Universal decoding for finite-state channels

Universal decoding procedures for finite-state channels are discussed. Although the channel statistics are not known, universal decoding can achieve an error probability with an error exponent that, for large enough block length (or constraint length in case of convolutional codes), is equal to the random-coding error exponent associated with the optimal maximum-likelihood decoding procedure for the given channel. The same approach is applied to sequential decoding, yielding a universal sequential decoding procedure with a cutoff rate and an error exponent that are equal to those achieved by the classical sequential decoding procedure.     

Iterative maximum-likelihood trellis decoding for block codes

An iterative trellis search technique is described for the maximum-likelihood (ML) soft decision decoding of block codes. The proposed technique derives its motivation from the fact that a given block code may be a subcode for a parent code whose associated trellis has substantially fewer edges. Through the use of list-Viterbi (1967) decoding and an iterative algorithm, the proposed technique allows for the use of a trellis for the parent code in the ML decoding of the desired subcode. Complexity and performance analyses, as well as details of potential implementations, indicate a substantial reduction in decoding complexity for linear block codes of practical length while achieving ML or near-ML soft decision performance     

Efficient maximum-likelihood decoding of spherical lattice codes

A new framework for efficient exact Maximum- Likelihood (ML) decoding of spherical lattice codes is developed. It employs a double-tree structure: The first is that which underlies established tree-search decoders; the second plays the crucial role of guiding the primary search by specifying admissible candidates and is our present focus. Lattice codes have long been of interest due to their rich structure, leading to decoding algorithms for unbounded lattices, as well as those with axis-aligned rectangular shaping regions. Recently, spherical Lattice Space-Time (LAST) codes were proposed to realize the optimal diversity-multiplexing tradeoff of MIMO channels. We address the so-called boundary control problem arising from the spherical shaping region defining these codes. This problem is complicated because of the varying number of candidates to consider at each search stage; it is not obvious how to address it effectively within the frameworks of existing decoders. Our proposed strategy is compatible with all sequential tree-search detectors, as well as auxiliary processing such as the MMSEGDFE and lattice reduction. We demonstrate the superior performance and complexity profiles achieved when applying the proposed boundary control in conjunction with two current efficient ML detectors and show an improvement of 1dB over the state-of-the-art at a comparable complexity.     

Efficient maximum-likelihood decoding of Q-ary modulatedReed-Muller codes

We derive an efficient soft-decision maximum-likelihood decoding algorithm for a class of Q-ary phase-shift keyed peak-to-average power ratio limited codes for orthogonal frequency division modulation, by generalizing the fast Hadamard transform decoding of first-order Reed-Muller codes     

Simple maximum-likelihood decoding of generalized first-order Reed-Muller codes

An efficient decoder for the generalized first-order Reed-Muller code RM/sub q/ (1, m) is essential for the decoding of various block-coding schemes for orthogonal frequency-division multiplexing with reduced peak-to-mean power ratio. We present an efficient and simple maximum-likelihood decoding algorithm for RM/sup q/ (1, m). It is shown that this algorithm has lower complexity than other previously known maximum-likelihood decoders for RM/sub q/ (1, m).     

Bit-error probability for maximum-likelihood decoding of linearblock codes and related soft-decision decoding methods

In this correspondence, the bit-error probability P_b for maximum-likelihood decoding of binary linear block codes is investigated. The contribution P_b(j) of each information bit j to P_b is considered and an upper bound on P_b(j) is derived. For randomly generated codes, it is shown that the conventional approximation at high SNR P_b≈(d_H/N).P_s, where P_s represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P_b when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit-error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for soft-decision decoding methods which require a generator matrix with a particular structure such as trellis decoding, multistage decoding, or algebraic-based soft-decision decoding, equivalent schemes that reduce the bit-error probability are discussed. Although the gains achieved at practical bit-error rates are only a fraction of a decibel, they remain meaningful as they are of the same orders as the error performance differences between optimum and suboptimum decodings. Most importantly, these gains are free as they are achieved with no or little additional circuitry which is transparent to the conventional implementation     

Low-complexity maximum-likelihood detection of coded signals sentover finite-state Markov channels

We propose a decision-feedback decoder for coded signals transmitted over finite-state Markov channels. The decoder achieves maximum-likelihood sequence detection (in the absence of feedback errors) with very low complexity by exploiting previous bit decisions and the Markov structure of the channel. We also propose a similar decoder, the output-feedback decoder, that does not use previous bit decisions and therefore does not suffer from error propagation. The decoder performance is determined using a new sliding window analysis technique as well as by simulation. Both decoders exhibit excellent bit error rate performance with a relatively low complexity that is independent of the channel decorrelation time     

A maximum-likelihood soft-decision sequential decoding algorithmfor binary convolutional codes

We present a trellis-based maximum-likelihood soft-decision sequential decoding algorithm (MLSDA) for binary convolutional codes. Simulation results show that, for (2, 1, 6) and (2, 1, 16) codes antipodally transmitted over the AWGN channel, the average computational effort required by the algorithm is several orders of magnitude less than that of the Viterbi algorithm. Also shown via simulations upon the same system models is that, under moderate SNR, the algorithm is about four times faster than the conventional sequential decoding algorithm (i.e., stack algorithm with Fano metric) having comparable bit-error probability     

A new adaptive two-stage maximum-likelihood decoding algorithm for linear block codes

In this paper, we propose a new two-stage (TS) structure for computationally efficient maximum-likelihood decoding (MLD) of linear block codes. With this structure, near optimal MLD performance can be achieved at low complexity through TS processing. The first stage of processing estimates a minimum sufficient set (MSS) of candidate codewords that contains the optimal codeword, while the second stage performs optimal or suboptimal decoding search within the estimated MSS of small size. Based on the new structure, we propose a decoding algorithm that systematically trades off between the decoding complexity and the bounded block error rate performance. A low-complexity complementary decoding algorithm is developed to estimate the MSS, followed by an ordered algebraic decoding (OAD) algorithm to achieve flexible system design. Since the size of the MSS changes with the signal-to-noise ratio, the overall decoding complexity adaptively scales with the quality of the communication link. Theoretical analysis is provided to evaluate the potential complexity reduction enabled by the proposed decoding structure.     

A trellis-based recursive maximum-likelihood decoding algorithm forbinary linear block codes

This paper presents an efficient trellis-based maximum-likelihood decoding algorithm for binary linear block codes. This algorithm is recursive in nature and is devised based on the structural properties and optimum sectionalization of a code trellis. The complexity of the proposed decoding algorithm is analyzed. Numerical results show that the proposed decoding algorithm significantly reduces the decoding complexity. A recursive method for finding the optimum sectionalization of a trellis in terms of computational complexity is given     

On the design and maximum-likelihood decoding of space-time trellis codes

In this letter, we present a simple generalization of the maximum ratio combining principle for space-time coded systems. This result leads to a maximum-likelihood decoder implementation that does not depend on the number of receive antennas and avoids the loss in performance incurred in the decoders proposed by Tarokh and Lo (1998) and Biglieri et al. The insights offered by this decoding rule allow for a simple and elegant proof for the space-time code design criterion in systems with large number of receive antennas. We further present an upper bound on probability of error that captures the dependence of space-time code design on the number of receive antennas. Finally, we present a computationally efficient approach for constructing space-time trellis codes that exhibit satisfactory performance in systems with variable number of receive antennas.     

Bounds on the maximum-likelihood decoding error probability oflow-density parity-check codes

We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent     

Offset invariance in maximum-likelihood decoding for a class ofpartial response channels

In this letter we show that for a class of partial response channels with discrete-time pulse response of the form (1-D)P(D) whose output samples are corrupted by independent samples of additive white Gaussian noise with mean m, a maximum likelihood sequence detector designed for the case of m=0 is also the maximum likelihood sequence detector for an arbitrary value of m. The studied class of partial response channels is widely used for the characterization of digital magnetic recording channels where the DC offset is frequently an issue     

Efficient maximum-likelihood decoding of LDPC codes over the binary erasure channel

We propose an efficient maximum-likelihood (ML) decoding algorithm for decoding low-density parity-check (LDPC) codes over the binary-erasure channel (BEC). We also analyze the computational complexity of the proposed algorithm.     

Decoding of low-density parity-check codes over finite-state binary Markov channels

We propose a modified algorithm for decoding of low-density parity-check codes over finite-state binary Markov channels. The proposed approach clearly outperforms systems in which the channel statistics are not exploited in the decoding, even when the channel parameters are not known a priori at the decoder.     

Capacity-achieving input covariance for single-user multi-antenna channels

We characterize the capacity-achieving input covariance for multi-antenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenvectors are found for zero-mean channels with arbitrary fading profiles and a wide range of correlation and keyhole structures. For the eigenvalues, in turn, we present necessary and sufficient conditions as well as an iterative algorithm that exhibits remarkable properties: universal applicability, robustness and rapid convergence. In addition, we identify channel structures for which an isotropic input achieves capacity.     

Comment on "Efficient maximum-likelihood decoding of q-ary modulated Reed-Muller codes"

It is shown that in the letter by Grant and van Nee (IEEE Commun. Lett., vol.2, p.134-6, 1998) the decoding algorithm was derived incorrectly, and therefore, maximum.-likelihood decoding performance is not achieved. The correct version of the decoding algorithm is then given.     

Improved approximate maximum-likelihood receiver for differential space-time block codes over Rayleigh-fading channels

In this paper, an approximate maximum-likelihood (ML) receiver for differential space-time block codes is investigated. The receiver is derived from the ML criterion and is shown to mitigate error floor occurring in a conventional differential receiver very well. Because the receiver employs knowledges of signal-to-noise ratio (SNR) and fading rate, we study mismatched cases when these parameters are not accurate. It is shown that the receiver is more sensitive to the mismatched parameters when the fading rate is high. Then, a union bound on the bit error probability is derived. The bounds show good agreement with the simulation results at high fading rate and at high SNR. Finally, a modified receiver, denoted as multistage receiver, is proposed to compensate the so-called intrablock interference caused by the time-varying characteristic of the channel within a transmission block. The multistage receiver offers further reduction of error floor of about half order of magnitude as compared with an approximate ML receiver.     

Performance of RCPC codes with soft-decision decoding overNakagami-m fading channels

The analytical upper bounds on the pairwise error probability of rate compatible punctured convolutional (RCPC) codes, using coherent BPSK signals over slow frequency nonselective Nakagami-m fading channels with AWGN, are evaluated. With perfect channel state information (CSI) assumption, we use a direct integral with the Nakagami-m probability density function to obtain a closed form upper bound. For the case without CSI, we find an approximated upper bound for the high SNR cases and the approximation can be justified for signal to noise ratio (SNR) E _s/N₀ ≫ 1.5 dB