Diagnosis of weaknesses in modern error correction codes: a physics approach

One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the Bit-Error-Rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.Comment: 9 pages, 8 figure

Optical Time-Frequency Packing: Principles, Design, Implementation, and Experimental Demonstration

Time-frequency packing (TFP) transmission provides the highest achievable spectral efficiency with a constrained symbol alphabet and detector complexity. In this work, the application of the TFP technique to fiber-optic systems is investigated and experimentally demonstrated. The main theoretical aspects, design guidelines, and implementation issues are discussed, focusing on those aspects which are peculiar to TFP systems. In particular, adaptive compensation of propagation impairments, matched filtering, and maximum a posteriori probability detection are obtained by a combination of a butterfly equalizer and four 8-state parallel Bahl-Cocke-Jelinek-Raviv (BCJR) detectors. A novel algorithm that ensures adaptive equalization, channel estimation, and a proper distribution of tasks between the equalizer and BCJR detectors is proposed. A set of irregular low-density parity-check codes with different rates is designed to operate at low error rates and approach the spectral efficiency limit achievable by TFP at different signal-to-noise ratios. An experimental demonstration of the designed system is finally provided with five dual-polarization QPSK-modulated optical carriers, densely packed in a 100 GHz bandwidth, employing a recirculating loop to test the performance of the system at different transmission distances.Comment: This paper has been accepted for publication in the IEEE/OSA Journal of Lightwave Technolog

Graph-Based Decoding in the Presence of ISI

We propose an approximation of maximum-likelihood detection in ISI channels based on linear programming or message passing. We convert the detection problem into a binary decoding problem, which can be easily combined with LDPC decoding. We show that, for a certain class of channels and in the absence of coding, the proposed technique provides the exact ML solution without an exponential complexity in the size of channel memory, while for some other channels, this method has a non-diminishing probability of failure as SNR increases. Some analysis is provided for the error events of the proposed technique under linear programming.Comment: 25 pages, 8 figures, Submitted to IEEE Transactions on Information Theor

Non-Binary Message-Passing Algorithms for Magnetic Channels with Data-Dependent Noise

The paper proposes an implementation of the message passing algorithm adapted to iterative channel detection. The algorithm uses soft messages associated to non binary symbols in order to cancel cycles in the equivalent Tanner graphs, achieving optimal performance after a low number of iterations. This architecture, suited to very fast channel detectors, is applied to magnetic recording channels and adapted to the non stationary nature of the magnetic media noise

Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission

We consider a nonlinear Fourier transform (NFT)-based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a probabilistic eigenvalue shaping (PES) scheme as a means to increase the data rate of the system. We exploit the fact that for an NFT-based transmission scheme the pulses in the time domain are of unequal duration by transmitting them with a dynamic symbol interval and find a capacity-achieving distribution. The PES scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a low-density parity-check encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed PES scheme. We verify our results with simulations of the discrete-time model as well as with split-step Fourier simulations.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

Modeling Of Power Line Communication Channel For Automatic Meter Reading System With LDPC Codes

In this era of modernization, one of the promising emerging technologies is Power Line Communication (PLC) system. In previous research fields, modeling of PLC channel, mostly for indoor applications has been studied. However, the need to study that for outdoor applications, such as the Automatic Meter Reading (AMR) systems is also vital. Moreover, standardization bodies have considered the use of LDPC codes restricted for indoor systems. Thus, in this paper, not only we model the PLC channel based on AMR applications, but also, we apply LDPC coding scheme to the system. To accomplish the objectives, firstly, we model the PLC-AMR channel, which includes multipath phenomenon. Additionally, PLC noise, usually occurring in the channel, is modeled. The modulation technique applied is BPSK and the performance of the system with varying load impedances is compared. The coded system consists of irregular LDPC codes, with two different constructions of the Parity-Check matrix, namely that by Radford Neal and reduced size of DVBS2. The performances of respective systems are then compared. Using LDPC by Radford Neal, the performances are analyzed with varied code rates