Analytical tools for optimizing the error correction performance of arithmetic codes

In joint source-channel arithmetic coding (JSCAC) schemes, additional redundancy may be introduced into an arithmetic source code in order to be more robust against transmission errors. The purpose of this work is to provide analytical tools to predict and evaluate the effectiveness of that redundancy. Integer binary arithmetic coding (AC) is modeled by a reduced-state automaton in order to obtain a bit-clock trellis describing the encoding process. Considering AC as a trellis code, distance spectra are then derived. In particular, an algorithm to compute the free distance of an arithmetic code is proposed. The obtained code properties allow to compute upper bounds on both bit error and symbol error probabilities and thus to provide an objective criterion to analyze the behavior of JSCAC schemes when used on noisy channels. This criterion is then exploited to design efficient error-correcting arithmetic codes. Simulation results highlight the validity of the theoretical error bounds and show that for equivalent rate and complexity, a simple optimization yields JSCACs that outperform classical tandem schemes at low to medium SNR.

[1]  Khalid Sayood,et al.  Joint Source Channel Coding Using Arithmetic Codes , 2009, Joint Source Channel Coding Using Arithmetic Codes.

[2]  Victor Buttigieg,et al.  On variable-length error-correcting codes , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[3]  Patrick G. Farrell,et al.  Variable-length error-correcting codes , 2000 .

[4]  John G. Cleary,et al.  Integrating error detection into arithmetic coding , 1997, IEEE Trans. Commun..

[5]  G. Olmo,et al.  Joint source/channel coding and MAP decoding of arithmetic codes , 2005, IEEE Transactions on Communications.

[6]  Richard Clark Pasco,et al.  Source coding algorithms for fast data compression , 1976 .

[7]  Jossy Sayir.  On coding by probability transformation , 1999 .

[8]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[9]  V.W.S. Chan,et al.  Principles of Digital Communication and Coding , 1979 .

[10]  J. Chou,et al.  Arithmetic coding-based continuous error detection for efficient ARQ-based image transmission , 2000, IEEE Journal on Selected Areas in Communications.

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

[12]  G. David Forney,et al.  Geometrically uniform codes , 1991, IEEE Trans. Inf. Theory.

[13]  Thomas Guionnet,et al.  Soft decoding and synchronization of arithmetic codes: application to image transmission over noisy channels , 2003, IEEE Trans. Image Process..

[14]  Kannan Ramchandran,et al.  Arithmetic coding based continuous error detection for efficient ARQ-based image transmission , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[15]  Khalid Sayood,et al.  State machine interpretation of arithmetic codes for joint source and channel coding , 2006, Data Compression Conference (DCC'06).

[16]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[17]  David Haccoun,et al.  High-rate punctured convolutional codes for Viterbi and sequential decoding , 1989, IEEE Trans. Commun..

[18]  J. Vitter,et al.  Practical Implementations of Arithmetic Coding , 1991 .

[19]  Jossy Sayir.  Arithmetic coding for noisy channels , 1999, Proceedings of the 1999 IEEE Information Theory and Communications Workshop (Cat. No. 99EX253).

[20]  Erik G. Ström,et al.  On the union bound applied to convolutional codes , 2001, IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211).

[21]  Jorma Rissanen,et al.  Generalized Kraft Inequality and Arithmetic Coding , 1976, IBM J. Res. Dev..

[22]  Khalid Sayood,et al.  Joint source channel coding using arithmetic codes and trellis coded modulation , 2001, Proceedings DCC 2001. Data Compression Conference.