Coding techniques have always been a major area of scientific interest. Due to this interest, many coding schemes were invented. Eventually, their implementation in various systems contributed in the evolvement of Wir...Coding techniques have always been a major area of scientific interest. Due to this interest, many coding schemes were invented. Eventually, their implementation in various systems contributed in the evolvement of Wireless Communications. A breakthrough was definitely Turbo coding. Particularly, the concept of joining two or more convolutional encoders in parallel (PCCC) or in serial (SCCC), along with the iterative decoding technique, literally raised the expectations of the anticipated BER performance. In fact, Concatenated Convolutional Codes clearly outperform convolutional codes. Moreover, various systems, either under development or either for future use, will have high standards. The previous systems should present exceptional tolerance of noise effects and consequently a low overall number of received errors. For this purpose a new PCCC design was developed. The system’s performance analysis, using an AWGN channel, showed better results for various iterations compared to other schemes such as typical PCCC, SCCC and finally a Convolutional encoder with a Viterbi decoder.展开更多
In this paper,we study turbo codes from the digital signal processing point of view by defining turbo codes over the complex field.It is known that iterative decoding and interleaving between concatenated parallel cod...In this paper,we study turbo codes from the digital signal processing point of view by defining turbo codes over the complex field.It is known that iterative decoding and interleaving between concatenated parallel codes are two key elements that make turbo codes perform significantly better than the conventional error control codes.This is analytically illustrated in this paper.We show that the decoded noise mean power in the iterative decoding decreases when the number of iterations increases,as long as the interleaving decorrelates the noise after each iterative decoding step.An analytic decreasing rate and the limit of the decoded noise mean power are given.The limit of the decoded noise mean power of the iterative decoding of a turbo code with two parallel codes with their rates less than 1/2 is one third of the noise power before the decoding,which can not be achieved by any non-turbo codes with the same rate.From this study,the role of designing a good interleaver can also be clearly seen.展开更多
It is well known that turbo decoding always begins from the first component decoder and supposes that the apriori information is '0' at the first iterative decoding. To alternatively start decoding at two comp...It is well known that turbo decoding always begins from the first component decoder and supposes that the apriori information is '0' at the first iterative decoding. To alternatively start decoding at two component decoders, we can gain two soft output values for the received observation of an input bit. It is obvious that two soft output values comprise more sufficient extrinsic information than only one output value obtained in the conventional scheme since different start points of decoding result in different combinations of the a priori information and the input codewords with different symbol orders due to the permutation of an interleaver. Summarizing two soft output values for erery bit before making hard decisions, we can correct more errors due to their complement. Consequently, turbo codes can achieve better error correcting performance than before in this way. Simulation results show that the performance of turbo codes using the novel proposed decoding scheme can get a growing improvement with the increment of SNR in general compared to the conventional scheme. When the bit error probability is 10-5 , the proposed scheme can achieve 0.5 dB asymptotic coding gain or so under the given simulation conditions.展开更多
In this paper, a new method to approximate the compensation term in the Jacobian logarithm used by the MAP decoder is proposed. Using the proposed approximation, the complex functions In（.） and exp（.） in the Exact...In this paper, a new method to approximate the compensation term in the Jacobian logarithm used by the MAP decoder is proposed. Using the proposed approximation, the complex functions In（.） and exp（.） in the Exact-log-MAP algorithm can be estimated with high accuracy and lower computational complexity. The efficacy of the proposed approximation is investigated and demonstrated by applying it to iteratively decoded BICM （Bit Interleaved Coded Modulation）.展开更多
文摘Coding techniques have always been a major area of scientific interest. Due to this interest, many coding schemes were invented. Eventually, their implementation in various systems contributed in the evolvement of Wireless Communications. A breakthrough was definitely Turbo coding. Particularly, the concept of joining two or more convolutional encoders in parallel (PCCC) or in serial (SCCC), along with the iterative decoding technique, literally raised the expectations of the anticipated BER performance. In fact, Concatenated Convolutional Codes clearly outperform convolutional codes. Moreover, various systems, either under development or either for future use, will have high standards. The previous systems should present exceptional tolerance of noise effects and consequently a low overall number of received errors. For this purpose a new PCCC design was developed. The system’s performance analysis, using an AWGN channel, showed better results for various iterations compared to other schemes such as typical PCCC, SCCC and finally a Convolutional encoder with a Viterbi decoder.
文摘In this paper,we study turbo codes from the digital signal processing point of view by defining turbo codes over the complex field.It is known that iterative decoding and interleaving between concatenated parallel codes are two key elements that make turbo codes perform significantly better than the conventional error control codes.This is analytically illustrated in this paper.We show that the decoded noise mean power in the iterative decoding decreases when the number of iterations increases,as long as the interleaving decorrelates the noise after each iterative decoding step.An analytic decreasing rate and the limit of the decoded noise mean power are given.The limit of the decoded noise mean power of the iterative decoding of a turbo code with two parallel codes with their rates less than 1/2 is one third of the noise power before the decoding,which can not be achieved by any non-turbo codes with the same rate.From this study,the role of designing a good interleaver can also be clearly seen.
文摘It is well known that turbo decoding always begins from the first component decoder and supposes that the apriori information is '0' at the first iterative decoding. To alternatively start decoding at two component decoders, we can gain two soft output values for the received observation of an input bit. It is obvious that two soft output values comprise more sufficient extrinsic information than only one output value obtained in the conventional scheme since different start points of decoding result in different combinations of the a priori information and the input codewords with different symbol orders due to the permutation of an interleaver. Summarizing two soft output values for erery bit before making hard decisions, we can correct more errors due to their complement. Consequently, turbo codes can achieve better error correcting performance than before in this way. Simulation results show that the performance of turbo codes using the novel proposed decoding scheme can get a growing improvement with the increment of SNR in general compared to the conventional scheme. When the bit error probability is 10-5 , the proposed scheme can achieve 0.5 dB asymptotic coding gain or so under the given simulation conditions.
文摘In this paper, a new method to approximate the compensation term in the Jacobian logarithm used by the MAP decoder is proposed. Using the proposed approximation, the complex functions In（.） and exp（.） in the Exact-log-MAP algorithm can be estimated with high accuracy and lower computational complexity. The efficacy of the proposed approximation is investigated and demonstrated by applying it to iteratively decoded BICM （Bit Interleaved Coded Modulation）.
