On the Coding Gain of Polar Codes for High Speed Communications over AWGN Channels
Tufail Ahmad, Farhan Khan · 2020
Polar codes are the first provably capacity achieving codes for any symmetric binary-input discrete memory-less channel. 3GPP has recently approved polar codes as the official coding scheme for the control channels of 5G wireless systems. Next generation wireless systems are intended to provide extremely high data speeds as are being provided by the currently deployed optical systems. In literature, myriads of forward error correction (FEC) codes have already been analyzed for optical networks to provide data rates as high as of the order of 10 Gb/sec. To appreciate the coding gain of polar codes for extremely high data rates in next generation radio systems, results of variety of FEC schemes employed in optical communications are used here as benchmark for comparison. In this paper, Polar codes are evaluated in terms of error correction (EC) performance and design method for high speed communications and the comparison made with other FEC codes is useful for both optical and wireless networks in high data rate arena over AWGN channels. Modern optical transport networks (OTNs) cannot support retransmission of the corrupted data due to high volume of data traffic. OTNs require strong FEC schemes to provide an output bit error rate (BER) of 10−15or lower. Error performance of a channel code is usually described by its net coding gain (NCG) in communications. Coding gain for FEC codes of larger and moderate block lengths cannot be determined explicitly by Monte Carlo (MC) simulations at high signal to noise ratio (SNR) due to prohibitive simulations time. For polar codes, even for very large block lengths, a much simpler algorithm i.e.; density evolution with Gaussian approximation (DE-GA) is used in this paper for code construction and error rate calculation in high SNR regime. Usually Shannons theoretical limits of error performance are used to calculate maximum NCG that a code can achieve asymptotically, but comparing the performance of a finite length code to the asymptotic performance is not fair. This paper also calculates the maximum NCG that can be achieved by a FEC code with finite block length to make performance comparisons more meaningful and practical. The paper presents a brief survey of G.975.1 recommended and recently proposed third generation FEC codes for optical communications, and investigates whether polar codes, with the same overhead and block lengths, can fare with these FEC schemes in terms of EC performance. Most of the proposed FEC codes for next generation OTNs, based on LDPC and turbo codes, have error floors in low BER regime. Empirical code designs and heuristics help to push down their error floors and improve performance at the cost of extra complexity. Polar codes do not have error floors and are designed easily using DE-GA. Analysis of polar codes in this paper is restricted to its successive cancellation (SC) decoding as it provides a nice balance between complexity and EC performance.