Polar codes for optical communications

Abstract

Optical communication systems have become the backbone of long distance communication networks due to their ability to transport data at high rates. A typical modern optical communication system should be capable to achieve data rates of 100 Gb/s or beyond. At such a high data rate, it is not feasible to retransmit the corrupted data. For reliable communication at improved power efficiency, communication systems use forward error correction (FEC) schemes. FEC schemes should have low latency to provide high throughput and good error performance to achieve an output bit error rate (BER) of 10−15 or lower in optical channels. Moreover, implementation schemes of these FEC codes should be simple, as telecommunications equipments in optical access networks can only accommodate restricted hardware complexity. In this contribution, we study existing ITU-T G.975.1 recommended FEC schemes and recently proposed state-of-the-art FEC codes for optical networks. Next, we analyze polar codes, a recently proposed class of error-correcting codes with advantageous properties in terms of error performance, structure, latency and design method. Throughout our analysis we assume that optical channels can be modeled as additive white Gaussian noise (AWGN) channels. We investigate whether polar codes can compete with the above mentioned FEC schemes in the arena of optical communications. We conclude that polar codes outdo all G.975.1 recommended FEC codes in terms of error performance with the same overhead and relatively shorter block lengths. We also highlight some of the issues/aspects which need to be addressed to enhance the error performance of polar codes at finite block lengths so that they can catch up with (or surpass) recently proposed third generation FEC codes. Most of the proposed FEC codes for next generation optical networks are based on LDPC and turbo codes. Unfortunately, these codes have error floors at very low BER. Post-processing algorithms along with special construction techniques for these codes are proposed in literature to suppress their error floors. These special designs improve their error performance at the cost of extra complexity. Luckily, polar codes do not suffer from error floor problem in low BER regions. Moreover, polar codes have regular structure which makes its hardware implementation simple. There are various polar decoders proposed in literature with desirable properties in terms of error performance and complexity. These features make polar code an attractive candidate to be thoroughly analyzed for application in optical communications. Our analysis of polar codes in this thesis is restricted to its successive cancellation (SC) decoding as it provides a nice balance between complexity and error performance. Error performance of polar codes with larger and moderate block lengths cannot be determined explicitly by Monte Carlo (MC) simulations for optical communication systems operating at high signal to noise ratio (SNR) due to prohibitive simulations time. To make sure that polar codes perform well in low BER regions, we use analytical methods to find bounds on their error rate. We use density evolution (DE) with Gaussian approximation (GA) for the construction and error performance estimation of polar codes. We conclude that DE-GA is a reliable algorithm for construction and error performance evaluation of polar codes by observing that our results obtained with simulations and DE-GA algorithm in low SNR region agree close enough to expect that there will not be too much deviation in high SNR region. The performance of a code in optical communications is usually described by its net coding gain (NCG). Using Shannon’s performance limits, maximum value of NCG that a FEC can achieve asymptotically can be calculated . But comparing the performance of a finite length code to the asymptotic performance of a FEC is not fair. Therefore in this thesis, we calculate the maximum NCG that can be achieved by a FEC with finite block length to make our performance comparisons more meaningful.