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A transmitter sends a packetized message over a fading channel using packet-level erasure coding and physical-layer channel coding of each resultant packet. Given an overall code rate, this paper finds the optimal rates of the erasure code and the channel code to minimize the transmit power required for a certain message error probability. This paper considers a practically important fading model in which the number of block fades in a transmitted channel codeword increases with the codeword length. Such a model applies, for example, in a time-varying channel with a fixed coherence time. The rate at which diversity grows with codeword length plays an important role in the optimization problem. If the diversity growth factor is large enough, then the erasure code plays a minor role, having an optimal rate that is essentially nondecreasing with decreasing overall rate. We prove analytically that, on a channel with linear growth in diversity, as overall rate decreases, the optimal erasure code rate eventually increases to its maximum possible value (e.g., a rate of 1 for an erasure code with no overhead). Additionally, we also consider the optimization problem of minimizing the message error probability given a transmit power. Numerical results again show that erasure coding is not necessary when overall code rates are sufficiently low. [ABSTRACT FROM PUBLISHER]

This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal approximation on the rate for successful decoding. Applying this approach to a variety of feedback systems using nonbinary (NB) low-density parity-check (LDPC) codes shows that greater than 90% of capacity can be achieved with average blocklengths fewer than 500 transmitted bits. One result is that the performance with ten increments closely approaches the performance with an infinite number of increments. The paper focuses on binary-input additive-white Gaussian noise (BI-AWGN) channels but also demonstrates that the normal approximation works well on examples of fading channels as well as high-SNR AWGN channels that require larger QAM constellations. This paper explores both variable-length feedback codes with termination (VLFT) and the more practical variable length feedback (VLF) codes without termination that require no assumption of noiseless transmitter confirmation. For VLF, we consider both a two-phase scheme and CRC-based scheme. [ABSTRACT FROM AUTHOR]

Root and Varaiya proved the existence of a code that can communicate reliably over any linear Gaussian channel for which the channel mutual information level exceeds the transmitted rate. This paper provides several examples of scalar (single-input single-output) fading channels and shows that on these channels the performance of low-density parity-check (LDPC) codes lies in close proximity to the performance limits identified by Root and Varaiya. Specifically, we consider periodic fading channels and partial-band jamming (PBJ) channels. A special case of periodic fading is the variation of signal-to-noise ratio across orthogonal frequency division modulation sub-channels. The robustness of LDPC codes to periodic fading and PBJ across parameterizations of these different channels is demonstrated through the consistency of the required mutual information to provide a specified bit error rate. For the periodic fading case, the Gaussian approximation to density evolution has been adapted such that asymptotic threshold measures can be compared to simulated code performance in various periodic fading scenarios. [ABSTRACT FROM AUTHOR]

Foschini's diagonally layered space-time transmission system known as D-BLAST is an architecture designed for a Rayleigh fading environment using multiple element antenna arrays at both the transmit and receive sites to achieve very high spectral efficiencies. In this paper, we propose a simple coding technique for D-BLAST that uses a single trellis code with finite-traceback Viterbi decoding. We examine the performance of universal trellis codes that are designed to have a distance structure that is matched to the periodic signal-to-noise ratio (SNR) variation of the channel created by D-BLAST, under the assumption that the channel is static during one burst but may change from burst to burst. We show that a universal 64-state trellis code on a 2 × 2 D-BLAST system with long enough blocklengths displays universal behavior working on almost every 2 × 2 channel with at least the mutual information required by a standard 64-state AWGN trellis code. The only 2 × 2 channel where more mutual information is required is a certain rotation of the zero eigenvalue channel. We also presnt 4 × 4 and 8 × 8 examples. [ABSTRACT FROM AUTHOR]

This correspondence gives practical examples of space-time trellis codes performing as predicted by Root and Varaiya's compound channel theorem. Specifically, 32-state and 64-state 2 × 2 space-time trellis codes are presented that provide a bit-error rate (BER) of 10[sup -5] on all 2 × 2 matrix channels with an excess mutual information (MI) within 8% of the excess MI required by standard trellis codes of the same complexity operating only in additive white Gaussian noise (AWGN). Not surprisingly, the universal space-time trellis-coded modulations (ST-TCMs) provide average bit- and frame-error rates in quasi-static Rayleigh fading (QRF) that are comparable to those achieved by ST-TCMs designed specifically for QRF as well as standard TCMs followed by the Alamouti space-time block code. However, all of these other schemes require more excess MI in the worst case, and some have a significantly wider variation in the required excess MI. The correspondence also compares the universal and quasi-static Rayleigh fading design approaches analytically and bounds the worst case distance of a trellis code on a 2 × 2 channel using the distances of the code on singular and unitary channels. This bound is extended to the more general n[sub T] × n[sub R] scenario. [ABSTRACT FROM AUTHOR]

Proposes a Markov model to approximate the values and statistical properties of the correlated flat Rayleigh fading. Discussion on the channel model for Rayleigh fading; Algorithms for the Markov model for the phase process; Derivation of capacity bounds for a simplified discrete Markov channel.

For a block-fading channel, this paper optimizes the allocation of redundancy between packet-level erasure coding (which provides additional packets to compensate for packet loss) and physical layer channel coding (which lowers the probability of packet loss). After some manipulation, standard optimization techniques determine the trade-off between the amount of packet-level erasure coding and physical-layer channel coding that minimizes the transmit power required to provide reliable communication. Our results indicate that the optimal combination of packet-level erasure coding and physical-layer coding provides a significant benefit over pure physical-layer coding when no form of channel diversity is present within a packet transmission. However, the benefit of including packet-level erasure coding diminishes as more diversity becomes available within a packet transmission. Even with no diversity within a packet transmission, this paper shows that as the total redundancy becomes large the optimal redundancy for packet-level erasure coding reaches a limit while the optimal redundancy for physical-layer coding continues to increase. Hence providing limitless redundancy at the packet-level with rateless codes such as fountain codes is not the best use of limitless redundancy for block-fading channels. [ABSTRACT FROM PUBLISHER]