Short Codes with Mismatched Channel State Information: A Case Study

The rising interest in applications requiring the transmission of small amounts of data has recently lead to the development of accurate performance bounds and of powerful channel codes for the transmission of short-data packets over the AWGN channel. Much less is known about the interaction between error control coding and channel estimation at short blocks when transmitting over channels with states (e.g., fading channels, phase-noise channels, etc...) for the setup where no a priori channel state information (CSI) is available at the transmitter and the receiver. In this paper, we use the mismatched-decoding framework to characterize the fundamental tradeoff occurring in the transmission of short data packet over an AWGN channel with unknown gain that stays constant over the packet. Our analysis for this simplified setup aims at showing the potential of mismatched decoding as a tool to design and analyze transmission strategies for short blocks. We focus on a pragmatic approach where the transmission frame contains a codeword as well as a preamble that is used to estimate the channel (the codeword symbols are not used for channel estimation). Achievability and converse bounds on the block error probability achievable by this approach are provided and compared with simulation results for schemes employing short low-density parity-check codes. Our bounds turn out to predict accurately the optimal trade-off between the preamble length and the redundancy introduced by the channel code.Comment: 5 pages, 5 figures, to appear in Proceedings of the IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2017

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

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-latency Ultra Reliable 5G Communications: Finite-Blocklength Bounds and Coding Schemes

Future autonomous systems require wireless connectivity able to support extremely stringent requirements on both latency and reliability. In this paper, we leverage recent developments in the field of finite-blocklength information theory to illustrate how to optimally design wireless systems in the presence of such stringent constraints. Focusing on a multi-antenna Rayleigh block-fading channel, we obtain bounds on the maximum number of bits that can be transmitted within given bandwidth, latency, and reliability constraints, using an orthogonal frequency-division multiplexing system similar to LTE. These bounds unveil the fundamental interplay between latency, bandwidth, rate, and reliability. Furthermore, they suggest how to optimally use the available spatial and frequency diversity. Finally, we use our bounds to benchmark the performance of an actual coding scheme involving the transmission of short packets

Near-Optimal Coding for Many-user Multiple Access Channels

This paper considers the Gaussian multiple-access channel (MAC) in the asymptotic regime where the number of users grows linearly with the code length. We propose efficient coding schemes based on random linear models with approximate message passing (AMP) decoding and derive the asymptotic error rate achieved for a given user density, user payload (in bits), and user energy. The tradeoff between energy-per-bit and achievable user density (for a fixed user payload and target error rate) is studied, and it is demonstrated that in the large system limit, a spatially coupled coding scheme with AMP decoding achieves near-optimal tradeoffs for a wide range of user densities. Furthermore, in the regime where the user payload is large, we also study the spectral efficiency versus energy-per-bit tradeoff and discuss methods to reduce decoding complexity at large payload sizes.Comment: 35 pages, 4 figures. A shorter version of this paper appeared in ISIT 202

Robust Distributed Estimation over Multiple Access Channels with Constant Modulus Signaling

A distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered. The proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i.i.d. case both for a per-sensor power constraint, and a total power constraint. When the distributions of the sensing noise are not identical, a bound on the variances is shown to establish strong consistency. The estimator is shown to be asymptotically normal with a variance (AsV) that depends on the characteristic function of the sensing noise. Optimization of the AsV is considered with respect to a transmission phase parameter for a variety of noise distributions exhibiting differing levels of impulsive behavior. The robustness of the estimator to impulsive sensing noise distributions such as those with positive excess kurtosis, or those that do not have finite moments is shown. The proposed estimator is favorably compared with the amplify and forward scheme under an impulsive noise scenario. The effect of fading is shown to not affect the consistency of the estimator, but to scale the asymptotic variance by a constant fading penalty depending on the fading statistics. Simulations corroborate our analytical results.Comment: 28 pages, 10 figures, submitted to IEEE Transactions on Signal Processing for consideratio