The Phase Errors And Error Control By LDPC Codes Under Very Low SNR Condition

Extra-long distance transmission gives rise to very low signal-to-noise ratio(SNR) in deep space communication. In order to satisfy non-linearity of power amplifier, constant envelope M-ary Phase Shift Keying(MPSK) is recommended, which results in unequal bit-error protection. Low-density parity-check(LDPC) codes have been adopted as channel coding schemes, which can achieve near Shannon limit error performance. Therefore, it is of importance to investigate the phase error and error control by LDPC codes under very low SNR condition.In this dissertation, the horizontal update process of BP decoding is first analyzed, and a reduced-complexity decoding is proposed. Secondly, the multiplier-nonlinearity affected phase error pattern of MPSK and BP decoding under unequal bit-error protection is studied. Thirdly, two modified weighted bit flipping(WBF) algorithms are proposed, and a reliability adjustment scheme is improved. At last, the physical significance of Log-MAP decoding is investigated and the decoding complexity of traditional WBF algorithms is optimized. An initial reliability adjustment scheme is also improved for BP decoding under unequal bit-error protection.Furthermore, researches of this dissertation are summarized as follows.1. Proposition of a reduced-complexity BP decoding for LDPC codeThe reliability information of BP decoding, which is delivered form check node to bit node, can be expressed as the form of natural logarithm. The antilogarithm can be written as fraction form, whose denominator is summation of22 cd ?exponential terms, wherecd denotes the row weight of regular LDPC codes. Computing the denominator with less than22 cd ?terms is proposed to simplify the horizontal update process of BP decoding with negligible performance degradation.2. Construction of the multiplier non-linearity affected phase error patternAt the radio frequency receiver, multiplier is used to achieve frequency mixing, which involves the hyperbolic tangent function. The 3 and 5 order terms of Taylor series expansion are considered to approximate the tangent function, then the mixer’s nonlinear state is obtained. Based on this, the probability density of phase error is derived, and used to determine the desired bit log likelihood ratio of BP decoding.3. Proposition of two WBF decoding algorithms for LDPC codesCalculating the reliability of the parity checks with summation of the variable nodes’ magnitude, two modified WBF algorithms are achieved, which are applicable for LDPC codes with low row/column weight. Simulation results show that the performance of one of the improved algorithms is better than that of modified WBF(MWBF) and improved MWBF(IMWBF) algorithms about 1.31 dB and 0.95 dB at bit error rate of 10-5 over an AWGN channel, respectively, while the average number of decoding iterations is significantly reduced.4. Investigation of reliability adjustment schemesTheoretical analysis shows that the “error” in the reliability of parity checks, which is proportional to the row weight, will be accumulated in flipping function of sum of the magnitude based WBF(SMWBF) algorithms. An offset factor is introduced to adjust the reliability of parity checks, then “reliability accumulation error” in flipping function is diminished, and the performance of LDPC codes with large row/column weight is improved. This modification scheme can also be applied to the two traditional reliability ratio WBF algorithms.As to LDPC coded MPSK system, a reliability based adjustment scheme is improved to increase the initial reliability of the bit, and error propagation during BP decoding is diminished to a certain degree.5. Study of physical significance of Log-MAP decoding for LDPC codesThe derivation results show that the bit-flipping function of Log-MAP decoding includes two parts: extrinsic reliability information(ERI) and intrinsic reliability information(IRI). Taking different approaches to approximate these two parts, three reduced-complexity decodings, i.e., maximum-logarithm MAP(Max-Log MAP), weighted one-step majority-logic and one-step majority-logic, can be achieved.6. Proposition of two early stop criteria for WBF algorithmsThe first proposed early stop criterion(ESC) for WBF algorithms is based on the sign of flipping function of the bit to be flipped. The decoding process is terminated once the flipping function is negative. A hybrid ESC is also improved to increase the successful detection probability of the undecodable blocks of IMWBF algorithm. According to hybrid ESC, the decoding process is proceeded if flipping the bit with negative flipping function can reduce the hamming weight of the syndrome. The simulation results show that the hybrid ESC can significantly reduce the average number of required iterations with negligible performance loss, which achieves appealing tradeoff between complexity and performance.