Coding and Decoding Schemes for MSE and Image Transmission

In this work we explore possibilities for coding and decoding tailor-made for mean squared error evaluation of error in contexts such as image transmission. To do so, we introduce a loss function that expresses the overall performance of a coding and decoding scheme for discrete channels and that exchanges the usual goal of minimizing the error probability to that of minimizing the expected loss. In this environment we explore the possibilities of using ordered decoders to create a message-wise unequal error protection (UEP), where the most valuable information is protected by placing in its proximity information words that differ by a small valued error. We give explicit examples, using scale-of-gray images, including small-scale performance analysis and visual simulations for the BSMC.Comment: Submitted to IEEE Transactions on Information Theor

Communication Strategies for Low-Latency Trading

The possibility of latency arbitrage in financial markets has led to the deployment of high-speed communication links between distant financial centers. These links are noisy and so there is a need for coding. In this paper, we develop a gametheoretic model of trading behavior where two traders compete to capture latency arbitrage opportunities using binary signalling. Different coding schemes are strategies that trade off between reliability and latency. When one trader has a better channel, the second trader should not compete. With statistically identical channels, we find there are two different regimes of channel noise for which: there is a unique Nash equilibrium yielding ties; and there are two Nash equilibria with different winners.Comment: Will appear in IEEE International Symposium on Information Theory (ISIT), 201

The Error Probability of Generalized Perfect Codes via the Meta-Converse

We introduce a definition of perfect and quasiperfect codes for discrete symmetric channels based on the packing and covering properties of generalized spheres whose shape is tilted using an auxiliary probability measure. This notion generalizes previous definitions of perfect and quasiperfect codes and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to coincide with the estimate provided by the metaconverse lower bound. We illustrate how the proposed definition naturally extends to cover almost-lossless source-channel coding and lossy compression.ER

On Optimal Finite-length Binary Codes of Four Codewords for Binary Symmetric Channels

Finite-length binary codes of four codewords are studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood decoding. For any block-length, best linear codes of four codewords have been explicitly characterized, but whether linear codes are better than nonlinear codes or not is unknown in general. In this paper, we show that for any block-length, there exists an optimal code of four codewords that is either linear or in a subset of nonlinear codes, called Class-I codes. Based on the analysis of Class-I codes, we derive sufficient conditions such that linear codes are optimal. For block-length less than or equal to 8, our analytical results show that linear codes are optimal. For block-length up to 300, numerical evaluations show that linear codes are optimal.Comment: accepted by ISITA 202

The Error Probability of Generalized Perfect Codes

This paper has been presented at : IEEE International Symposium on Information Theory 2018We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This new definition generalizes previous definitions and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to attain the meta-converse lower bound.This work has been funded in part by the European Research Council (ERC) under grants 714161 and 725411, by the Spanish Ministry of Economy and Competitiveness under Grants TEC2016-78434-C3 and IJCI-2015-27020, by the National Science Foundation under Grant CCF-1513915 and by the Center for Science of Information, an NSF Science and Technology Center under Grant CCF-0939370

Towards Massive, Ultrareliable, and Low-Latency Wireless Communication with Short Packets

Most of the recent advances in the design of high-speed wireless systems are based on information-theoretic principles that demonstrate how to efficiently transmit long data packets. However, the upcoming wireless systems, notably the fifth-generation (5G) system, will need to support novel traffic types that use short packets. For example, short packets represent the most common form of traffic generated by sensors and other devices involved in machine-to-machine (M2M) communications. Furthermore, there are emerging applications in which small packets are expected to carry critical information that should be received with low latency and ultrahigh reliability. Current wireless systems are not designed to support short-packet transmissions. For example, the design of current systems relies on the assumption that the metadata (control information) is of negligible size compared to the actual information payload. Hence, transmitting metadata using heuristic methods does not affect the overall system performance. However, when the packets are short, metadata may be of the same size as the payload, and the conventional methods to transmit it may be highly suboptimal. In this paper, we review recent advances in information theory, which provide the theoretical principles that govern the transmission of short packets. We then apply these principles to three exemplary scenarios (the two-way channel, the downlink broadcast channel, and the uplink random access channel), thereby illustrating how the transmission of control information can be optimized when the packets are short. The insights brought by these examples suggest that new principles are needed for the design of wireless protocols supporting short packets. These principles will have a direct impact on the system design.The work of G. Durisi has been in part supported by the Swedish Research Council under Grant 2012-4571. The work of T. Koch has been supported in part by the European Community’s Seventh Framework Programme FP7/2007-2013 under Grant 333680, in part by the Ministerio de Economía y Competitividad of Spain under Grants TEC2013-41718-R, RYC-2014-16332, and TEC2015-69648-REDC, and in part by the Comunidad de Madrid under Grant S2013/ICE-2845. The work of P. Popovski has been in part supported by the European Research Council (ERC Consolidator Grant Nr. 648382 WILLOW) within the Horizon 2020 Program. The simulations were performed in part on resources at Chalmers Centre for Computational Science and Engineering (C3SE) provided by the Swedish National Infrastructure for Computing (SNIC)