Reduced-state Viterbi Algorithm Research Articles

Asynchronous Convolutional-Coded Physical-Layer Network Coding

This paper investigates the decoding process of asynchronous convolutional-coded physical-layer network coding (PNC) systems. Specifically, we put forth a layered decoding framework for convolutional-coded PNC consisting of three layers: symbol realignment layer, codeword realignment layer, and joint channel-decoding network coding (Jt-CNC) decoding layer. Our framework can deal with phase asynchrony (phase offset) and symbol arrival-time asynchrony (symbol misalignment) between the signals simultaneously transmitted by multiple sources. A salient feature of this framework is that it can handle both fractional and integral symbol misalignments. For the decoding layer, instead of Jt-CNC, previously proposed PNC decoding algorithms (e.g., XOR-CD and reduced-state Viterbi algorithms) can also be used with our framework to deal with general symbol misalignments. Our Jt-CNC algorithm, based on belief propagation, is BER-optimal for synchronous PNC and near optimal for asynchronous PNC. Extending beyond convolutional codes, we further generalize the Jt-CNC decoding algorithm for all cyclic codes. Our simulation shows that Jt-CNC outperforms the previously proposed XOR-CD algorithm and reduced-state Viterbi algorithm by 2 dB for synchronous PNC. For both phase-asynchronous and symbol-asynchronous PNC, Jt-CNC performs better than the other two algorithms. Importantly, for real wireless network experimentation, we implemented our decoding algorithm in a PNC prototype built on the USRP software radio platform. Our experiment shows that the proposed Jt-CNC decoder works well in practice.

A reduced complexity estimation algorithm for ultrasound images de-blurring

In this paper we propose a deconvolution technique for ultrasound images based on a Maximum Likelihood (ML) estimation procedure. In our approach the ultrasonic radio-frequency (RF) signal is considered as a sequence affected by Intersymbol Interference (ISI) and AWG noise. In order to reduce the computational cost, the estimation is performed with a reduced-state Viterbi algorithm. The channel effect is estimated in two different ways: either measuring the transducer response with an experimental setting or with blind homomorphic techniques. We observed an enhancement in image quality with respect to different metrics. Extensive tests were made to estimate the quantization alphabet that gives the best performances.

Reduced state Viterbi differential phase detection of MDPSK signals

An improved differential phase detection scheme that uses a reduced state Viterbi algorithm (RSVDPD) is proposed for the reception of M-ary differential phase shift keying (MDPSK) signals. The transmitted sequence is estimated from the received signal phases only. The number of trellis states equals that of the signal constellation points M. The branch metric is computed by tracing back the surviving path connected to each state. The bit error rate (BER) performance with RSVDPD is evaluated using computer simulation for 4DPSK transmission in additive white Gaussian noise (AWGN) channels.

A generalized Viterbi algorithm for detection of partial response recording systems

In this work, we study a receiver for a high density recording system and compare it with the PRML recording system. In the receiver, the playback signal of a high density recording system is equalized to a higher-order partial response (PR) target. Also, a reduced-state Viterbi algorithm, called the generalized Viterbi algorithm (GVA), is used for detecting the PR system. In the GVA, the states are grouped into L subsets or lists and the best S paths in each list are selected for extension. Simulation results demonstrate that coding gain over the PRML system can be obtained even for the receiver with less complexity than that of the PRML system.

Bit error rate analysis of reduced-state Viterbi differential detection of M-ary DPSK signals

A tight upper bound of bit error rate (BER) is derived for approximate maximum likelihood differential detection (DD) implemented by the reduced state Viterbi algorithm (VA) known as RSVDD. The BER performance of RSVDD is compared with Viterbi DD (VDD) for M-ary DPSK in additive white Gaussian noise (AWGN) channels.

Reduced-state Viterbi differential detection using a recursively estimated phase reference for M-ary DPSK

The reduced-state Viterbi algorithm (VA), with feedback incorporated into the structure of path metric computations is presented for the differential detection of M-ary DPSK signals. The number of states in the trellis of the VA is reduced to M, and the phase reference used for differential detection is estimated recursively for each state in the trellis, along the surviving path ending in each state. The proposed differential detection is called reduced-state Viterbi differential detection (RSV DD). The most simple form of RSV DD, decision feedback DD (DF DD), is also derived. It allows only a single path to survive, so that a symbol-by-symbol decision is made. The BER performances possible with the proposed RSV DD and DF DD schemes are evaluated by means of computer simulations for 4DPSK transmission over AWGN and Rayleigh fading channels.

Sequential sequence estimation for channels with intersymbol interference of finite or infinite length

A sequential sequence estimator for channels with finite or infinite intersymbol interference (ISI) is proposed. It consists of a whitened matched filter followed by a sequential algorithm. A key component of a sequential estimator is a suitable metric that accounts for the unequal search depth. This metric is derived for the ISI channel. Computer simulations for three different channels show that the sequential sequence estimator has considerably less computational complexity than a maximum-likelihood sequence estimator using the Viterbi algorithm (MLSE-VA), while still maintaining the optimum estimation performance of the MLSE-VA, a performance not achievable with any reduced-state Viterbi algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Adaptive reduced-state Viterbi algorithm detector

The paper describes a novel development of the Viterbi algorithm detector that is suitable for the detection of a convolutionally coded digital signal. The technique enables a substantial reduction in equipment complexity to be achieved, relative to that of the Viterbi algorithm detector, with only a very small reduction in tolerance to noise. Results of computer-simulation tests are presented showing the performance of the system and giving also a measure of its complexity, for the particular case of a coded 8-level PSK signal. An outline is also presented of a possible implementation of the new detector for the given application.

Performance comparison of detection methods derived from maximum-likelihood sequence estimation

The performance of various detection methods which are derived from full maximum-likelihood sequence estimation (MLSE) was investigated for channels introducing linear distortion and additive noise. The Viterbi algorithm may be applied to full MLSE, to maximum-likelihood soft-decision decoding of convolutional codes, or to the combined operations of detection in the presence of intersymbol interference and soft-decision decoding. In the latter case it was found that the free Euclidean distance of the coding and modulation scheme may be reduced, causing a decrease in coding gain. The pure equalisation techniques investigated include a prefilter which truncates the effective memory of a channel, a heuristic reduced-state Viterbi algorithm, and two hybrid receivers which incorporate a decision feedback equaliser into the simplified MLSE process. The performance of these equalisation techniques and one receiver which used a decision feedback equaliser and a soft-decision decoder for a convolutional code recommended by the CCITT, were investigated by computer simulation for a variety of channels. It was found that for all but the most severely distorted channels, significant coding gain could be achieved. For such channels the reduced-state method provided the best performance, while the other techniques were marred by severe error burst effects.

Data transmission at 19.2 kbit/s over telephone circuits

The paper describes a theoretical study of two different 19200 bit/s q.a.m. data-transmission systems suitable for use over voice-band telephone circuits. One of the systems employs a 64-point q.a.m. signal with an element rate of 3200 bauds, and the other employs a 256-point q.a.m. signal with an element rate of 2400 bauds. A near-maximum-likelihood detection process, derived from a reduced-state Viterbi-algorithm detector, is used at the receiver in each case. Results of computer-simulation tests are presented, comparing the tolerances of the two systems to additive white Gaussian noise, where the data are transmitted over models of four different telephone circuits. The effects, on the tolerance to noise, of inaccuracies in the estimates of the level and carrier phase of the received signal are also studied.