Although binary turbo codes can achieve a significant amount of coding gain, they generally do not have good bandwidth efficiency unless they are heavily punctured. The simplest way to attain both power and bandwidth efficiency is to adopt nonbinary modulation schemes, such as 8PSK and 16QAM, in conjunction with a turbo code. This approach requires bit logarithmic likelihood ratios (LLRs) from the nonbinary demodulator for binary turbo decoding. When these bit LLRs are formed, different bits are unequally protected against channel corruption. Because the systematic and parity-check bits of a turbo codeword play different roles in the process of decoding, mapping them with different levels of protection to signal constellation results in different bit-error rate (BER) performances. In this paper, it is shown that the threshold BER can be improved when systematic bits are more protected while the decoding error floor can be lowered when parity-check bits are more protected. This provides an additional dimension of waveform design by mapping systematic or parity-check bits to different bit positions in the non-binary signal constellation.

Although a significant amount of coding gain can be achieved, binary turbo codes do not have good bandwidth efficiency unless they are heavily punctured. Turbo trellis coded modulation (TTCM) can provide good turbo code performance without bandwidth expansion. However, it requires unique code design. The simplest way to attain both power and bandwidth efficiency is to adopt high-order modulation schemes with a commonly studied binary turbo code. This approach requires a conversion of the demodulator output associated with the nonbinary channel symbol into bit metrics to input to the binary turbo decoder. This paper investigates various conversion functions for 8PSK and 16PSK constellations. The turbo-coded bit-error-rate performances are compared using these metrics. It is shown that the likelihood metric, which is the optimum for the uncoded case, does not provide the optimum performance in the coded case. This paper also indicates that this turbo-coded waveform can perform as well as TTCM.

Abstract The classical turbo‐decoding algorithm is based on the assumption that the input sequence to the decoder has been disturbed by a noise process that has a Gaussian distribution. For a differentially coherent phase shift keying (DPSK) waveform, the output statistics of a differentially coherent demodulator is nonGaussian. When this sequence is fed directly into the turbo decoder, particularly under a fading environment, the mismatch between decoder algorithm assumptions and actual input statistics can result in significant decoder performance degradation. This paper investigates the bit error performance for such a mismatch for the DPSK waveform. Techniques for forming enhanced turbo‐decoding metrics with biased channel side information (CSI) are proposed. Using these new metrics, error performance in fading conditions is shown to improve significantly. Copyright © 2003 John Wiley & Sons, Ltd.

The classical turbo decoding algorithm is based on the assumption that the input sequence to the decoder has been disturbed by a noise process that has a Gaussian distribution. For a DPSK waveform, the output statistics of a differentially coherent demodulator is nonGaussian. When this sequence is fed directly into the turbo decoder, particularly under a fading environment, the mismatch between decoder algorithm assumptions and actual input statistics can result in significant decoder performance degradation. This paper investigates the bit error performance for such a mismatch for the DPSK waveform. Techniques for forming enhanced turbo-decoding metrics with biased channel side information (CSI) are proposed. Using these new metrics, error performance in fading conditions is shown to improve significantly.

In the wireless indoor environment, the channel may vary slowly as users and the interferers may move at slow speeds. A frequency-hopped code-division multiple-access system can adapt to the different interference levels in hopping patterns and assign the slots different bit rates to increase the system capacity. We show that the maximum throughput bit-rate/channel-assignment problem is NP-hard. Several practical ad hoc bit-allocation algorithms are designed based on the insights derived from exhaustive searches. The algorithms that achieve the most system capacity perform interference avoidance. Users concentrate their throughput in a small fraction of the slots with low interference by transmitting large signal constellations, while avoiding the channels with large interference. Simulations show that the flexibility of users to adjust their bit rates to the interference environment can significantly increase the system capacity.

A VLSI design for computing exponentiation in finite fields is developed. An algorithm to generate a relatively long pseudorandom number sequence is presented. It is shown that the period of this sequence is significantly increased compared to that of the sequence generated by the most commonly used maximal length shift register scheme.>

The concept of using a self-dual normal basis to design the Massey-Omura finite-field multiplier is presented. An algorithm is given to locate a self-dual normal basis for GF(2/sup m/) for odd m. A method to construct the product function for designing the Massey-Omura multiplier is developed. It is shown that the construction of the product function based on a self-dual basis is simpler than that based on an arbitrary normal basis.>

Massey and Omura recently developed a new multiplication algorithm for Galois fields based on the normal basis representation. This algorithm shows a much simpler way to perform multiplication in finite field than the conventional method. The necessary and sufficient conditions are presented for an element to generate a normal basis in the field GF(2^{m}), wherem = 2^{k}p^{n}andp^{n}has two as a primitive root. This result provides a way to find a normal basis in the field.

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that can be easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. In this paper, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal basis representation used together with this multiplier, a pipeline architecture is developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable, and therefore, naturally suitable for VLSI implementation.

FH/MFSK has been Proposed for a multiuser spread spectrum digital communication system to combat both self-jamming and intentional jamming. An independence assumption at the energy detector outputs is used to evaluate such a system for a digitized voice mobile radio system [11]. This paper presents a correlated model and compares its performance to an independence model under the symbol error probability criterion. A Gaussian process model is also developed for comparison. It is found that the conventional Gaussian approximation is inadequate in predicting the number of users that can be accommodated by an FH/MFSK system using the conventional receiver. Furthermore, for the cases we evaluated, the independence model provides an excellent approximation to the correlated model. Additionally, a conditional Chernoff bound is presented for the more general case of frequency-hopping systems with multiple hops per symbol.

The error probability performance of differential detection of narrow-band FM is determined and compared with the analogous results for limiter-discriminator detection of the same modulation. It is shown that over a large class of benign and hostile environments, e.g., Gaussian IF filter,1 \leq BT \leq 3, h \leq 1, AWGN, partial-band noise jamming, the differential detector offers no theoretical performance advantage over the limiter-discriminator receiver with integrate-and-dump postdetection filtering.