Institute for Systems Research
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Item I-Q TCM: Reliable Communication Over the Rayleigh Fading Channel Close to the Cutoff Rate(1996) Al-Semari, Saud A.; Fuja, Tom E.; ISRThis paper presents some trellis codes that provide high coding gain over the frequency non-selective slowly Raleigh distributed fading channel. It is shown that the use of two encoders in parallel - used to specify the in-phase and quadrature components of the transmitted signal - results in greater minimum time diversity than the conventional design in which a single encoder is used. Using this approach - which we label ﲉ-Q TCM - codes with bandwidth efficiencies of 1,2, and 3 bits/sec/Hz are described for various constraint lengths. The performance of these codes is bounded analytically and approximated via simulation; the results show a large improvement in the BER when compared with conventional TCM schemes when perfect channel state information (CSI) is available to the receiver. Indeed, when this approach is applied to channels with independent Rayleigh fading, the resulting coding gain is close to that implied by the cutoff rate limit, even for only moderately complex systems.The proposed codes are also simulated under less ideal assumptions. For instance, results for a 1 bit/sec/Hz IQ-TCM code without CSI show a significant gain over conventional coding. Finally, simulations over channels with correlated fading were undertaken; it is concluded that an interleaver span of 4v yields performance close to what is achieved with ideal interleaving.
Item Performance Analysis of Coherent TCM Systems with Diversity Reception in Slow Rayleigh Fading(1996) Al-Semari, Saud A.; Fuja, Tom E.; ISRCoherent trellis coded modulation (TCM) systems employing diversity combining are analyzed. Three different kinds of combining are considered: maximal ratio, equal gain, and selection combining. For each combining scheme, the cutoff rate parameter is derived assuming transmission over a fully- interleaved channel with flat, slow, Rayleigh fading; in addition, tight upper bounds on the pairwise error probabilities are derived. These upper bounds are expressed in product form to permit bounding of the BER via the transfer function approach. In each case it is assumed that the diversity branches are independent and that the channel state information (CSI) can be recovered perfectly.Also included is an analysis of maximal ratio combining when the diversity branches are correlated; the cutoff rate and a tight upper bound on the pairwise error probability are derived. It is shown that, with double diversity, a branch correlation coefficient as high as 0.5 results in only slight performance degradation.
Item Channel Codes That Exploit the Residual Redundancy in CELP- Encoded Speech(1996) Alajaji, Fady; Phamdo, N.; Fuja, Tom E.; ISRWe consider the problem of reliably transmitting CELP-encoded speech over noisy communication channels. Our objective is to design efficient coding/decoding schemes for the transmission of the CELP line spectral parameters (LSP's) over very noisy channels.We begin by quantifying the amount of ﲲesidual redundancy inherent in the LSP's of Federal Standard 1016 CELP. This is done by modeling the LSP's as first and second-order Markov chains. Two models for LSP generation are proposed; the first model characterizes the intra-frame correlation exhibited by the LSP's, while the second model captures both intra-frame and inter-frame correlation. By comparing the entropy rates of the models thus constructed with the CELP rates, it is shown that as many as one-third of the LSP bits in every frame of speech are redundant.
We next consider methods by which this residual redundancy can be exploited by an appropriately designed channel decoder. Before transmission, the LSP's are encoded with a forward error control (FEC) code; we consider both block (Reed- Solomon) codes and convolutional codes. Soft-decision decoders that exploit the residual redundancy in the LSP's are implemented assuming additive white Gaussian noise (AWGN) and independent Rayleigh fading environments. Simulation results employing binary phaseshift keying (BPSK) indicate coding gains of 2 to 5 dB over soft-decision decoders that do not exploit the residual redundancy.
Item I-Q TCM: Reliable Communication over the Rayleigh Fading Channel Close to the, Cutoff Rate(1995) Al-Semari, Saud A.; Fuja, Tom E.; ISRThis paper presents some trellis codes that provide high coding gain over the frequency non-selective slowly Rayleigh distributed fading channel. It is shown that the use of two encoders in parallel - used to specify the in-phase and qudrature components of the transmitted signal - results in great minimum time diversity than the conventional design in which a single encoder is used. Using this approach - which we label ﲉ-Q TCM - codes with bandwidth efficiencies of 1,2 and 3 bits/sec/Hz are described for various constraint lengths. The performance of these codes is bounded analytically and approximated via simulation; the results show a large improvement in the BER when compared with conventional TCM schemes. Indeed, when this approach is applied to channels with independent Rayleigh fading, the resulting coding gain is close to that implies by the cutoff rate limit, even for only moderately complex systems.The proposed codes are also simulated over channels with correlated fading; it is concluded that an interleaver span of 4v yields performance close to what is achieved with ideal interleaving.
Item Channel Codes That Exploit the Residual Redundancy in CELP- Encoded Speech(1995) Alajaji, Fady; Phamdo, N.; Fuja, Tom E.; ISRWe consider the problem of reliably transmitting CELP-encoded speech over noisy communication channels. Our objective is to design efficient coding/decoding schemes for the transmission of the CELP line spectral parameters (LSP's) over very noisy channels.We begin by quantifying the amount of ﲲesidual redundancy inherent in the LSP's of Federal Standard 1016 CELP. This is done by modeling the LSP's as first-and second-order Markov chains. Two models for LSP generation are proposed; the first model characterizes the intra-frame correlation exhibited by the LSP's, while the second model captures both intra-frame and inter-frame correlation. By comparing the entropy rates of the models thus constructed with the CELP rates, it is shown that as many as one-third of the LSP bits in every frame of speech are redundant.
We next consider methods by which this residual redundancy can be exploited by an appropriately designed channel decoder. Before transmission, the LSP's are encoded with a forward error control (FEC) code; we consider both (Reed-Solomon) codes and convolutional codes. Soft-decision decoders that exploit the residual redundancy in the LSP's are implemented assuming additive white Gaussian noise (AWGN) and independent Rayleigh fading environments. Simulation results employing binary phase-shifting keying (BPSK) indicate coding gains of 2 to 5 dB over soft-decision decoders that do not exploit the residual redundancy.
Item Optical Orthogonal Codes with Unequal Auto- and Cross- Correlation Constraints(1992) Yang, G-C.; Fuja, Tom E.; ISRAn optical orthogonal code (OOC)is collection of binary sequences with good auto-and cross-correlation properties; they were defined by Salehi and others as a means of obtaining code division multiple access on optical networks. Up to now all work on OOC's have assumed that the constraint placed on the auto- correlation and that placed on the cross-correlation are the same. In this paper we consider codes for which the two constraints are not equal. Specifically, we develop bounds on the size of such OOC's and demonstrate construction techniques for building them. The results demonstrate that a significant increase in the code size is possible by letting the auto- correlation constraint exceed the cross-correlation constraint. These results suggest that for a given performance requirement the optimal OOC may be one with unequal constraints.This paper also views OOC's with unequal auto- and cross-correlation constraints as constant-weight unequal error protection (UEP) codes with two levels of protection. The bounds derived are interpreted from this viewpoint and are compared with previous work on UEP codes.
Item The Performance of Focused Error Control Codes(1990) Alajaji, Fady; Fuja, Tom E.; ISRConsider an additive noise channel with inputs and outputs in the field GF (q ) where q > 2; every time a symbol is transmitted over such a channel, there are q - 1 different errors that can occur, corresponding to the q - 1 non-zero elements that the channel can add to the transmitted symbol. In many data communication/ storage systems, there are some errors that occur much more frequently than others; however, traditional error correcting codes- designed with respect to the Hamming metric - treat each of these q - 1 errors the same. Fuja and Heegard have designed a class of codes, called focused error control codes, that offer different levels of protection against "common" and "uncommon" errors; the idea is to define the level of protection in a way based not only on the number of errors, but the kind as well. In this paper, the performance of these codes is analyzed with respect to idealized "skewed" channels as well as realistic non-binary modulation schemes. It is shown that focused codes, used in conjunction with PSK and QAM signaling, can provide more than 1.0 dB of additional coding gain when compared with Reed- Solomon codes for small blocklengths.