In this study, a class of Generalized Low-Density Parity-Check (GLDPC) codes is designed for data transmission over a Partial-Band Jamming (PBJ) environment. The GLDPC codes are constructed by replacing parity-che...In this study, a class of Generalized Low-Density Parity-Check (GLDPC) codes is designed for data transmission over a Partial-Band Jamming (PBJ) environment. The GLDPC codes are constructed by replacing parity-check code constraints with those of nonsystematic Bose-Chaudhuri-Hocquenghem (BCH), referred to as Low-Density Parity-Check (LDPC)-BCH codes. The rate of an LDPC-BCH code is adjusted by selecting the transmission length of the nonsystematic BCH code, and a low-complexity decoding algorithm based on message- passing is presented that employs A Posteriori Probability (APP) fast BCH transform for decoding the BCH check nodes at each decoding iteration. Simulation results show that the LDPC-BCH codes with a code rate of 1/8.5 have a bit error rate performance of 1 x10-8 at signal-noise-ratios of -6.97 dB, -4.63 dB, and 2.48 dB when the fractions of the band jammed are 30%, 50%, and 70%, respectively.展开更多
Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the di...Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3.展开更多
In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic f...In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic feature under the condition of the frame length known. And then candidate polynomials are achieved which meet the restrictions. Among the candidate polynomials, the most optimal polynomial is selected based on the minimum rule of the weights sum of the syndromes. Finally, the best polynomial was factorized to get the generator polynomial recognized. Simulation results show that the method has strong capability of anti-random bit error. Besides, the algorithm proposed is very simple, so it is very practical for hardware im-plementation.展开更多
Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlarge...Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlargement of CSS codes applied to nonnarrow-sense BCH codes.The second one is derived from the method of defining sets of classical cyclic codes.The asymmetric quantum BCH codes and subsystem BCH codes here have better parameters than the ones available in the literature.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 61101072 and 61132002)
文摘In this study, a class of Generalized Low-Density Parity-Check (GLDPC) codes is designed for data transmission over a Partial-Band Jamming (PBJ) environment. The GLDPC codes are constructed by replacing parity-check code constraints with those of nonsystematic Bose-Chaudhuri-Hocquenghem (BCH), referred to as Low-Density Parity-Check (LDPC)-BCH codes. The rate of an LDPC-BCH code is adjusted by selecting the transmission length of the nonsystematic BCH code, and a low-complexity decoding algorithm based on message- passing is presented that employs A Posteriori Probability (APP) fast BCH transform for decoding the BCH check nodes at each decoding iteration. Simulation results show that the LDPC-BCH codes with a code rate of 1/8.5 have a bit error rate performance of 1 x10-8 at signal-noise-ratios of -6.97 dB, -4.63 dB, and 2.48 dB when the fractions of the band jammed are 30%, 50%, and 70%, respectively.
基金supported by National Natural Science Foundation of China (Grant No.10971145)by the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20100181110073)
文摘Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3.
文摘In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic feature under the condition of the frame length known. And then candidate polynomials are achieved which meet the restrictions. Among the candidate polynomials, the most optimal polynomial is selected based on the minimum rule of the weights sum of the syndromes. Finally, the best polynomial was factorized to get the generator polynomial recognized. Simulation results show that the method has strong capability of anti-random bit error. Besides, the algorithm proposed is very simple, so it is very practical for hardware im-plementation.
基金supported by the National High Technology Research and Development Program of China (Grant No. 2011AA010803)the National Natural Science Foundation of China (Grant No. 60403004)the Outstanding Youth Foundation of Henan Province (Grant No. 0612000500)
文摘Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlargement of CSS codes applied to nonnarrow-sense BCH codes.The second one is derived from the method of defining sets of classical cyclic codes.The asymmetric quantum BCH codes and subsystem BCH codes here have better parameters than the ones available in the literature.