High-SNR Asymptotics of Mutual Information for Discrete Constellations with Applications to BICM

Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.Research supported by the European Community’s Seventh’s Framework Programme (FP7/2007-2013) under grant agreements No. 271986 and No. 333680, by the Swedish Research Council, Sweden (under grants #621-2006-4872 and #621-2011-5950) and by the Ministerio de Economía y Competitividad of Spain (TEC2009-14504-C02-01, CSD2008-00010, and TEC2012-38800-C03-01)

LDPC codes for optical channels: Is the "FEC limit" a good predictor of post-FEC BER?

We answer the question in the title negatively. More precisely, the FEC limit is invalid for soft decision decoding and low to medium code rates. A better predictor is the generalized mutual information

Amplifier Limited Information Rates in High-Speed Optical Fiber Communication Systems

Due to the high transmission capacity, optical fiber systems have been extensively applied, as significant components, in the modern telecommunication infrastructure to meet the ever-increasing demand of data traffic. Optical amplifiers have been employed to amplify optical signals and to compensate for the transmission losses. They play a key role in relaying the signals in ultra-wideband optical fiber communication systems. However, the amplified spontaneous emission (ASE) noise will be introduced during such process, and it will degrade the performance of optical fiber systems and will pose constraints on the transmission information rates. The mutual information (MI) and the generalized mutual information (GMI) have been applied and investigated, as figures of merit, to evaluate the information rates in communication systems. The MI measures the highest achievable information rate (bits per symbol) that can be realized in a channel based on ideal symbol-wise encoder and decoder. The GMI, also known as the bit-interleaved coded modulation (BICM) capacity, indicates an upper bound on the number of bits per symbol that can be reliably transmitted through a channel based on the bit-wise decoding. Although the MI and the GMI are equal when the signal-to-noise ratio (SNR) tends to infinity, the MI is strictly higher than the GMI in any practical transmission scenarios. This discrepancy depends on the constellation cardinality and the binary labeling. In this work, we have investigated the impact of ASE noise on the MI and the GMI, and have developed corresponding analyses and estimations across different modulation formats, in linear optical fiber communication systems. Our work aims to explore the limit and requirements on optical amplifiers and to provide a comprehensive insight for the design of next-generation ultra-wideband optical fiber communication systems

Amplifier limited information rates in high-speed optical fiber communication systems

Due to the high transmission capacity, optical fiber systems have been widely applied in the modern telecommunication infrastructure to meet the ever-increasing demand of data traffic. Optical amplifiers have been employed to amplify optical signals and to compensate for the transmission losses. They play a key role in relaying the signals in ultra-wideband optical fiber communication systems. However, the amplified spontaneous emission (ASE) noise will be introduced and will pose constraints on the transmission information rates. The mutual information (MI) and the generalized mutual information (GMI) have been applied to evaluate the information rates in communication systems. In this work, we have investigated the impact of ASE noise on the MI and the GMI, and developed corresponding analyses across different modulation formats. Our work aims to explore the limit and requirements on optical amplifiers in next-generation ultra-wideband optical fiber communication systems

Bit-Wise Decoders for Coded Modulation and Broadcast Coded Slotted ALOHA

This thesis deals with two aspects of wireless communications. The first aspect is about efficient point-to-point data transmission. To achieve high spectral efficiency, coded modulation, which is a concatenation of higher order modulation with error correction coding, is used. Bit-interleaved coded modulation (BICM) is a pragmatic approach to coded modulation, where soft information on encoded bits is calculated at the receiver and passed to a bit-wise decoder. Soft information is usually obtained in the form of log-likelihood ratios (also known as L-values), calculated using the max-log approximation. In this thesis, we analyze bit-wise decoders for pulse-amplitude modulation (PAM) constellations over the additive white Gaussian noise (AWGN) channel when the max-log approximation is used for calculating L-values. First, we analyze BICM systems from an information theoretic perspective. We prove that the max-log approximation causes information loss for all PAM constellations and labelings with the exception of a symmetric 4-PAM constellation labeled with a Gray code. We then analyze how the max-log approximation affects the generalized mutual information (GMI), which is an achievable rate for a standard BICM decoder. Second, we compare the performance of the standard BICM decoder with that of the ML decoder. We show that, when the signal-to-noise ratio (SNR) goes to infinity, the loss in terms of pairwise error probability is bounded by 1.25 dB for any two codewords. The analysis further shows that the loss is zero for a wide range of linear codes. The second aspect of wireless communications treated in this thesis is multiple channel access. Our main objective here is to provide reliable message exchange between nodes in a wireless ad hoc network with stringent delay constraints. To that end, we propose an uncoordinated medium access control protocol, termed all-to-all broadcast coded slotted ALOHA (B-CSA), that exploits coding over packets at the transmitter side and successive interference cancellation at the receiver side. The protocol resembles low-density parity-check codes and can be analyzed using the theory of codes on graphs. The packet loss rate performance of the protocol exhibits a threshold behavior with distinct error floor and waterfall regions. We derive a tight error floor approximation that is used for the optimization of the protocol. We also show how the error floor approximation can be used to design protocols for networks, where users have different reliability requirements. We use B-CSA in vehicular networks and show that it outperforms carrier sense multiple access currently adopted as the MAC protocol for vehicular communications. Finally, we investigate the possibility of establishing a handshake in vehicular networks by means of B-CSA