Efficient detection and decoding of q-ary LDPC coded signals over partial response channels

EURASIP Journal on Wireless Communications and Networking, Jan 2013

In this study, we consider the ways for concatenating the intersymbol interference (ISI) detector with a q-ary low-density parity-check (LDPC) decoder for transmissions over partial response (PR) channels. LDPC codes allow achieving performance close to the channel capacity in additive white Gaussian noise channels, while designing receivers employing these codes for transmissions over channels affected by ISI is still an open issue. Turbo equalization schemes are considered with a novel joint message-passing-based receiver, which is derived from a recently proposed joint algorithm for binary LDPC codes. Simulation results provide performance evaluation of these systems over three different PR channels, together with an analysis of the trade-off between error-rate performance and complexity.

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Efficient detection and decoding of q-ary LDPC coded signals over partial response channels

Andrea Marinoni 0 Pietro Savazzi 0 Paolo Gamba 0 0 Dipartimento di Ingegneria Industriale e dell'Informazione, University of Pavia , Pavia, Italy In this study, we consider the ways for concatenating the intersymbol interference (ISI) detector with a q-ary lowdensity parity-check (LDPC) decoder for transmissions over partial response (PR) channels. LDPC codes allow achieving performance close to the channel capacity in additive white Gaussian noise channels, while designing receivers employing these codes for transmissions over channels affected by ISI is still an open issue. Turbo equalization schemes are considered with a novel joint message-passing-based receiver, which is derived from a recently proposed joint algorithm for binary LDPC codes. Simulation results provide performance evaluation of these systems over three different PR channels, together with an analysis of the trade-off between error-rate performance and complexity. - equal weight, while irregular LDPC codes do not exhibit this property. Non-binary (or q-ary) LDPC codes have codewords (and also a PC matrix) whose symbols are elements of the finite field GF(q), with q > 2. These non-binary LDPC codes can allow significantly enhanced performance with respect to the binary case, by increasing the finite field dimension [7]. However, the decoding complexity is O(Ntq2), where N is the block length, t is the average column weight, and q is the alphabet size [7,8]. Recent papers reveal that q-ary LDPC may be applied to magnetic recording channels, allowing reduced complexity schemes [9] and robustness to burst errors [10], making the q-ary solution comparable with the binary case. Historically, considering an LDPC-coded system, the most popular scheme to improve error-correction performance over channels affected by ISI has been to serially concatenate a soft-output detection algorithm and the binary LDPC decoder. However, a greater performance improvement can be achieved by incorporating the channel detector in the iterative decoder: this implies a turbo concatenation of the two system blocks and several papers in literature call that configuration turbo equalization (TE). Further, in [11-13], an LDPC-coded detection-anddecoding system implemented by a joint algorithm based on the message-passing (MP) algorithm is addressed. In this article, we extend the joint detection-anddecoding scheme to q-ary LDPC codes. Furthermore, we compare the proposed approach to TE, paying particular attention to the properties of the detector and the decoder selected for each one. Some preliminary results of this study are presented in [14]. The article is organized as follows. The first sections introduce the system model for the different architectures that are discussed in the article, namely TE, first turbo equalization iteration (FTEI), and the proposed joint MPbased architecture. For the FTEI scheme, no extrinsic information is exchanged, since only the first iteration is performed by doing soft separate detection and decoding. Further, the computational complexity of each receiver scheme considered is discussed in a dedicated section. Finally, simulation results are given, and some remarks about future research development conclude the article. 2 System model In this section, we analyze the performance of a novel receiver algorithm for q-ary LDPC-coded signals over PR channels, comparing its performance with those obtained by TE and FTEI schemes. The basic system model is shown in Figure 1. The qary LDPC encoder output is a length-N codeword = [ i]i=1,...,N , i GF(q = 2p) i = 1, . . . , N such that where H = {Hij}i=1,...,M,j=1,...,N , Hij GF(q = 2p) is the parity-check matrix. The binary representation of each codeword { }n is transmitted by an antipodal binary pulse-amplitude modulator through a PR channel having a memory of length bits. Each receiver architecture that has been taken into account employs a q-ary LDPC decoder and a BCJR detector that can either be bit-based (BB) or symbolbased (SB). 2.1 BB detector The BB detector is represented by the standard BCJR algorithm [3]. The symbol-wise a posteriori probabilities (APPs) are approximated applying the BCJR algorithm to the PR channel and then multiplying the APPs that form a symbol [15,16]. The symbol-wise APPs are passed to the q-ary LDPC decoder to initialize the a priori probabilities. 2.2 SB detector The SB detector [15,17] modifies the way the probability functions are updated when compared to the original BCJR algorithm. Hoeher [17] develops a method, called optimal subblock-by-subblock detector, in order to calculate the APP of a block of p consecutive bits. Cheng et al. [15] show that simplifications of the algorithm can be made for the case of the binary-input ISI channels, specifically for p . Let a GF(q = 2p) be an information symbol. It is possible to map each symbol in GF(q = 2p) to a distinct sequence of p bits; in other terms, the binary representation of a is b0p1 (...truncated)


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Andrea Marinoni, Pietro Savazzi, Paolo Gamba. Efficient detection and decoding of q-ary LDPC coded signals over partial response channels, EURASIP Journal on Wireless Communications and Networking, 2013, pp. 18, Volume 2013, Issue 1, DOI: 10.1186/1687-1499-2013-18