the proposed systems for some combinations of code rates. It is found that the proposed system can achieve high Ie for desired BER and β by selecting a suitable combination of code rates depending on the channel conditions. Moreover, it is shown that the proposed system has better BER performance than RS-coded PPM in the range of small β.

In this letter, we study low-density parity-check (LDPC) codes for noisy channels with insertion and deletion (ID) errors. We first propose a design method of irregular LDPC codes for such channels, which can be used to simultaneously obtain degree distributions for different noise levels. We then show the asymptotic/finite-length decoding performances of designed codes and compare them with the symmetric information rates of cascaded ID-noisy channels. Moreover, we examine the relationship between decoding performance and a code structure of irregular LDPC codes.

We propose the coherent subcarrier multiplexed (SCM) system with distributing local oscillator (LO) in local loop. The proposed system can realize multichannel transmission with one optical carrier by using the SCM technique and has no need to have LO at each station. Therefore the proposed system becomes cost-effective. The proposed SCM system uses bandpass filter to select a specific channel. We analyze CNR of the system with frequency-shift keying (FSK) in a multioctave configuration. First, the general expression of CNR is derived and is shown for the following parameters such as the number of channels, the position of station on the loop, and the number of stations on the loop. Second, optimal phase modulation (PM) index is derived, and the optimal CNR, minimum required power of lasers, and maximum number of stations that the proposed system can serve are shown by using it. Moreover CNR of the proposed system is compared with that of the system having LO at each station in local loop. It is shown that the proposed system can obtain good performance at the expense of slight increase of the output power of only two lasers at the central station. Therefore the proposed system is cost-effective and practical.

Over the past two decades, irregular low-density parity-check (LDPC) codes have not been able to decode information corrupted by insertion and deletion (ID) errors without markers. In this paper, we bring to light the existence of irregular LDPC codes that approach the symmetric information rates (SIR) of the channel with ID errors, even without markers. These codes have peculiar shapes in their check-node degree distributions. Specifically, the check-node degrees are scattered and there are degree-2 check nodes. We propose a code construction method based on the progressive edge-growth algorithm tailored for the scattered check-node degree distributions, which enables the SIR-approaching codes to progress in the finite-length regime. Moreover, the SIR-approaching codes demonstrate asymptotic and finite-length performance that outperform the existing counterparts, namely, concatenated coding of irregular LDPC codes with markers and spatially coupled LDPC codes.

This paper proposes and theoretically evaluates two different schemes of code acquisition for pulse-position modulation (PPM) and overlapping PPM (OPPM) fiber-optic code-division multiple-access (CDMA) systems, namely threshold-based and demodulator-based code acquisition. Single-dwell detector and serial-search algorithm are employed for both schemes. Theoretical analysis is carried out for shot-noise-limited photon-counting receiver. Discussions upon effects of various parameter settings on the performance of code acquisition for PPM/OPPM fiber-optic CDMA systems, such as index of overlap, PPM/OPPM multiplicity, average photon counts per information nat, and darkcurrents, are presented. It is shown that when the threshold is properly selected, the threshold-based code acquisition system offers better performance, in terms of mean number of training frames, than the demodulator-based one.

We propose a coding/decoding strategy that surpasses the symmetric information rate of a binary insertion/deletion (ID) channel and approaches the Markov capacity of the channel. The proposed codes comprise inner trellis codes and outer irregular low-density parity-check (LDPC) codes. The trellis codes are designed to mimic the transition probabilities of a Markov input process that achieves a high information rate, whereas the LDPC codes are designed to maximize an iterative decoding threshold in the superchannel (concatenation of the ID channels and trellis codes).

We investigate dispersion compensation using dispersion-compensating fibers (DCFs) for ultrashort light pulse code division multiple access (CDMA) communication systems in a multi-user environment. We employ fiber link that consists of a standard single-mode fiber (SMF) connected with two different types of DCFs. Fiber dispersion can be effectively decreased by adjusting the length ratios of DCFs to SMF appropriately. Some criteria for dispersion compensation are proposed and their performances are compared. We theoretically derive a bit error rate (BER) of ultrashort light pulse CDMA systems including the effects of the dispersion and multiple access interference (MAI). Moreover, we reveal the mutual relations among BER performance, fiber dispersion, MAI, the number of chips, a bandwidth of a signal, and a transmission distance for the first time. As a result, we show that our compensation strategy improves system performance drastically.

We theoretically analyze the performance of coherent ultrashort light pulse code-division multiple-access (CDMA) communication systems with a nonlinear optical thresholder. The coherent ultrashort light pulse CDMA is a promising system for an optical local area network (LAN) due to its advantages of asynchronous transmission, high information security, multiple access capability, and optical processing. The nonlinear optical thresholder is based on frequency chirping induced by self-phase modulation (SPM) in optical fiber, and discriminates an ultrashort pulse from multiple access interference (MAI) with picosecond duration. The numerical results show that the thermal noise caused in a photodetector dominates the bit error rate (BER). BER decreases as the fiber length in the nonlinear thresholder and the photocurrent difference in the photodetector increase. Using the nonlinear optical thresholder allows for the response time of the photodetector to be at least 100 times the duration of the ultrashort pulses. We also show that the optimum cut-off frequency at the nonlinear thresholder to achieve the minimum BER increases with fiber length, the total number of users, and the load resistance in the photodetector.

We propose Polarization-Shift-Keying (POLSK) homodyne system using phase-diversity receivers and theoretically analyze its bit-error-rate (BER) performance. Since the proposed system uses polarization modulation and homodyne detection, it can cancel the phase noise and is attractive at a high bit-rate transmission. It is found that the receiver sensitivity of the proposed POLSK homodyne system is the same as that of POLSK heterodyne system and is much better than that of DPSK phase-diversity homodyne systems at high signal-to-noise ratio (SNR). We also cosider theoretically the effect of the fluctuation of state of polarization (SOP) on the BER performance of POLSK homodyne system.

The nonuniformity of signal constellation on coded phase/frequency modulation is investigated to obtain further improvement on the error performance over conventional uniformly spaced coded phase/frequency modulation. The analytical method for evaluating the Euclidean distance of nonuniform FSK/PSK signal is presented. In particular, the joint design of m/(m1) systematic convolutional encoders and nonuniform 2FSK/2mPSK are considered, and especially for 2FSK/4PSK and 2FSK/8PSK the behavior of the free Euclidean distance is evaluated by varying the modulation index, the rotation angles which determine the nonuniform signal constellation, and the mapping rule by set partitioning. The results show that by designing compared with the conventional coded uniform phase/frequency modulation may be obtained without increasing average or peak power or changing the bandwidth of the transmitted signals. The maximum value of the free Euclidean distance of codes can be obtained when the PSK signal constellation of one carrier frequency is the same as those of the other carrier frequency, and the mapping rule used in coded uniform FSK/PSK system is not always good enough when the nonuniformity in the signal constellation is introduced.

The capacity of Multi-pulse PPM (MPPM) and performance of Reed-Solomon coded MPPM in optical photon communications are evaluated. Transmission rate, energy efficiency and error probability of MPPM are presented for noiseless channel. It is shown that MPPM yields higher limits of energy efficiencies as well as transmission rate than PPM in band limited channel. Moreover, it is shown that MPPM combined with Reed-Solomon (RS) codes achieves higher energy efficiency of more than twice as that of RS coded PPM, which McEliece studied, in practical range of error probability.

For insertion and deletion channels, there are many coding schemes based on low-density parity-check (LDPC) codes, such as spatially coupled (SC) LDPC codes and concatenated codes of irregular LDPC codes and markers. However, most of the previous works have problems, such as poor finite-length performance and unrealistic settings for codeword lengths and decoding iterations. Moreover, when using markers, the decoder receives log-likelihood (LLR) messages with different statistics depending on code bit position. In this paper, we propose a novel concatenation scheme using protograph-based LDPC code and markers that offers excellent asymptotic/finite-length performance and a structure that controls the irregularity of LLR messages. We also present a density evolution analysis and a simple optimization procedure for the proposed concatenated coding scheme. For two decoding scenarios involving decoding complexity, both asymptotic decoding thresholds and finite-length performance demonstrate that the newly designed concatenated coding scheme outperforms the existing counterparts: the irregular LDPC code with markers, the SC-LDPC code, and the protograph LDPC code, which is optimized for an additive white Gaussian noise channel, with markers.

We propose parallel rate-variable punctured convolutional coded PPM in photon communication to achieve high energy information efficiency Ie for desired bit error rate (BER) and transmission bandwidth. We theoretically show the BER performance, bandwidth expansion factor β and necessary Ie to achieve BER10-6 of the proposed systems for some combinations of code rates. It is found that the proposed system can achieve high Ie for desired BER and β by selecting a suitable combination of code rates depending on the channel conditions. Moreover, it is showm that the proposed system has better BER performance than RS-coded PPM in the range of small β.

We propose Polarization-Shift-Keying (POLSK) homodyne system using phase-diversity receivers and theoretically analyze its bit-error-rate (BER) performance. Since the proposed system uses polarization modulation and homodyne detection, it can cancel the phase noise and is attractive at a high bit-rate transmission. It is found that the receiver sensitivity of the proposed POLSK homodyne system is the same as that of POLSK heterodyne system and is much better than that of DPSK phase-diversity homodyne systems at high signal-to-noise ratio (SNR). We also cosider theoreically the effect of the fluctuation of state of polarization (SOP) on the BER performance of POLSK homodyne system.

A fast Viterbi decoding technique with path reduction in optical channels is presented. This decoding exploits the asymmetric characteristic of optical channels. In the decoding trellis, the branches with low or no possibility being correct path are eliminated based on the detected signal level. The number of Add-Compare-Select (ACS) operations which occupy the dominant part of Viterbi decoding is considerably reduced due to branch eliminations, and fast decoding is realized by decoding asynchronously to received sequence. The reduction of the number of ACS operations is derived for the codes with rate 1/2. It is shown that the number of ACS operations is considerably reduced compared with the conventional Viterbi decoding. The bit error probability of the proposed decoding is derived for noiseless photon counting channel. It is also shown that the decoding technique can be applied to the cases using avalanche photo diode (APD) based receiver with dark current noise at a cost of negligible degradation on the bit error probability.

This paper theoretically evaluates the performance of overlapping pulse-position modulation (OPPM) fiber-optic code-division multiple-access (FO-CDMA) systems in the presence of code synchronization errors. The analysis is carried out with a constraint on throughput-pulsewidth product. Discussions on effects of various system parameters, such as timing offset, index of overlap, number of users, are presented. The results show that the OPPM FO-CDMA systems with high index of overlaps have better resistance against imperfect synchronization. In fact, the acceptable performance could be maintained even with timing offsets of up to 30% of chip pulsewidth. On the other hand, strict code synchronization is necessarily required, preferably within a half code chip pulsewidth.

The cutoff rate of Multi-pulse Pulse Position Modulation (MPPM) is evaluated in noiseless photon counting channel. The cutoff rate per slot and the cutoff rate per photon are shown for MPPM. It is found that MPPM performs better than PPM in the practical range of average number of photons per pulse. Moreover, it is shown that, in the case with binary digit, MPPM can be seen as the parallel combination of completely correlated binary erasure channels (BECs). From this perspective, both the capacity and the cutoff rate are investigated. It is shown that the capacity of MPPM is larger than the sum of the capacities of BECs, but that the cutoff rate of MPPM is smaller than the sum of the cutoff rates of BECs when a large number of bits are transmitted in one frame. Therefore, it is found that, when large number of bits are transmitted in one frame, coding/decoding on each BEC independently has advantages in system complexity rather than coding/decoding over BECs jointly to achieve a given bit error probability.

We propose a multiple dwell serial search (MDSS) code acquisition for optical code-division multiple-access (O-CDMA) systems and theoretically analyze its performance. The search/lock strategy (SLS) is used as verification scheme for the multiple dwell detector. The operation of SLS is modeled by finite Markov chain to analyze the performance of the proposed system. Effect of system parameters, such as number of users, threshold and mean photon count per chip, on the performance of the proposed system is investigated. The theoretical result shows that the performance of the proposed system is less sensitive to parameter settings than the conventional single dwell serial search (SDSS) code acquisition system is. In addition, the proposed MDSS code acquisition system offers shorter mean acquisition time than that of conventional SDSS system.

Optical fiber communications require multiple-access schemes to access a shared channel among multiple users. The coherent ultrashort light pulse code-division multiple-access (CDMA) system is one such scheme, and it also offers asynchronous-access communication. This system usually employs 2-level, i.e., binary, m-sequences as signature codes because of their low correlation. If the number of active users is greater than the length of the m-sequence, i.e., code length, distinct m-sequences are used. However, the distinct 2-level m-sequences do not exhibit low correlation, resulting in performance degradation. We therefore propose a coherent ultrashort light pulse CDMA communication system with distinct 4-level, i.e., quaternary, m-sequences to improve system performance when the number of users is greater than the code length. We created the 4-level m-sequences from 2-level m-sequences, and assess the correlation of the 4-level m-sequences. We also theoretically derive the bit error rate (BER) of the proposed system taking into account multiple-access interference (MAI), beat noise, amplified spontaneous emission (ASE), shot noise, and thermal noise. The numerical results show that BER for distinct 4-level m-sequences is more than an order of magnitude smaller than that for distinct 2-level m-sequences. BER is limited by MAI and beat noise when the power of the received signal is high, otherwise BER is limited by ASE, shot noise, and thermal noise.

In racetrack memories (RM), a position error (insertion or deletion error) results from unstable data reading. For position errors in RM with multiple read-heads (RHs), we propose a protograph-based LDPC coded system specified by a protograph and a protograph-aware permutation. The protograph-aware permutation facilitates the design and analysis of the coded system. By solving a multi-objective optimization problem, the coded system attains the properties of fast convergence decoding, a good decoding threshold, and a linear minimum distance growth. In addition, the coded system can adapt to varying numbers of RHs without any modification. The asymptotic decoding thresholds with a limited number of iterations verify the good properties of the system. Furthermore, for varying numbers of RHs, the simulation results with both small and large number of iterations, exhibit excellent decoding performances, both with short and long block lengths, and without error floors.