On a generalised typicality with respect to general probability distributions

The method of typical sequences is a fundamental tool in asymptotic analyses of information theory. The conditional typicality lemma is one of the most commonly used lemmas in the method of typical sequences. Recent works have generalised the definition of typicality to general alphabets or general probability distributions. However, there is still a lack of the conditional typicality lemma based on the definition of typicality with respect to general distributions on the product space. In this paper, we propose a generalised joint typicality for general alphabets and with respect to general probability distributions, and obtain the counterpart of conventional conditional and joint typicality lemmas based on the generalised typicality. As applications of the typicality lemmas, we prove the packing and coverings for the proposed generalised typicality, and then recover the direct part of the capacity theorem on the general Gelfand-Pinsker coding. We also prove a mutual covering lemma for the generalised typicality, and then obtain the Marton-type inner bound to the capacity region of the general broadcast channel

Peter—apocalyptic seer: the influence of the apocalypse genre on Matthew’s portrayal of Peter

This study fills a gap in previous research concerning the portrayal of Peter in Matthew, especially the research of narrative-critical studies. Although narrative-critical studies generally recognize that Matthew has portrayed Peter and the disciples as recipients of revelation at points, they almost entirely neglect the apocalypses or apocalyptic literature more broadly as a potentially helpful background for this motif, nor does the motif itself figure significantly into their conclusions. Therefore, Part 1 of this study examines fourteen different Jewish and Christian apocalypses in order to determine generic aspects of how the apocalypses portray their seers, and to identify specific textual features that support these generic aspects of a seer’s portrayal. These specific textual features then provide the guiding coordinates for Part 2, which assesses the influence of the generic portrayal of apocalyptic seers on the portrayal of Peter and the disciples in Matthew’s Gospel and main source, Mark’s Gospel. Like the apocalypses, both Evangelists deploy the features of exclusionary statements, narrative isolation, dissemination details, and emphasis of cognitive humanity and emotional-physical humanity to portray Peter and the disciples as the exclusive recipients of revealed mysteries, and as humans who encounter the mysteries of the divine realm. This leads to the conclusion that both Evangelists envisaged Peter and the disciples as apocalyptic seers in some sense. However, Matthew’s redaction of Markan source material, incorporation of Q source material, and his own special material yield a more fully developed, or more explicit, portrayal of Peter and the disciples as apocalyptic seers than his Markan predecessor. The study concludes by focusing directly on Peter’s significance for Matthew and his earliest audience. The research suggests that Peter’s significance was, in part, as principal apocalyptic seer, which requires revision to the predominant scholarly conclusions about Peter in Matthew

The distinctiveness of Quaker prose, 1650-1699: a corpus-based enquiry

This study ascertains what is recognisably distinctive about seventeenth-century Quaker prose compared to other contemporary varieties of prose, and identifies characteristic features of that style. By compiling and investigating through corpus analysis techniques a collection of texts from a wide range of authors, I reveal key elements of the language through quantitative methods not previously applied to this subject. The study is not genre-based nor is it a literary investigation of a single author. The corpus is unusual in comprising texts by many different people within the same community of practice, demonstrating a remarkable uniformity of style and discourse. Typical stylistic features include a speech-like informal register, idiosyncratic syntax and sentence length, and I suggest reasons why Quakers developed this sociolect. In key Quaker lexis I found unexpected frequencies and usage, including findings that differ from assertions in the critical literature. Corpus analysis provides new insights into early Quakerism as well as establishing a new mode of research. My findings clarify understanding of early Quaker writing, experience and practice, dispelling some present-day misconceptions

Linear Coding, Applications and Supremus Typicality

Detta arbete börjar med att presentera en kodningssats gällande linjärkodning över ändliga ringar för kodning av korrelerade diskretaminneslösa källor. Denna sats inkluderar som specialfall motsvarandeuppnåbarhetssatser från Elias och Csiszár gällande linjär kodning överändliga kroppar. Dessutom visas det att för varje uppsättning av ändligakorrelerade diskreta minneslösa källor, så finns alltid en sekvens avlinjära kodare över vissa ändliga icke-kropp-ringar som uppnårdatakompressionsgränsen bestämd av Slepian-Wolf-regionen. Därmed slutervi problemet med linjär kodning över ändlig icke-kropps-ringar föri.i.d. datakomprimering med positiv bekräftelse gällande existens. Vi studerar också kodning av funktioner, där avkodaren är intresseradav att återskapa en diskret mappning av data som genererats av flerakorrelerade i.i.d. källor och som kodats individuellt. Vi föreslårlinjär kodning över ändliga ringar som en alternativ lösning på dettaproblem. Vi visar att linjär kodning över ändliga ringar presterarbättre än sin ändliga-kropp-motsvarighet, liksom dessutomSlepian-Wolf-kodning, i termer av att uppnå bättre kodningshastigheterför kodning av flera diskreta funktioner. För att generalisera ovannämnda genomförbarhetssatser, både gällandedatakompression och funktionskodningsproblemet, till Markov-källor(homogena irreducerbara Markov-källor), så introducerar vi ett nyttkoncept gällande klassificering av typiska sekvenser, benämndSupremus-typiska sekvenser. Den asymptotiska likafördelningsprincipensamt en generaliserad version av typiskhets-hjälpsatsen förSupremus-typiska sekvenser bevisas. Jämfört med traditionell (stark ochsvag) typiskhet, så tillåter Supremus-typiskhet oss att härleda bättretillgängliga verktyg och resultat, som låter oss bevisa att linjärkodning över ringar är överlägsen andra metoder. I motsats härtillmisslyckas argument baserade på den traditionella versionen antingen medatt nå liknande resultat eller så är de härledda resultaten svåra attanalysera på grund av en utmanande utvärdering av entropitakt. För att ytterligare undersöka den grundläggande skillnaden mellantraditionell typiskhet och Supremus-typiskhet och dessutom göra våraresultat än mer allmänt gällande, så betraktar vi ävenasymptotiskt medelvärdesstationära ergodiska källor. Våra resultat visaratt en inducerad transformation med avseende på en ändligt mätbar mängdöver ett rekurrent asymptotiskt medelvärdesstationärt dynamiskt systemmed ett sigma-ändlig sannolikhetsmått är asymptotisktmedelvärdesstationär. Följaktligen så gällerShannon-McMillan-Breiman-teoremet, liksom Shannon-McMillan-teoremet, föralla reducerade processer härledda ur rekurrenta asymptotisktmedelvärdesstationära stokastisk processer. Alltså ser vi att dettraditionella typiskhetkonceptet endast realiserarShannon-McMillan-Breiman-teoremet i ett globalt hänseende, medanSupremus-typiskhet leder till att resultatet håller samtidigt även föralla härledda reducerade sekvenser.This work first presents a coding theorem on linear coding over finite rings for encoding correlated discrete memoryless sources. This theorem covers corresponding achievability theorems from Elias and Csiszár on linear coding over finite fields as special cases. In addition, it is shown that, for any set of finite correlated discrete memoryless sources, there always exists a sequence of linear encoders over some finite non-field rings which achieves the data compression limit, the Slepian--Wolf region. Hence, the optimality problem regarding linear coding over finite non-field rings for i.i.d. data compression is closed with positive confirmation with respect to existence. We also address the function encoding problem, where the decoder is interested in recovering a discrete function of the data generated and independently encoded by several correlated i.i.d. sources. We propose linear coding over finite rings as an alternative solution to this problem. It is demonstrated that linear coding over finite rings strictly outperforms its field counterpart, as well as the Slepian--Wolf scheme, in terms of achieving better coding rates for encoding many discrete functions. In order to generalise the above achievability theorems, on both the data compression and the function encoding problems, to the Markovian settings (homogeneous irreducible Markov sources), a new concept of typicality for sequences, termed Supremus typical sequences, is introduced. The Asymptotically Equipartition Property and a generalised typicality lemma of Supremus typical sequences are proved. Compared to traditional (strong and weak) typicality, Supremus typicality allows us to derive more accessible tools and results, based on which it is once again proved that linear technique over rings is superior to others. In contrast, corresponding arguments based on the traditional versions either fail to draw similar conclusions or the derived results are often hard to analyse because it is complicated to evaluate entropy rates. To further investigate the fundamental difference between traditional typicality and Supremus typicality and to bring our results to a more universal setting, asymptotically mean stationary ergodic sources, we look into the ergodic properties featured in these two concepts.Our studies prove that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon-McMillan-Breiman Theorem, as well as the Shannon-McMillan Theorem, holds simultaneously for all reduced processes of any finite-state recurrent asymptotically mean stationary random process.From this, we see that the traditional typicality concept only realises the Shannon-McMillan-Breiman Theorem in the global sequence, while Supremus typicality engraves the simultaneous effects claimed in the previous statement into all reduced sequences as well.QC 20150225</p