scholarly journals An Efficient Feedback Coding Scheme With Low Error Probability for Discrete Memoryless Channels

2015 ◽  
Vol 61 (6) ◽  
pp. 2953-2963 ◽  
Author(s):  
Cheuk Ting Li ◽  
Abbas El Gamal
Keyword(s):  
Error Probability ◽  
Coding Scheme ◽  
Memoryless Channels

scholarly journals Lower bounds to error probability for coding on discrete memoryless channels. I

1967 ◽  
Vol 10 (1) ◽  
pp. 65-103 ◽  
Author(s):  
C.E. Shannon ◽  
R.G. Gallager ◽  
E.R. Berlekamp
Keyword(s):  
Lower Bounds ◽  
Error Probability ◽  
Memoryless Channels

scholarly journals Evaluation of the union bound for the decoding error probability using characteristic functions

2021 ◽  
pp. 71-85
Author(s):  
Andrey Trofimov ◽  
Feliks Taubin
Keyword(s):  
Numerical Integration ◽  
Wide Class ◽  
Error Probability ◽  
Integral Form ◽  
Characteristic Functions ◽  
Maximum Likelihood Decoding ◽  
Coding Schemes ◽  
Memoryless Channels ◽  
Union Bound ◽  
Final Expression

Introduction: Since the exact value of a decoding error probability cannot usually be calculated, an upper bounding technique is used. The standard approach for obtaining the upper bound on the maximum likelihood decoding error probability is based on the use of the union bound and the Chernoff bound, as well as its modifications. For many situations, this approach is not accurate enough. Purpose: Development of a method for exact calculation of the union bound for a decoding error probability, for a wide class of codes and memoryless channels. Methods: Use of characteristic functions of logarithm of the likelihood ratio for an arbitrary pair of codewords, trellis representation of codes and numerical integration. Results: The resulting exact union bound on the decoding error probability is based on a combination of the use of characteristic functions and the product of trellis diagrams for the code, which allows to obtain the final expression in an integral form convenient for numerical integration. An important feature of the proposed procedure is that it allows one to accurately calculate the union bound using an approach based on the use of transfer (generating) functions. With this approach, the edge labels in the product of trellis diagrams for the code are replaced by their corresponding characteristic functions. The final expression allows, using the standard methods of numerical integration, to calculate the values of the union bound on the decoding error probability with the required accuracy. Practical relevance: The results presented in this article make it possible to significantly improve the accuracy of the bound of the error decoding probability, and thereby increase the efficiency of technical solutions in the design of specific coding schemes for a wide class of communication channels.

scholarly journals Lower bounds to error probability for coding on discrete memoryless channels. II

1967 ◽  
Vol 10 (5) ◽  
pp. 522-552 ◽  
Author(s):  
C.E. Shannon ◽  
R.G. Gallager ◽  
E.R. Berlekamp
Keyword(s):  
Lower Bounds ◽  
Error Probability ◽  
Memoryless Channels

Research on Reed-Solomon Code in Complementary Code Keying Modulation Technology

2010 ◽  
Vol 44-47 ◽  
pp. 1070-1074
Author(s):  
Xi Su ◽  
Peng Bai ◽  
Yan Ping Feng ◽  
Yuan Yuan Wu
Keyword(s):  
Error Correction ◽  
System Performance ◽  
Error Probability ◽  
High Speed ◽  
High Signal ◽  
Decoding Algorithms ◽  
Coding Scheme ◽  
Reed Solomon Code ◽  
Simulation Results ◽  
Rs Coding

As the high speed expanding scheme adopted by IEEE802.11b standard, the Complementary Code Keying modulation technology can only perform well in error probability with high signal noise ratio. However, when SNR is comparably low or the number of users in the same channel augments suddenly, the system’s error probability soars. On the basis of the research on Complementary Code Keying, RS coding and decoding algorithms, this paper analyzed code parameters’ influence on error correction and accordingly promoted a coding scheme suitable for Complementary Code Keying: RS（255,239）. Simulation Results demonstrated that once SNR is upon 5.1dB the system performance would be greatly enhanced.

Application of Convolution Code in CCK Modulation Technology

2010 ◽  
Vol 29-32 ◽  
pp. 2680-2685
Author(s):  
Xi Su ◽  
Peng Bai ◽  
Yan Ping Feng ◽  
Yuan Yuan Wu
Keyword(s):  
Channel Coding ◽  
System Performance ◽  
Error Probability ◽  
High Speed ◽  
High Signal ◽  
Soft Decision ◽  
Coding Gain ◽  
Coding Scheme ◽  
Simulation Results ◽  
Soft Decision Decoding

Adopted by IEEE802.11b standard as the high speed expanding scheme, CCK modulation technology performs well in error probability with high signal noise ratio. However, the CCK system’s error probability soars when SNR is comparably low or the number of users in the same channel increases suddenly. Based on CCK algorithm and convolution code’s structure, this paper analyzed code parameters’ influence on error probability and proposed a channel coding scheme suitable for CCK modulation: convolution code （2,1,7）with 3bit soft decision decoding. Simulation Results demonstrated that system performance is greatly improved when SNR is upon 1.3dB and 2dB’s additional coding gain is attained compared with hard decision decoding.

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