Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications

From its introduction to its quindecennial, network coding has built a strong reputation for enhancing packet recovery and achieving maximum information flow in both wired and wireless networks. Traditional studies focused on optimizing the throughput of the system by proposing elaborate schemes able to reach the network capacity. With the shift toward distributed computing on mobile devices, performance and complexity become both critical factors that affect the efficiency of a coding strategy. Instantly decodable network coding presents itself as a new paradigm in network coding that trades off these two aspects. This paper review instantly decodable network coding schemes by identifying, categorizing, and evaluating various algorithms proposed in the literature. The first part of the manuscript investigates the conventional centralized systems, in which all decisions are carried out by a central unit, e.g., a base-station. In particular, two successful approaches known as the strict and generalized instantly decodable network are compared in terms of reliability, performance, complexity, and packet selection methodology. The second part considers the use of instantly decodable codes in a device-to-device communication network, in which devices speed up the recovery of the missing packets by exchanging network coded packets. Although the performance improvements are directly proportional to the computational complexity increases, numerous successful schemes from both the performance and complexity viewpoints are identified

High-speed turbo-TCM-coded orthogonal frequency-division multiplexing ultra-wideband systems

One of the UWB proposals in the IEEE P802.15 WPAN project is to use a multiband orthogonal frequency-division multiplexing (OFDM) system and punctured convolutional codes for UWB channels supporting a data rate up to 480 Mbps. In this paper, we improve the proposed system using turbo TCM with QAM constellation for higher data rate transmission. We construct a punctured parity-concatenated trellis codes, in which a TCM code is used as the inner code and a simple parity-check code is employed as the outer code. The result shows that the system can offer a much higher spectral efficiency, for example, 1.2 Gbps, which is 2.5 times higher than the proposed system. We identify several essential requirements to achieve the high rate transmission, for example, frequency and time diversity and multilevel error protection. Results are confirmed by density evolution. Copyright (C) 2006 Yanxia Wang et al

Generalized Spatially-Coupled Parallel Concatenated Codes With Partial Repetition

A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes (PCCs) with a fraction of information bits repeated q times. GSC-PCCs can be seen as a generalization of the original spatially-coupled parallel concatenated codes proposed by Moloudi et al. [2]. To characterize the asymptotic performance of GSC-PCCs, we derive the corresponding density evolution equations and compute their decoding thresholds. The threshold saturation effect is observed and proven. Most importantly, we rigorously prove that the rate-R GSC-PCC ensemble with 2-state convolutional component codes achieves at least a fraction 1-R/R+q of the capacity of the binary erasure channel (BEC) for repetition factor q ≥ 2 and this multiplicative gap vanishes as q tends to infinity. To the best of our knowledge, this is the first class of SC-TCs that are proven to be capacity-achieving. Further, the connection between the strength of the component codes, the decoding thresholds of GSC-PCCs, and the repetition factor is established. The superiority of the proposed codes with finite blocklength is exemplified by comparing their error performance with that of existing SC-TCs via computer simulations

Research Letter Design LDPC Codes without Cycles of Length 4 and 6

We present an approach for constructing LDPC codes without cycles of length 4 and 6. Firstly, we design 3 submatrices with different shifting functions given by the proposed schemes, then combine them into the matrix specified by the proposed approach, and, finally, expand the matrix into a desired parity-check matrix using identity matrices and cyclic shift matrices of the identity matrices. The simulation result in AWGN channel verifies that the BER of the proposed code is close to those of Mackay's random codes and Tanner's QC codes, and the good BER performance of the proposed can remain at high code rates

The private and public correlation cost of three random variables with collaboration

© 2016 IEEE. In this paper, we consider the problem of generating arbitrary three-party correlations from a combination of public and secret correlations. Two parties - called Alice and Bob - share perfectly correlated bits that are secret from a collaborating third party, Charlie. At the same time, all three parties have access to a separate source of correlated bits, and their goal is to convert these two resources into multiple copies of some given tripartite distribution ℙ(XYZ). We obtain a single-letter characterization of the tradeoff between public and private bits that are needed to achieve this task. The rate of private bits is shown to generalize Wyner's classic notion of common information held between a pair of random variables. The problem we consider can be contrasted fruitfully with the task of secrecy formation, in which ℙ(XYZ) is generated using public communication and local randomness but with Charlie functioning as an adversary instead of a collaborator. We describe in detail the differences between the collaborative and adversarial scenarios

Approximate decoding for network coded inter-dependent data

In this paper, we consider decoding of loss tolerant data encoded by network coding and transmitted over error-prone networks. Intermediate network nodes typically perform the random linear network coding in a Galois field and a Gaussian elimination is used for decoding process in the terminal nodes. In such settings, conventional decoding approaches can unfortunately not reconstruct any encoded data unless they receive at least as many coded packets as the original number of packets. In this paper, we rather propose to exploit the incomplete data at a receiver without major modifications to the conventional decoding architecture. We study the problem of approximate decoding for inter-dependent sources where the difference between source vectors is characterized by a unimodal distribution. We propose a mode-based algorithm for approximate decoding, where the mode of the source data distribution is used to reconstruct source data. We further improve the mode-based approximate decoding algorithm by using additional short information that is referred to as position similarity information (PSI). We analytically study the impact of PSI size on the approximate decoding performance and show that the optimal size of PSI can be determined based on performance requirements of applications. The proposed approach has been tested in an illustrative example of data collection in sensor networks. The simulation results confirm the benefits of approximate decoding for inter-dependent sources and further show that 93.3% of decoding errors are eliminated when the approximate decoding uses appropriate PSI

Constant weight strings in constant time: a building block for code-based post-quantum cryptosystems

Code based cryptosystems often need to encode either a message or a random bitstring into one of fixed length and fixed (Hamming) weight. The lack of an efficient and reliable bijective map presents a problem in building constructions around the said cryptosystems to attain security against active attackers. We present an efficiently computable, bijective function which yields the desired mapping. Furthermore, we delineate how the said function can be computed in constant time. We experimentally validate the effectiveness and efficiency of our approach, comparing it against the current state of the art solutions, achieving three to four orders of magnitude improvements in computation time, and validate its constant runtim