We consider the problem of transmitting correlated data after independent encoding to a central receiver through orthogonal channels. We assume that the channel state information is not known at the transmitter. The receiver has access to both the source correlation and the channel state information. We provide a generic framework for analyzing the performance of joint iterative decoding, using density evolution. Using differential evolution, we design punctured systematic LDPC codes to maximize the region of achievable channel conditions, with joint iterative decoding. The main contribution of this paper is to demonstrate that properly designed LDPC can perform well simultaneously over a wide range of channel parameters.
In this paper, we consider spatial-division multiple-access (SDMA) systems with one base station with multiple antennae and a number of single antenna mobiles under noisy limited CSIT feedback. We propose a robust noisy limited feedback design for SDMA systems. The solution consists of a real-time robust SDMA precoding, user selection and rate adaptation as well as an offline feedback index assignment algorithm. The index assignment problem is cast into a Traveling Sales Man problem (TSP). Based on the specific structure of the feedback constellation and the precoder, we derive a low complex b…
The topic of this study is the outage behavior of multiple-antenna slow fading channels with quantized feedback and partial power control. A fixed-rate communication system is considered. It is known from the literature that with error-free feedback, the outage-optimal quantizer for power control has a circular structure. Moreover, the diversity gain of the system increases polynomially with the cardinality of the power control codebook. Here, a similar system is studied, but when the feedback link is error-prone. We prove that in the high-SNR regime, the optimal quantizer structure with noisy…
We address noisy message-passing decoding of lowdensity parity-check (LDPC) codes over additive white Gaussian noise channels. Message-passing decoders in which certain processing units iteratively exchange messages are common for decoding LDPC codes. The exchanged messages are in general subject to internal noise in hardware implementation of these decoders. We model the internal decoder noise as additive white Gaussian noise (AWGN) degrading exchanged messages. Using Gaussian approximation of the exchanged messages, we perform a two-dimensional density evolution analysis for the noisy LDPC d…
In this paper, we consider the performance of the Noisy Gradient Descent Bit Flipping (NGDBF) algorithm under re-decoding of failed frames. NGDBF is a recent algorithm that uses a non-deterministic gradient descent search to decode low-density parity check (LDPC) codes. The proposed re-decode procedure obtains improved performance because the perturbations are independent at each re-decoding phase, therefore increasing the likelihood of successful decoding. We examine the benefits of re-decoding for an LDPC code from the IEEE 802.3an standard, and find that only a small fraction of re-decoded …
The Gaussian $K$-user interference and $M\times K$ X channels are investigated with no instantaneous channel state information (CSI) at transmitters. First, it is assumed that the CSI is fed back to all nodes after a finite delay (delayed CSIT), and furthermore, the transmitters operate in full-duplex mode, i.e., they can transmit and receive simultaneously. Achievable results are obtained on the degrees of freedom (DoF) of these channels under the above assumption. It is observed that, in contrast with no CSIT and full CSIT models, when CSIT is delayed, the achievable DoFs for both channels w…
This paper investigates the Diversity-Multiplexing gain Trade-off (DMT) of a training based reciprocal Single Input Multiple Output (SIMO) system, with (i) perfect Channel State Information (CSI) at the Receiver (CSIR) and noisy CSI at the Transmitter (CSIT), and (ii) noisy CSIR and noisy CSIT. In both the cases, the CSIT is acquired through Reverse Channel Training (RCT), i.e., by sending a training sequence from the receiver to the transmitter. A channel-dependent fixed-power training scheme is proposed for acquiring CSIT, along with a forward-link data transmit power control scheme. With pe…
This work analyses the Generalized Degrees-of-Freedom (GDoF) of the 2-User Multiple-Input Single-Output (MISO) Broadcast Channel (BC) in the so-called Distributed CSIT regime, with application to decentralized wireless networks. This regime differs from the classical limited CSIT one in that the CSIT is not just noisy but also imperfectly shared across the transmitters (TXs). Hence, each TX precodes data on the basis of local CSIT and statistical quality information at other TXs. We derive the GDoF result and obtain the surprising outcome that by specific accounting of the pathloss information…
The asymptotic iterative decoding performances of low-density parity-check (LDPC) codes using min-sum (MS) and sum-product (SP) decoding algorithms on memoryless binary-input output-symmetric (MBIOS) channels are analyzed in this paper. For MS decoding, the analysis is done by upper bounding the bit error probability of the root bit of a tree code by the sequence error probability of a subcode of the tree code assuming the transmission of the all-zero codeword. The result is a recursive upper bound on the bit error probability after each iteration. For SP decoding, we derive a recursively dete…
Reliable communication over delay-constrained block-fading channels with discrete inputs and mismatched (imperfect) channel state information at the transmitter (CSIT) is studied. The CSIT mismatch is modeled as Gaussian random variables, whose variances decay as a power of the signal-to-noise ratio (SNR). A special focus is placed on the large-SNR decay of the outage probability when power control with long-term power constraints is used. Without explicitly characterizing the corresponding power allocation algorithms, we derive the outage exponent as a function of the system parameters, inclu…
This work studies the optimal Degrees-of-Freedom (DoF) of the $K$-User MISO Broadcast Channel (BC) with delayed Channel-State Information at the Transmitter (CSIT) and with additional current noisy CSIT where the current channel estimation error scales in~$P^{-α}$ for $α\in[0,1]$. This papers establishes for the first time the optimal DoF in this setting thanks to a new transmission scheme which achieves the elusive DoF-optimal combining of the Maddah-Ali and Tse scheme (MAT) introduced in their seminal work in $2010$ with Zero-Forcing (ZF) for an arbitrary number of users. The derived sum DoF…
A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported …
We consider a broadcast communication system over parallel sub-channels where the transmitter sends three messages: a common message to two users, and two confidential messages to each user which need to be kept secret from the other user. We assume partial channel state information at the transmitter (CSIT), stemming from noisy channel estimation. The first contribution of this paper is the characterization of the secrecy capacity region boundary as the solution of weighted sum-rate problems, with suitable weights. Partial CSIT is addressed by adding a margin to the estimated channel gains. T…
This paper considers low-density parity-check (LDPC) decoders affected by deviations introduced by the electronic device on which the decoder is implemented. Noisy density evolution (DE) that allows to theoretically study the performance of these LDPC decoders can only consider symmetric deviation models due to the all-zero codeword assumption. A novel DE method is proposed that admits the use of asymmetric deviation models, thus widening the range of faulty implementations that can be analyzed. DE equations are provided for three noisy decoders: belief propagation, Gallager B, and quantized m…
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies limits in processing noisy signals with noisy circuits by investigating the effect of noise on standard iterative decoders for low-density parity-check codes. Concentration of decoding performance around its average is shown to hold when noise is introduced into message-passing and local computation. Density evolution equations for simple faulty iterative decoder…
We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded and transmitted over two independent binary memoryless symmetric channels. Each channel capacity is assumed to be characterized by a single parameter which is not known at the transmitter. The receiver has knowledge of both the source correlation and the channel parameters. We call a system universal if it retains near-capacity performance without channel knowledge at the transmitter. Kudekar et al. recently showed that terminated low-density parity-check (LDPC) convolutional codes (a.k.a. spatially-co…
We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded (using codes of fixed rate) and transmitted over two independent binary memoryless symmetric channels. The capacity of each channel is characterized by a single parameter which is not known at the transmitter. The goal is to design systems that retain near-optimal performance without channel knowledge at the transmitter. It was conjectured that it may be hard to design codes that perform well for symmetric channel conditions. In this work, we present a provable capacity-achieving sequence of LDGM ensem…
In a digital communication system, information is sent from one place to another over a noisy communication channel using binary symbols (bits). Original information is encoded by adding redundant bits, which are then used by low--density parity--check (LDPC) codes to detect and correct errors that may have been introduced during transmission. Error correction capability of an LDPC code is severely degraded due to harmful structures such as small cycles in its bipartite graph representation known as Tanner graph (TG). We introduce an integer programming formulation to generate a TG for a given…
We introduce a new family of concatenated codes with an outer low-density parity-check (LDPC) code and an inner low-density generator matrix (LDGM) code, and prove that these codes can achieve capacity under any memoryless binary-input output-symmetric (MBIOS) channel using maximum-likelihood (ML) decoding with bounded graphical complexity, i.e., the number of edges per information bit in their graphical representation is bounded. In particular, we also show that these codes can achieve capacity on the binary erasure channel (BEC) under belief propagation (BP) decoding with bounded decoding co…
Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the i…
The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansions for low-density parity-check codes used over a highly noisy binary symmetric channel. We prove that in the asymptotic limit of large size, with high probability, the Bethe expression gives an exact formula for the entropy (per bit) of the input word conditioned on the output of the channel. Our methods also apply to more general models.
Unlocking Exponential and Unbounded Robust Gains in Shannon Capacity of Classical Multiple Access Channels with Causal CSIT via Quantum Entanglement Assistance
In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information by adding redundant bits. Low-density parity-check (LDPC) convolutional codes, a member of the LDPC code family, encode the original information to improve error correction capability. In practice these codes are used to decode very long information sequences, where the information arrives in subsequent packets over time, such as video streams. We consider t…
The use of open-loop coding can be easily extended to a closed-loop concatenated code if the channel has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive an optimal linear feedback scheme by optimizing over the received signal-to-noise ratio. From this optimization, an asymptotically optimal linear feedbac…
The problem of source coding with side information (SCSI) is closely related to channel coding. Therefore, existing literature focuses on using the most successful channel codes namely, LDPC codes, turbo codes, and their variants, to solve this problem assuming classical unique decoding of the underlying channel code. In this paper, in contrast to classical decoding, we have taken the list decoding approach. We show that syndrome source coding using list decoding can achieve the theoretical limit. We argue that, as opposed to channel coding, the correct sequence from the list produced by the l…
The use of open-loop coding can be easily extended to a closed-loop concatenated code if the channel has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive the optimal linear feedback scheme by optimizing over the received signal-to-noise ratio. From this optimization, an asymptotically optimal linear feedba…
Would Learning Help? Adaptive CRC-QC-LDPC Selection for Integrity in 5G-NR V2X
Istanbul Technical University（伊斯坦布尔理工大学）；The Ohio State University（俄亥俄州立大学）；Emerging Energy Contracting Est.（新兴能源承包公司）；Politehnica University of Timişoara（蒂米什瓦拉理工大学）；King Saud University（沙特国王大学）；Lebanese University（黎巴嫩大学）；Holy Spirit University of Kaslik (USEK)（卡思利克圣灵大学）
Obtaining accurate global channel state information (CSI) at multiple transmitter devices is critical to the performance of many coordinated transmission schemes. Practical CSI local feedback often leads to noisy and partial CSI estimates at each transmitter. With rate-limited bi-directional backhaul, transmitters have the opportunity to exchange few CSI-related bits to establish global channel state information at transmitter (CSIT). This work investigates possible strategies towards this goal. We propose a novel decentralized algorithm that produces minimum mean square error (MMSE)-optimal g…
Existing literature on source coding with side information (SCSI) mostly uses the state-of-the-art channel codes namely LDPC codes, turbo codes, and their variants and assume classical unique decoding. In this paper, we present an algebraic approach to SCSI based on the list decoding of the underlying channel codes. We show that the theoretical limit of SCSI can be achieved in the proposed list decoding based framework when the correlation between the source and side information is $q$-ary symmetric. We argue that, as opposed to channel coding, the correct sequence from the list produced by th…
A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equaliza…
