Distributed Arithmetic Coding Over Binary Erasure Channel

In this paper, the Binary Erasure Channel (BEC) is researched by Distributed Arithmetic Coding (DAC) based on Slepian-Wolf coding framework. The source and side information are modelled as a virtual BEC. The DAC decoder uses maximum a posteriori (MAP) as the criterion to recover the source. A deep residual network is used to boost the DAC decoding process. The experimental results show that our algorithm nearly achieves the same performance with LT codes under different erasure probabilities.

Bhattacharyya Parameter of Monomial Codes for the Binary Erasure Channel: From Pointwise to Average Reliability

Monomial codes were recently equipped with partial order relations, a fact that allowed researchers to discover structural properties and efficient algorithm for constructing polar codes. Here, we refine the existing order relations in the particular case of the binary erasure channel. The new order relation takes us closer to the ultimate order relation induced by the pointwise evaluation of the Bhattacharyya parameter of the synthetic channels, which is still a partial order relation. To overcome this issue, we appeal to a related technique from network theory. Reliability network theory was recently used in the context of polar coding and more generally in connection with decreasing monomial codes. In this article, we investigate how the concept of average reliability is applied for polar codes designed for the binary erasure channel. Instead of minimizing the error probability of the synthetic channels, for a particular value of the erasure parameter p, our codes minimize the average error probability of the synthetic channels. By means of basic network theory results, we determine a closed formula for the average reliability of a particular synthetic channel, that recently gain the attention of researchers.

Threshold Computation for Spatially Coupled Turbo-Like Codes on the AWGN Channel

In this paper, we perform a belief propagation (BP) decoding threshold analysis of spatially coupled (SC) turbo-like codes (TCs) (SC-TCs) on the additive white Gaussian noise (AWGN) channel. We review Monte-Carlo density evolution (MC-DE) and efficient prediction methods, which determine the BP thresholds of SC-TCs over the AWGN channel. We demonstrate that instead of performing time-consuming MC-DE computations, the BP threshold of SC-TCs over the AWGN channel can be predicted very efficiently from their binary erasure channel (BEC) thresholds. From threshold results, we conjecture that the similarity of MC-DE and predicted thresholds is related to the threshold saturation capability as well as capacity-approaching maximum a posteriori (MAP) performance of an SC-TC ensemble.

Guessing with a Bit of Help

What is the value of just a few bits to a guesser? We study this problem in a setup where Alice wishes to guess an independent and identically distributed (i.i.d.) random vector and can procure a fixed number of k information bits from Bob, who has observed this vector through a memoryless channel. We are interested in the guessing ratio, which we define as the ratio of Alice’s guessing-moments with and without observing Bob’s bits. For the case of a uniform binary vector observed through a binary symmetric channel, we provide two upper bounds on the guessing ratio by analyzing the performance of the dictator (for general k ≥ 1 ) and majority functions (for k = 1 ). We further provide a lower bound via maximum entropy (for general k ≥ 1 ) and a lower bound based on Fourier-analytic/hypercontractivity arguments (for k = 1 ). We then extend our maximum entropy argument to give a lower bound on the guessing ratio for a general channel with a binary uniform input that is expressed using the strong data-processing inequality constant of the reverse channel. We compute this bound for the binary erasure channel and conjecture that greedy dictator functions achieve the optimal guessing ratio.

Low Delay Inter-Packet Coding in Vehicular Networks

In Cooperative Intelligent Transportation Systems (C-ITSs), vehicles need to wirelessly connect with Roadside units (RSUs) over limited durations when such point-to-point connections are possible. One example of such communications is the downloading of maps to the C-ITS vehicles. Another example occurs in the testing of C-ITS vehicles, where the tested vehicles upload trajectory records to the roadside units. Because of real-time requirements, and limited bandwidths, data are sent as User Datagram Protocol (UDP) packets. We propose an inter-packet error control coding scheme that improves the recovery of data when some of these packets are lost; we argue that the coding scheme has to be one of convolutional coding. We measure performance through the session averaged probability of successfully delivering groups of packets. We analyze two classes of convolution codes and propose a low-complexity decoding procedure suitable for network applications. We conclude that Reed–Solomon convolutional codes perform better than Wyner–Ash codes at the cost of higher complexity. We show this by simulation on the memoryless binary erasure channel (BEC) and channels with memory, and through simulations of the IEEE 802.11p DSRC/ITS-G5 network at the C-ITS test track AstaZero.