Performance Analysis of Block Codes over Finite-state Channels in Delay-sensitive Communications

As the mobile application landscape expands, wireless networks are tasked with supporting different connection profiles, including real-time traffic and delay-sensitive communications. Among many ensuing engineering challenges is the need to better understand the fundamental limits of forward error correction in non-asymptotic regimes. This dissertation seeks to characterize the performance of block codes over finite-state channels with memory and also evaluate their queueing performance under different encoding/decoding schemes. In particular, a fading formulation is considered where a discrete channel with correlation over time introduces errors. For carefully selected channel models and arrival processes, a tractable Markov structure composed of queue length and channel state is identified. This facilitates the analysis of the stationary behavior of the system, leading to evaluation criteria such as bounds on the probability of the queue exceeding a threshold. Specifically, this dissertation focuses on system models with scalable arrival profiles based on Poisson processes, and finite-state memory channels. These assumptions permit the rigorous comparison of system performance for codes with arbitrary block lengths and code rates. Based on this characterization, it is possible to optimize code parameters for delay-sensitive applications over various channels. Random codes and BCH codes are then employed as means to study the relationship between code-rate selection and the queueing performance of point-to-point data links. The introduced methodology offers a new perspective on the joint queueing-coding analysis for finite-state channels, and is supported by numerical simulations. Furthermore, classical results from information theory are revisited in the context of channels with rare transitions, and bounds on the probabilities of decoding failure are derived for random codes. An analysis framework is presented where channel dependencies within and across code words are preserved. The results are subsequently integrated into a queueing formulation. It is shown that for current formulation, the performance analysis based on upper bounds provides a good estimate of both the system performance and the optimum code parameters. Overall, this study offers new insights about the impact of channel correlation on the performance of delay-aware communications and provides novel guidelines to select optimum code rates and block lengths

Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no \emph{a priori} channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, for the case when a coded packet of $168$ symbols is transmitted using a channel code of rate $0.48$ bits/channel use, over a block-fading channel with block size equal to $8$ symbols, PAT requires an additional $1.2$ dB of energy per information bit to achieve a packet error probability of $10^{-3}$ compared to a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics decoding, whose performance are close ($1$ dB gap at $10^{-3}$ packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa

Irregular Turbo Codes in Block-Fading Channels

We study irregular binary turbo codes over non-ergodic block-fading channels. We first propose an extension of channel multiplexers initially designed for regular turbo codes. We then show that, using these multiplexers, irregular turbo codes that exhibit a small decoding threshold over the ergodic Gaussian-noise channel perform very close to the outage probability on block-fading channels, from both density evolution and finite-length perspectives.Comment: to be presented at the IEEE International Symposium on Information Theory, 201

Finite-Blocklength Bounds on the Maximum Coding Rate of Rician Fading Channels with Applications to Pilot-Assisted Transmission

We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state information is available at the receiver, allow one to quantify the tradeoff between the rate gains resulting from the exploitation of time-frequency diversity and the rate loss resulting from fast channel variations and pilot-symbol overhead

Low-Complexity Joint Channel Estimation and List Decoding of Short Codes

A pilot-assisted transmission (PAT) scheme is proposed for short blocklengths, where the pilots are used only to derive an initial channel estimate for the list construction step. The final decision of the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. The method is applied to an ordered statistics decoder for communication over a Rayleigh block-fading channel. Gains of up to $1.2$ dB as compared to traditional PAT schemes are demonstrated for short codes with QPSK signaling. The approach can be generalized to other list decoders, e.g., to list decoding of polar codes.Comment: Accepted at the 12th International ITG Conference on Systems, Communications and Coding (SCC 2019), Rostock, German

Low-Density Parity-Check Codes for Nonergodic Block-Fading Channels

We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Unfortunately, optimal constructions for maximum-likelihood decoding do not perform well under iterative decoding. To overcome this limitation, we then introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes with multiplexed parallel turbo codes suitable for nonergodic channels and recently reported in the literature.Comment: Submitted to the IEEE Transactions on Information Theor