A BCJR-DFE Based Receiver for Achieving NearCapacity Performance on Inter Symbol InterferenceChannelsKrishna R. NarayananDept. of Electrical EngineeringTexas A&M UniversityCollege Station, TX [email protected] NangareDept. of Electrical EngineeringTexas A&M UniversityCollege Station, TX [email protected] non-iterative receiver is proposed to achieve near capacity performance oninter-symbol interference channels. There are two main ingredients in the proposeddesign - i) the use of a BCJR-DFE equalizer which produces optimal soft estimatesof the inputs to the ISI channel given all the observations from the channel and Lpast symbols exactly, where L is the memory in the ISI channel. ii) The use of anencoder structure that ensures that L past symbols can be used in the DFE in anerror free manner through the use of a capacity achieving code for a memorylesschannel. This DFE based receiver has several advantages over an iterative (turbo)receiver such as - low complexity, codes that are optimized for memoryless channelscan be used with channels with memory and finally the channel does not need tobe known at the transmitter, making this a better choice than turbo equalizerswhen long latencies can be tolerated. This general principle also applies to othersignal processing functions such as non-coherent detection, synchronization, timingrecovery etc making the proposed encoder and receiver structure a viable alternativeto iterative signal processing.1 IntroductionIterative signal processing has become a popular paradigm in communications. Severalpapers have demonstrated the benefit of iterating between a soft output decoder and afront end signal processing block such as an equalizer, synchronizer, channel estimatoror timing recovery block. Several papers have even shown that it is possible to carefullydesign low density parity check codes (LDPC) codes for use with such iterative signalprocessing techniques in order to achieve near capacity performance [1,2]. In this paper,we show that turbo or iterative signal processing is not necessary (and demonstrate analternate approach) in order to achieve near capacity performance. We show a simplereceiver structure whose complexity is only that of ONEiteration of the turbo receiverand yet achieves capacity1. The proposed receiver performs joint decoding and signalprocessing through a decision feedback mechanism.1We mean achieves the information rate corresponding to the input constellation and the inputdistributionIn this paper, we consider coding and equalization for ISI channels. However, this canbe used with other signal processing functions as well, and this is currently under study.The proposed receiver structure has several advantages over iterative receivers such as(i) The complexity is low. It is almost that of one iteration of an iterative receiver (ii)With the proposed receiver, codes optimized for single input memoryless channels suchas the additive white Gaussian noise (AWGN) channel perform well and hence there isno need to carefully design codes tailored to the channel or the specific signal processingfunction (iii) The channel does not need to be known at the transmitter and yet one codeprovides good performance on different realizations of the channel.There are two main ingredients in the proposed design - the use of a computationallyefficient BCJR-DFE equalizer at the receiver which produces optimal soft estimates ofthe inputs to the ISI channel given L past symbols exactly, where L is the memory in theISI channel and all the observations from the channel. The use of encoder and decoderstructures that ensures that L past symbols can be fed to the receiver in an error freemanner through the use of a capacity achieving code for a memoryless channel.The proposed receiver structure is not entirely new. There are at least four papersthat are closely related to this work. However, there are differences between this paperand each of these papers which is briefly summarized below. The proposed receiver is mo-tivated from the classic two part paper by Cioffi et al [3,4] where they show that MMSEdecision feedback equalization (DFE) with error free decision feedback is a canonicalstructure and predicts the performance of coding schemes accurately for any ISI chan-nel. Here, we show by replacing the MMSE filter by a BCJR algorithm (hence, theterm, BCJR-DFE), with ideal feedback we can exactly achieve capacity for any SNR andany input constellation. We propose a computationally efficient BCJR-DFE algorithm,whose complexity is only half that of the conventional BCJR algorithm. In order toachieve perfect decision feedback equalization, Cioffi et al propose to cancel the ISI atthe transmitter through precoding. In the proposed receiver, the DFE is at the receiverand, hence, the channel does not need to be known at the transmitter. It must be notedthat Varanasi and Guess [5] have also shown the optimality of ideal decision feedbackMulti user detection.Although this encoder structure was derived to facilitate a DFE receiver, in effectthis is nearly equivalent to the concept of interleaved multiplexed codewords that Pfister,Soriaga and Siegel used to derive information rates for ISI channels in their landmarkpaper [6]. In [6], they use the idea of m interleaved codes each of a different rate (therates are usually dependent on the channel) and a multi-stage decoder which involves mpasses of a APP (BCJR) decoder. The encoder structure here can be thought of as minterleaved codes but with some known symbols added between the codes. The presenceof these known symbols makes the channels completely memoryless. Hence, the receiverstructure proposed here does not require m uses of an a posteriori probabilities (APP)decoder as in [6]. It requires only one APP decoder. Further, m different codes are notrequired. Only one code of a fixed rate (almost independent on the channel taps butdependent only on the achievable information rate) is required.The receiver structure is also nearly the same that proposed in Fechtel and Meyr [7]and in Eyuboglu [8], where trellis codes are used along with DFE. The difference is inthe use of the novel BCJR-DFE and capacity achieving LDPC code both of which arerequired to achieve capacity. Further, we prove the optimality and utility of this scheme,which seems to have been forgotten in favor of turbo equalization.PILOTSPILOTSPILOTSPILOTSEach column is an LDPC coded wordData is transmittedrow