Formally Unimodular Packings for the Gaussian Wiretap Channel

This paper introduces the family of lattice-like packings, which generalizes lattices, consisting of packings possessing periodicity and geometric uniformity. The subfamily of formally unimodular (lattice-like) packings is further investigated. It can be seen as a generalization of the unimodular and isodual lattices, and the Construction A formally unimodular packings obtained from formally self-dual codes are presented. Recently, lattice coding for the Gaussian wiretap channel has been considered. A measure called secrecy function was proposed to characterize the eavesdropper's probability of correctly decoding. The aim is to determine the global maximum value of the secrecy function, called (strong) secrecy gain. We further apply lattice-like packings to coset coding for the Gaussian wiretap channel and show that the family of formally unimodular packings shares the same secrecy function behavior as unimodular and isodual lattices. We propose a universal approach to determine the secrecy gain of a Construction A formally unimodular packing obtained from a formally self-dual code. From the weight distribution of a code, we provide a necessary condition for a formally self-dual code such that its Construction A formally unimodular packing is secrecy-optimal. Finally, we demonstrate that formally unimodular packings/lattices can achieve higher secrecy gain than the best-known unimodular lattices.Comment: Accepted for publication in IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:2111.0143

Turvallisten ja luotettavien koodihilojen lukuteoreettinen ja geometrinen suunnittelu langattomassa viestinnässä

In data transmissions over wireless channels, the signal quality is weakened by random fading and noise of the electric field. This intrinsic property of the channel poses a challenge as the transmitted messages should be decodable at the receiver. On the other hand, it can be utilized for physical-layer security, in which the correct decoding probability drastically decreases when the signal quality weakens, hence securing the message from unintended receivers farther away. In this thesis, we study the design of lattices for lattice codes with an emphasis on lattice coset codes mostly in the Rayleigh fast fading channel model. Good lattice codes, i.e., solutions to the legitimate receiver's problem are known based on number-theoretic lattice constructions, whereas the design of lattice coset codes providing also physical-layer security is an open problem. We begin with a review of basic information theory, providing existence results and performance bounds on codes. Then, we specialize in lattice codes and lattice coset codes in wireless channels, deriving probability bounds for the legitimate receiver's error probability and the eavesdropper's correct decoding probability. In terms of these bounds, algebraic lattice constructions based on field extensions perform well, and for such lattices the bounds yield number-theoretic optimization problems. We study algebraic number theory extensively in order to have the tools to construct algebraic lattices and formulate and compute the probability bounds in terms of the properties of a given field extension. Finally, we compute the number-theoretic invariants and the eavesdropper's probability bound for algebraic lattices to assess and geometrize the different number-theoretic approaches that have been suggested to predict the eavesdropper's correct decoding probability for lattice coset codes.Langattomassa viestinnässä signaalinlaatua heikentävät sähkömagneettisten aaltojen satunnaissironta sekä taustakohina. Tämän erityispiirteen vuoksi viestinnän luotettavuuden takaaminen on langattomien kanavien perusongelma. Toisaalta sähkökentän häipymistä ja kohinaa voidaan hyödyntää fyysisen kerroksen salausmenetelmissä, joissa viestintä suunnitellaan sellaiseksi, että vastaanottajan oikean dekoodauksen todennäköisyys romahtaa signaalin laadun heikentyessä tarpeeksi. Tällöin kaukana oleva salakuuntelija ei pysty tulkitsemaan viestiä. Diplomityössä tutkitaan viestintähilojen suunnittelua hilakoodeja ja erityisesti hilojen jäännösluokkakoodeja varten pääasiassa nopeasti häipyvän Rayleigh-kanavan mallissa. Luotettavan viestinnän takaaville hilakoodeille tunnetaan lukuteoreettisia kostruktioita, kun taas myös fyysisen kerroksen salauksen takaavien hilojen jäännösluokkakoodien suunnittelu on avoin ongelma. Diplomityö aloitetaan kertaamalla informaatioteorian perustuloksia, jotka koskevat koodien olemassaoloa ja tiedonsiirtokapasiteettia. Tämän jälkeen erikoistutaan langattoman viestinnän kanavamalleihin sekä hilakoodeihin ja jäännösluokkakoodeihin. Näissä tapauksissa johdetaan ylärajat tarkoitetun vastaanottajan virhetodennäköisyydelle sekä salakuuntelijan oikean dekoodauksen todennäköisyydelle. Todennäköisyysrajojen perusteella lukukuntalaajennuksiin perustuvat algebralliset hilat suoriutuvat hyvin, ja tällaisten hilojen suunnittelu on lukuteoreettinen ongelma. Algebrallista lukuteoriaa tutkitaan laajasti ja saadaan algebrallisten hilojen konstruktio sekä työkalut viestinnän vertailukriteerien muotoiluun ja laskentaan lukuteoreettisin keinoin. Lopuksi lasketaan lukuteoreettiset invariantit sekä salakuuntelijan todennäköisyysraja joukolle algebrallisia hiloja. Tämän perustella arvioidaan ja geometrisoidaan salakuunteluongelmaan ehdotettuja jäännösluokkakoodien lukuteoreettisia hilasuunnittelukriteerejä

Distributed signal processing using nested lattice codes

Multi-Terminal Source Coding (MTSC) addresses the problem of compressing correlated sources without communication links among them. In this thesis, the constructive approach of this problem is considered in an algebraic framework and a system design is provided that can be applicable in a variety of settings. Wyner-Ziv problem is first investigated: coding of an independent and identically distributed (i.i.d.) Gaussian source with side information available only at the decoder in the form of a noisy version of the source to be encoded. Theoretical models are first established and derived for calculating distortion-rate functions. Then a few novel practical code implementations are proposed by using the strategy of multi-dimensional nested lattice/trellis coding. By investigating various lattices in the dimensions considered, analysis is given on how lattice properties affect performance. Also proposed are methods on choosing good sublattices in multiple dimensions. By introducing scaling factors, the relationship between distortion and scaling factor is examined for various rates. The best high-dimensional lattice using our scale-rotate method can achieve a performance less than 1 dB at low rates from the Wyner-Ziv limit; and random nested ensembles can achieve a 1.87 dB gap with the limit. Moreover, the code design is extended to incorporate with distributed compressive sensing (DCS). Theoretical framework is proposed and practical design using nested lattice/trellis is presented for various scenarios. By using nested trellis, the simulation shows a 3.42 dB gap from our derived bound for the DCS plus Wyner-Ziv framework

Application and Theory of Multimedia Signal Processing Using Machine Learning or Advanced Methods

This Special Issue is a book composed by collecting documents published through peer review on the research of various advanced technologies related to applications and theories of signal processing for multimedia systems using ML or advanced methods. Multimedia signals include image, video, audio, character recognition and optimization of communication channels for networks. The specific contents included in this book are data hiding, encryption, object detection, image classification, and character recognition. Academics and colleagues who are interested in these topics will find it interesting to read

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum