Unified Error Probability Analysis for Error Correcting Codes with Different Decoding Algorithms

The error rate of error correcting codes with soft-decision-decoding rarely has a closed-form expression. Bounding techniques are widely used to evaluate the performance of maximum-likelihood decoding algorithm. But the existing bounds are not tight enough especially for a low signal-to-noise ratios region and become looser when a suboptimum decoding algorithm is used. The radius of decision region is applied to evaluate the word error rate (WER) of error correcting codes with different decoding algorithms. Simulation results show that this method can effectively evaluate the WER of different decoders with 0.05dB maximum error.

[1]  Hongwen Yang,et al.  Evaluating the word error rate of channel codes via the squared radius distribution of decision regions , 2008, IEEE Communications Letters.

[2]  Shlomo Shamai,et al.  Variations on the Gallager bounds, connections, and applications , 2002, IEEE Trans. Inf. Theory.

[3]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[4]  Gregory Poltyrev,et al.  Bounds on the decoding error probability of binary linear codes via their spectra , 1994, IEEE Trans. Inf. Theory.

[5]  Dariush Divsalar,et al.  Transfer function bounds on the performance of turbo codes Pasadena , 1995 .

[6]  Liyun Dai,et al.  Evaluating Word Error Rate via Radius of Decision Region , 2011, 2011 IEEE Vehicular Technology Conference (VTC Fall).

[7]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[8]  Wang Zhongxun,et al.  A Low-Complexity Layered Decoding Algorithm for LDPC Codes , 2009, 2009 International Forum on Computer Science-Technology and Applications.

[9]  Patrick Robertson,et al.  A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain , 1995, Proceedings IEEE International Conference on Communications ICC '95.

[10]  John G. Proakis,et al.  Digital Communications , 1983 .

[11]  D. Divsalar.  A Simple Tight Bound on Error Probability of Block Codes with Application to Turbo Codes , 1999 .

[12]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[13]  Shlomo Shamai,et al.  Improved upper bounds on the ensemble performance of ML decoded low density parity check codes , 2000, IEEE Communications Letters.