Statistical Approach for Blind Recognition of Narrow-sense BCH Codes

2018 ◽  
Author(s):  
Jiho Kim ◽  
Soonhee Kwon ◽  
Dong-Joon Shin
Keyword(s):  
Statistical Approach ◽  
Bch Codes ◽  
Narrow Sense ◽  
Blind Recognition

scholarly journals Blind Recognition of Binary BCH Codes for Cognitive Radios

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Jing Zhou ◽  
Zhiping Huang
Keyword(s):  
Cognitive Radios ◽  
Recognition Algorithm ◽  
Bch Codes ◽  
Parity Check ◽  
Soft Decision ◽  
Likelihood Ratios ◽  
Primitive Polynomials ◽  
Cognitive Radio Systems ◽  
Radio Systems ◽  
Blind Recognition

A novel algorithm of blind recognition of Bose-Chaudhuri-Hocquenghem (BCH) codes is proposed to solve the problem of Adaptive Coding and Modulation (ACM) in cognitive radio systems. The recognition algorithm is based on soft decision situations. The code length is firstly estimated by comparing the Log-Likelihood Ratios (LLRs) of the syndromes, which are obtained according to the minimum binary parity check matrixes of different primitive polynomials. After that, by comparing the LLRs of different minimum polynomials, the code roots and generator polynomial are reconstructed. When comparing with some previous approaches, our algorithm yields better performance even on very low Signal-Noise-Ratios (SNRs) with lower calculation complexity. Simulation results show the efficiency of the proposed algorithm.

scholarly journals A class of narrow-sense BCH codes over $$\mathbb {F}_q$$ of length $$\frac{q^m-1}{2}$$

2019 ◽  
Vol 88 (2) ◽  
pp. 413-427 ◽  
Author(s):  
Xin Ling ◽  
Sihem Mesnager ◽  
Yanfeng Qi ◽  
Chunming Tang
Keyword(s):  
Bch Codes ◽  
Narrow Sense

Hermitian dual-containing narrow-sense constacyclic BCH codes and quantum codes

2019 ◽  
Vol 18 (10) ◽  
Author(s):  
Liqi Wang ◽  
Zhonghua Sun ◽  
Shixin Zhu
Keyword(s):  
Bch Codes ◽  
Quantum Codes ◽  
Narrow Sense

New quantum codes derived from a family of antiprimitive BCH codes

2017 ◽  
Vol 15 (07) ◽  
pp. 1750052 ◽  
Author(s):  
Yang Liu ◽  
Ruihu Li ◽  
Liangdong Lü ◽  
Luobin Guo
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Detailed Analysis ◽  
Communication System ◽  
Quantum Information Theory ◽  
Bch Codes ◽  
Quantum Codes ◽  
Narrow Sense ◽  
Classical Communication ◽  
Cyclotomic Cosets

The Bose–Chaudhuri–Hocquenghem (BCH) codes have been studied for more than 57 years and have found wide application in classical communication system and quantum information theory. In this paper, we study the construction of quantum codes from a family of [Formula: see text]-ary BCH codes with length [Formula: see text] (also called antiprimitive BCH codes in the literature), where [Formula: see text] is a power of 2 and [Formula: see text]. By a detailed analysis of some useful properties about [Formula: see text]-ary cyclotomic cosets modulo [Formula: see text], Hermitian dual-containing conditions for a family of non-narrow-sense antiprimitive BCH codes are presented, which are similar to those of [Formula: see text]-ary primitive BCH codes. Consequently, via Hermitian Construction, a family of new quantum codes can be derived from these dual-containing BCH codes. Some of these new antiprimitive quantum BCH codes are comparable with those derived from primitive BCH codes.

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