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Serial concatenation of simple codes and differential modulations Mitra, Jeebak

Abstract

Error-correcting codes are used in communication systems to provide reliable transmission on practical communication channels and thus reduce the number of retransmissions. The ability of a particular code to be able to detect and correct errors at the receiver depends on the individual code structure as well as on the decoding algorithm. Codes that provide strong error correcting capabilities usually involve a number of operations on the information bits and hence are not easily decodable at the receiver. Rather than relying on the use of a single high complexity code, a concatenation of two or more simple codes can be used. Serially concatenated encoding structures are very popular means to achieving close to capacity performance. Good performance of concatenated codes with practically viable decoding times is attributed to a technique known as iterative decoding. Iterative decoding can only be used in a situation where the component decoders are capable of generating soft information for the transmitted data. Soft information for symbol-by-symbol estimation is usually obtained by using the Bahl Cocke Jelinek Raviv (BCJR) algorithm or some sub-optimal version of it. Differential encoding of the data at the transmitter is regarded as an effective approach to combat phase ambiguities at the receiver, when using phase shift keying (PSK) schemes. Since the information is transmitted in difference of phases rather than the absolute phase of the transmitted symbol, there is more protection against an unknown channel phase at the receiver. The serial concatenation of an error correcting code with a differential encoder has been found to provide very good performance for various kinds of channel conditions. In this work we propose and analyse the design of a serially concatenated structure which is very simple to implement and is particularly favourable for a low power scenario such as deep space applications. The proposed system comprises of a concatenation of simple parity check codes and a differential encoder (DE). Individually, these codes are very weak codes as they provide minimal error-correcting capabilities. We optimise system design parameters through extensive analysis of the system structure using extrinsic information transfer (EXIT) charts. It is shown through simulations and analytical results that the proposed concatenated codes provide performance very close to capacity. Comparison of these simple parity check codes with certain other very powerful outer codes such as Low Density Parity Check (LDPC) codes show the superior performance of the proposed codes inspite of much lower decoding complexity. For the case, where channel phase is unknown or perfect synchronisation is not attainable at the receiver, several estimation algorithms have been proposed in the literature to combat the effects of channel phase. These algorithms can usually be divided into two categories. The first is those that use pilot symbols, which increases the transmission overhead. The second is to not have any explicit channel estimation mechanism. Here we adopt the second one and consider two approaches. One is based on the quantization of the unknown phase and is computationally intensive with the complexity depending on number of levels of quantization. The other is to do a blind estimation based on the information derived from received symbols. On the lines of the second approach we propose a simple method for noncoherent decoding that uses a posteriori information to estimate the channel phase. It is shown that the method works well for the cases of low to moderate variations in channel phase.

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