Krishna R. Narayanan

LDPC-based space-time coded OFDM systems over correlated fading channels: Performance analysis and receiver design

We consider a space-time coded (STC) orthogonal frequency-division multiplexing (OFDM) system with multiple transmitter and receiver antennas over correlated frequency- and time-selective fading channels. It is shown that the product of the time-selectivity order and the frequency-selectivity order is a key parameter to characterize the outage capacity of the correlated fading channel. It is also observed that STCs with large effective lengths and ideal built-in interleavers are more effective in exploiting the natural diversity in multiple-antenna correlated fading channels. We then propose a low-density parity-check (LDPC)-code-based STC-OFDM system. Compared with the conventional space-time trellis code (STTC), the LDPC-based STC can significantly improve the system performance by exploiting both the spatial diversity and the selective-fading diversity in wireless channels. Compared with the previously proposed turbo-code-based STC scheme, LDPC-based STC exhibits lower receiver complexity and more flexible scalability. We also consider receiver design for LDPC-based STC-OFDM systems in unknown fast fading channels and propose a novel turbo receiver employing a maximum a posteriori expectation-maximization (MAP-EM) demodulator and a soft LDPC decoder, which can significantly reduce the error floor in fast fading channels with a modest computational complexity. With such a turbo receiver, the proposed LDPC-based STC-OFDM system is a promising solution to highly efficient data transmission over selective-fading mobile wireless channels.

A novel ARQ technique using the turbo coding principle

A novel automatic repeat request (ARQ) technique based on the turbo coding principle is presented. The technique uses the log-likelihood ratios generated by the decoder during a previous transmission as a priori information when decoding retransmissions. Simulation results show a significant decrease in frame error rate, especially at low-to-moderate E/sub b//N/sub 0/.

A serial concatenation approach to iterative demodulation and decoding

Iterative demodulation and decoding of convolutionally encoded data is treated as a special case of the previously proposed serial concatenation of interleaved codes. It is shown that by exploiting the recursive nature of the differential modulation schemes (for example, DBPSK, DQPSK, CPM, etc.), large interleaving gains can be achieved similar to serial concatenation schemes. We also show that when memoryless modulation is used, precoding can be used to create a rate-1 recursive inner code in order to obtain interleaving gains without adding redundancy from the inner code.

Iterative Soft-Input Soft-Output Decoding of Reed–Solomon Codes by Adapting the Parity-Check Matrix

An iterative algorithm is presented for soft-input soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum-product algorithm (SPA) in conjunction with a binary parity-check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity-check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard-decision decoding (HDD) and compare favorably with other popular soft-decision decoding methods

Performance of trellis-coded CPM with iterative demodulation and decoding

Interleaved trellis-coded systems with full response continuous-phase modulation (CPM) are considered. Upper bounds on the bit-error rate performance are derived for coherent detection on the additive white Gaussian noise and flat Rayleigh fading channels by considering the trellis code, interleaver, and CPM modulator as a serially concatenated convolutional code. A coherent receiver that performs iterative demodulation and decoding is shown to provide good bit error performance. Finally, a noncoherent iterative receiver is proposed and is shown to perform close to the coherent iterative receiver.

Product accumulate codes: a class of codes with near-capacity performance and low decoding complexity

We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalars (1999) simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2.

Effect of precoding on the convergence of turbo equalization for partial response channels

The effect of the precoder on the convergence of turbo equalization for precoded partial response channels is studied. The idea is to consider the turbo decoding algorithm as a one-parameter dynamical system and to study the effect of the precoder on the fixed points of the system. It is showed that precoding results in a loss in fidelity during the first iteration and that this loss depends on the precoder. Further, the rate at which the extrinsic information increases with iterations is also dependent on the precoder. The net result of these two effects is used to explain several existing results in the literature about the performance of different precoders. A design criteria based on the convergence is then proposed, and the impact of precoding on the design of the outer code is then studied. Finally, the design of precoders in the presence of an error correcting code, such as a Reed-Solomon code, is studied.

On the performance of high-rate TPC/SPC codes and LDPC codes over partial response channels

This paper evaluates two-dimensional turbo product codes based on single-parity check codes (TPC/SPC) and low-density parity check (LDPC) codes for use in digital magnetic recording systems. It is first shown that the combination of a TPC/SPC code and a precoded partial response (PR) channel results in a good distance spectrum due to the interleaving gain. Then, density evolution is used to compute the thresholds for TPC/SPC codes and LDPC codes over PR channels. Analysis shows that TPC/SPC codes have a performance close to that of LDPC codes for large codeword lengths. Simulation results for practical block lengths show that TPC/SPC codes perform as well as LDPC codes in terms of bit error rate, but possess better burst error statistics which is important in the presence of an outer Reed-Solomon code. Further, the encoding complexity of TPC/SPC codes is only linear in the codeword length and the generator matrix does not have to be stored explicitly. Based on. the results in the paper and these advantages, TPC/SPC codes seem like a viable alternative to LDPC codes.

Minimal network coding for multicast

We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize the number of packets that undergo network coding. We also propose a decentralized algorithm to construct capacity achieving multicast codes when the processing at some nodes is restricted to routing. The proposed algorithms can be coupled with existing decentralized schemes to achieve minimum cost multicast

Joint Source Channel Coding With Side Information Using Hybrid Digital Analog Codes

We study the joint source-channel coding problem of transmitting a Gaussian source over a Gaussian channel in two cases: (i) the presence of interference known only to the transmitter and (ii) in the presence of side information about the source known only to the receiver. We introduce hybrid digital analog forms of the Costa and Wyner-Ziv coding schemes. We present the random coding counterpart of schemes based on lattices proposed by Kochman and Zamir. Then, we discuss applications of the hybrid digital analog schemes in the case of channel signal-to-noise ratio mismatch and for lossy multicasting of a common source with bandwidth compression.