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DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

The Lawrence algorithm is a universal binary variable-to-fixed length source coding algorithm. Here, a modified version of this algorithm is introduced and its asymptotic performance is investigated. For M (the segment set cardinality) large enough, it is shown that the rate Re as a function of the source parameter 8 satisfiesfor 0 < 8 < 1. Here h( . ) is the binary entropy function. In addition to this, it is proven that no codes exist that have a better asymptotic performance, thereby establishing the asymptotic optimality of our modified Lawrence code. The asymptotic bounds show that universal variable-to-fixed length codes can have a significantly lower redundancy than universal fixed-tovariable length codes with the same number of codewords.Index Terms-Universal source coding, enumerative coding, variable-to-fixed length codes, asymptotic redundancy. I. PRELIMINARIES BINARY memoryless information source generates a A sequence of independent and identically distributed random variables { % t ] r = , , c o , each of which assumes values in the finite set F= ( 0 , I}, called the source alphabet. Let 8 2 Pr{X, = I} = 1 -Pr{X, = 0}, t = 1, 2, . Then the entropy of the source (in bits per symbol) is equal to h(e) -e log (e) -(1 -e ) log (1 -e). (We assume throughout this paper that log ( a )'s have base 2 and that In ( e ) has base e.)In what follows, we will describe a universal variable-tofixed length coding strategy for the class of binary memoryless sources. With these codes, the (infinite length) source sequence is chopped up into sequences of variable length (segments), chosen from some finite set Y of segments, and each segment is assigned to a code sequence of fixed length(Note that we ignore the rounding of log M to an integer). This set of segments must be complete, i.e., every infinite sequence has a prefix in the segment set, since every sequence must be subdividable into segments. We also require

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An improved PCa localization method can possibly lead to better grading and staging of tumors, and support focal-treatment guidance. Moreover, future employment of the method in other types of angiogenic cancer can be considered.