Variants of Golomb Coding and the n-ary Versions

Golomb coding is a type of entropy encoding scheme for geometric distributions. It consists of two parts, and both parts are coded with variable-length coding, which requires a higher computational effort than fixed-length coding schemes. To solve this issue, the first part of this article presents a variant of Golomb coding that uses fixed-length coding to code the first part. The simulations show that the proposed coding scheme has a higher throughput than Golomb coding, due to the reduction of arithmetic complexity. In the second part, we discuss the <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-ary versions of Golomb coding and the proposed coding scheme.

[1]  맬바 헨리큐에스..  Lossless adaptive encoding of finite alphabet data , 2000 .

[2]  Fabrizio Lombardi,et al.  Application of arithmetic coding to compression of VLSI test data , 2005, IEEE Transactions on Computers.

[3]  Takehiro Moriya,et al.  Optimal Golomb-Rice Code Extension for Lossless Coding of Low-Entropy Exponentially Distributed Sources , 2018, IEEE Transactions on Information Theory.

[4]  Krishnendu Chakrabarty,et al.  Test data compression and decompression based on internal scanchains and Golomb coding , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[5]  Ian H. Witten,et al.  Arithmetic coding for data compression , 1987, CACM.

[6]  Khalid Sayood,et al.  An analog-to-digital converter with Golomb-Rice output codes , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[7]  Krishnendu Chakrabarty,et al.  Low-power scan testing and test data compression forsystem-on-a-chip , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  S. Yang,et al.  Efficient Integer Coding for Arbitrary Probability Distributions , 2006, IEEE Transactions on Information Theory.

[9]  Roberto Rinaldo,et al.  Lossless compression of video using temporal information , 2003, IEEE Trans. Image Process..

[10]  Krishnendu Chakrabarty,et al.  System-on-a-chip test-data compression and decompressionarchitectures based on Golomb codes , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[11]  Lajos Hanzo,et al.  Exponential Golomb and Rice Error Correction Codes for Generalized Near-Capacity Joint Source and Channel Coding , 2016, IEEE Access.

[12]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[13]  Zhuocheng Jiang,et al.  Universal Golomb–Rice Coding Parameter Estimation Using Deep Belief Networks for Hyperspectral Image Compression , 2018, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[14]  Hyunjin Kim,et al.  A Lossless Color Image Compression Architecture Using a Parallel Golomb-Rice Hardware CODEC , 2011, IEEE Transactions on Circuits and Systems for Video Technology.

[15]  Liang-Gee Chen,et al.  Architecture Design of Context-Based Adaptive Variable-Length Coding for H.264/AVC , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Joseph Euzebe Tate,et al.  Preprocessing and Golomb–Rice Encoding for Lossless Compression of Phasor Angle Data , 2016, IEEE Transactions on Smart Grid.

[17]  Solomon W. Golomb,et al.  Run-length encodings (Corresp.) , 1966, IEEE Trans. Inf. Theory.

[18]  Henrique S. Malvar.  Fast adaptive encoder for bi-level images , 2001, Proceedings DCC 2001. Data Compression Conference.

[19]  John P. Robinson.  Optimum Golomb Rulers , 1979, IEEE Transactions on Computers.

[20]  Guillermo Sapiro,et al.  The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS , 2000, IEEE Trans. Image Process..

[21]  Jian-Jiun Ding,et al.  Adaptive Golomb Code for Joint Geometrically Distributed Data and Its Application in Image Coding , 2013, IEEE Transactions on Circuits and Systems for Video Technology.

[22]  Henrique S. Malvar.  Lossless and Near-Lossless Audio Compression Using Integer-Reversible Modulated Lapped Transforms , 2007, 2007 Data Compression Conference (DCC'07).

[23]  David C. van Voorhis,et al.  Optimal source codes for geometrically distributed integer alphabets (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[24]  Tor Helleseth,et al.  Solomon W. Golomb—Mathematician, Engineer, and Pioneer , 2018, IEEE Transactions on Information Theory.

[25]  Neri Merhav,et al.  Optimal prefix codes for sources with two-sided geometric distributions , 2000, IEEE Trans. Inf. Theory.

[26]  Reza Hashemian.  Memory efficient and high-speed search Huffman coding , 1995, IEEE Trans. Commun..