Low Application Rate Error-correcting Code And Its Communication To A Minimum

Minimum Essential Emergency Communication (MEEC) is such a system that can be started-up and maintain communication, while regular communications fail or are inadequate when there are very strong noises and electromagnetic interference. MEEC is required to fulfill the following conditions simultaneously: ability of anti-interference and resisting noise, real-time communication, and low probability of intercept. For error correcting coding, MEEC needs low complexity of coding algorithm and decoding algorithm, good randomness of code and certain SNR (Signal-to-Noise Ratio) for low BER (Bit Error Rate), etc.Truncated simplex code has the specific characters: good randomness, low complexity of coding and flexible code rate. This paper chooses truncated simplex code in the case of low code rate. Decoded by SPAs (Sum Product Algorithms), LDPC (Low Density Parity Check) codes have very good performance in high code rate condition, but they do not suit to the application of low code rate. Simplex code is also a kind of Generalixed LDPC code, and it performs even worse than LDPC codes when decoded by SPAs. This paper uses B algorithm to decode simplex code. This combination can achieve good performance.B algorithm is an algorithm of fast correlation attacks on key generator employed in stream cipher system, when used in cryptography. B algorithm is also applicable in decoding in coding, as assimilated Galleger's main ideal of iterative probability decoding. This paper researches the complexity and performance of B algorithm in the decoding of truncated simplex code.According to the ideals of WBF(Weighted Bit Flipping) algorithm and SPA in decoding algorithms for LDPC code, this paper proposes a method of weighted B algorithm(WB algorithm), improved performance with a little complexity increase. In the case of information length k of 10 bits and code rate R of 0.008, k = 10 and R = 0.003, k = 15 and R = 0.003, WB algorithm achieves the BER performance of 10-5 at E sN 0 =- 12.5dB, - 14.6dB and - 15.7dB, while B algorithm at - 10.7dB, - 13.5dB and - 14.4dB. WB algorithm gains about 1.8dB, 1.1dB and 1.3dB over B algorithm.Based upon the characteristics of cyclic code, this paper proposes CBP (Cyclic code's Belief propagation) algorithm by expanding the check matrix. Also compares at the level of BER = 10-5, when k = 10 and R = 10 1023, k = 10 and R = 0.008, nomolised BP-based algotirhm are both 4dB, while CBP algorithm are - 12.4dB and - 13.1dB. CBP algorithm performs better than that of WB algorithm. In the case of k = 31 and R = 0.008, these two algorithms achieve BER performance of 10-5 for E sN 0 =- 14.94dB and - 14.2dB separately.By a mass of simulations, this paper analyzes the performance under different code rates, length of information bits, maximum iterative times and other conditions. Based on characteristics of spread spectrum code and truncated simplex code decoding by CBP algorithm or WB algorithm, this paper provides a concatenated code. Decoding this concatenated code by CBP algorithm or WB algorithm can get higher performance and lower complexity. For instance, CBP algorithm decoding concatenated code of k = 31 and R = 0.003 can achieve BER performance of 10-5 for E sN 0 =- 20dB.