Implementation of Variable-length Codes for Integer Numbers

Import 29/09/2010Cílem práce bylo seznámit se s několika typy kódování proměnných délek pro celá čísla, provést jejich implementaci z pohledu možného nasazení v kompresním frameworku a porovnat je z pohledu jejich efektivity. Zvoleny byly Fibonacciho kódy, Zobecněné Fibonacciho kódy, Goldbachovy kódy, Aditivní kódy, Golombovy a Riceovy kódy. Při hodnocení efektivity kódování jsem se zaměřil na to, zda a za jakých podmínek je dané kódování přínosem v porovnání s běžnou třiceti-dvoubitovou znaménkovou binární reprezentací. Implementace byla s výjimkou Aditivních kódů a Goldbachova G0 kódu provedena pro rozsah vstupních hodnot . Po konzultaci s vedoucím práce bylo od implementace Aditivních kódů upuštěno a v případě Goldbachova G0 kódu byla implementace omezena na maximální délku kódu 120 000 bitů. Porovnání efektivity bylo provedeno na poskytnuté sadě testovacích souborů, přičemž v případě Goldbachova kódování G0 byl rozsah testování omezen.The goal of the works was to acquaint with several types of encoding variable lenght for integral numbers, to analyze their implementation in terms of potencional use in the compression framework and to compare their effectiveness. I chose the Fibonacci code, the Generalized Fibonacci code, the Goldbach codes, the Additive codes, the Golomb and the Rice code. When evaluating the encoding efficiency, I focused on wether and under what conditions is the encoding useful in comperision with regular thirty-two sign binary representation. The implementation was made for a range of input value expect the Additive and Goldbach codes G0. The implementation of the Additive codes was canceled and the implementation of the Goldbach codes G0 was limited to a maximum code leght 120 000 bites, after the consultation with the supervisor. The comparing of the effectiveness was made on the provided test files. In case of Goldbach codes G0 the extent of testing was limited.Prezenční456 - Katedra informatikyvýborn

The Reliability Function of Lossy Source-Channel Coding of Variable-Length Codes with Feedback

We consider transmission of discrete memoryless sources (DMSes) across discrete memoryless channels (DMCs) using variable-length lossy source-channel codes with feedback. The reliability function (optimum error exponent) is shown to be equal to $\max\{0, B(1-R(D)/C)\},$ where $R(D)$ is the rate-distortion function of the source, $B$ is the maximum relative entropy between output distributions of the DMC, and $C$ is the Shannon capacity of the channel. We show that, in this setting and in this asymptotic regime, separate source-channel coding is, in fact, optimal.Comment: Accepted to IEEE Transactions on Information Theory in Apr. 201

Indeterminate-length quantum coding

The quantum analogues of classical variable-length codes are indeterminate-length quantum codes, in which codewords may exist in superpositions of different lengths. This paper explores some of their properties. The length observable for such codes is governed by a quantum version of the Kraft-McMillan inequality. Indeterminate-length quantum codes also provide an alternate approach to quantum data compression.Comment: 32 page

General form of almost instantaneous fixed-to-variable-length codes

A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the following. (i) Introducing $N$-bit-delay AIFV codes, constructed by multiple code trees with higher flexibility than the conventional AIFV codes. (ii) Proving that the proposed codes can represent any uniquely-encodable and uniquely-decodable variable-to-variable length codes. (iii) Showing how to express codes as multiple code trees with minimum decoding delay. (iv) Formulating the constraints of decodability as the comparison of intervals in the real number line. The theoretical results in this paper are expected to be useful for further study on AIFV codes.Comment: submitted to IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:1607.07247 by other author