This paper deals witha posterioriprobability (APP) decoding of high-rate convolutional codes, using the dual code's trellis. After deriving the dual APP (DAPP) algorithm from the APP relation, its trellis-based implementation is addressed. The challenge involved in practical implementation of a DAPP decoder is then highlighted. Metric representation schemes similar to the log domain used for log-APP decoding are shown to be unattractive for DAPP decoding due to quantization requirements. After explaining the nature of the DAPP metrics, an arc hyperbolic tangent (AHT) scheme is proposed and its equivalent arithmetic operations derived. By using an efficient approximation, an addition is translated to an addition in the AHT domain. Efficient techniques for normalization and extrinsic log-likelihood ratio (LLR ) calculation are presented which reduce implementation complexity significantly. Simulation results with different high-rate codes are given to show that the AHT-DAPP decoder performs similarly to a log-APP decoder and at the same time performs better than a decoder for a punctured code. A fully fixed-point model of an AHT-DAPP decoder is shown to perform close to an optimum decoder. The decoding complexity of the log-APP and AHT-DAPP decoders are listed and compared for several rate-$k/(k+1)$codes. It is shown that an AHT-DAPP decoder starts to be less complex from a code rate of$7/8$. When compared against a max-log-APP decoder, the AHT-DAPP decoder is less complex at a code rate of$9/10$and above.

We present a novel LDPC code construction technique and an algorithm that assists phase estimation on sub- blocks to provide a near-coherent performance on channels with a large phase noise. Sub-blocks are very small observation intervals on the received vector over which phase estimation techniques are applied to provide ambiguous phase estimates. Iterative decoding on LDPC codes are affected by these phase ambiguities on sub- blocks. In our earlier work, we resolved this sub-block phase ambiguity at the start of the decoding based on a set of check nodes called 'local check nodes (LCN)' that are connected locally within the sub-blocks. Due to the poor signal-to-noise ratio at the start of decoding, a large number of LCNs were required to provide a reliable phase ambiguity. In this paper, we show that random LDPC codes can be constructed such that their decoding is not affected by the presence of sub-block phase ambiguities. Because of this, the signal quality is improved due to the code convergence and hence requires significantly less local check nodes to resolve phase ambiguity. We present performance results for a binary LDPC code with BPSK modulation. They show that with little loss, the receiver could tolerate a Wiener phase noise of up to 3deg standard deviation per symbol.

An a posteriori probability (APP) decoder working on the trellis of the dual code is preferred if the code rate is high. However, a hardware realisation of this decoder is quite complex due to very fine quantisation requirements. This paper explains the nature of the metrics in this dual-APP decoder and points out the underlying reason behind the unsuitability of a traditional log domain approach. We propose a new metric representation scheme and discuss the arithmetic operations involved for a trellis based implementation. Simulation results are given, showing a better performance tradeoff of the proposed scheme against quantisation

We investigate the capacity of various ISI channels with adaptive white Gaussian noise. Previous papers showed a minimum E/sub b//N/sub 0/ of -4.6 dB, 3 dB below the capacity of a flat channel, is obtained using water pouring capacity formulas for the 1 + D channel. However, these papers did not take it into account that the channel power gain can be greater than one when water pouring is used. We present a generic power normalisation method of the channel frequency response, namely peak bandwidth normalisation, to facilitate the pair capacity comparison of various ISI channels. Three types of ISI channel, i.e., adder channels, RC channels and magnetic recording channels, are examined. By using our channel power gain normalisation, the capacity curves of these ISI channels are shown.

We investigate the capacity of various intersymbol interference (ISI) channels with additive white Gaussian noise (AWGN). Previous papers showed a minimum E/sub b//N/sub 0/ of -4.6 dB, 3 dB below the capacity of a flat channel, is obtained using water-pouring capacity formulas for the 1+D channel. However, these papers did not take into account that the channel power gain can be greater than one when water-pouring is used. We present a generic power normalization method of the channel frequency response, namely, peak bandwidth normalization (PBN), to facilitate the fair capacity comparison of various ISI channels. Three types of ISI channel, i.e., adder channels, RC channels, and magnetic recording channels, are examined. By using our channel power gain normalization, the capacity curves of these ISI channels are shown.

An investigation of unequal error protection (UEP) methods applied to JPEG image transmission using turbo codes is presented. The JPEG image is partitioned into two groups, i.e., DC components and AC components according to their respective sensitivity to channel noise. The highly sensitive DC components are better protected with a lower coding rate, while the less sensitive AC components use a higher coding rate. Simulation results are given to demonstrate how the UEP schemes outperforms the equal error protection (EEP) scheme in terms of bit error rate (BER) and peak signal to noise ratio (PSNR).

A coding scheme, termed turbo-codes was proposed, which achieves results very close to the Shannon-limit. The encoding and decoding of turbo-codes is reviewed. In particular, a comparison of the current methods used for terminating the trellis of the turbo-code are described. A novel approach to termination of the code is introduced which removes the need to transmit tail bits across the channel. A reduction in transmitted symbols by 2 percent is achieved for PCS CDMA type applications. Simulations confirm that the novel approach is better in terms of BER than other methods of termination.

New upper and lower bounds and approximations on the sequence, event, first event, and bit-error probabilities of convolutional codes are presented. Each of these probabilities are precisely defined and the relationship between them described. Some of the new bounds and approximations are found to be very close to computer simulations at very high error ratios. Simple modifications to the traditional union upper bound are also described for both hard- and soft-decision channels that allow better performance estimates to be made.

A general parity-check equation is presented that defines rotationally invariant trellis codes of rate k/(k+1) for two-dimensional signal sets. This parity-check equation is used to find rate k/(k+1) codes for 4PSK, 8PSK, 16PSK, and QAM signal sets by systematic code searches. The MPSK codes exhibit smaller free Euclidean distances than nonrotationally invariant linear codes with the same number of states. However, since the nonlinear codes have a smaller number of nearest neighbors, their performance at moderate signal to noise ratios is close to that of the best linear codes. The rotationally invariant QAM codes with 8, 32, 64, and 256 states achieve the same free Euclidean distance as the best linear codes. Transparency of user information under phase rotations is accomplished either by conventional differential encoding and decoding, or by integrating this function directly into the code trellis.>

Trellis coding using multidimensional quadrature amplitude modulation (QAM) signal sets is investigated. Finite-size 2D signal sets are presented that have minimum average energy, are 90 degrees rotationally symmetric, and have from 16 to 1024 points. The best trellis codes using the finite 16-QAM signal set with two, four, six, and eight dimensions are found by computer search (the multidimensional (multi-D) signal set is constructed from the 2-D signal set). The best moderate complexity trellis codes for infinite lattices with two, four six, and eight dimensions are also found. The minimum free squared Euclidean distance and number of nearest neighbors for these codes were used as the selection criteria. Many of the multi-D codes are fully rotationally invariant and give asymptotic coding gains up to 6.0 dB. From the infinite lattice codes, the best codes for transmitting J, J+1/4, J+1/3, J+1/2, J+2/3, and J+3/4 b/sym (J an integer) are presented.>

A 2L-dimensional multiple phase-shift keyed (L*MPSK) signal set is obtained by forming the Cartesian product of L two-dimensional MPSK signal sets. A systematic approach to partitioning L*MPSK signal sets that is based on block coding is used. An encoder system approach is developed. It incorporates the design of a differential precoder, a systematic convolutional encoder, and a signal set mapper. Trellis-coded L*4PSK, L*8PSK, and L*16PSK modulation schemes are found for 1>