Redundant Residue Number System Codes Research Articles

MODIFIED MODULUS PROJECTION ALGORITHM FOR ERROR CONTROL IN REDUNDANT RESIDUE NUMBER SYSTEM CODE

This paper presents a modified modulus projection algorithm for decoding Redundant Residue Num-ber System (RRNS) codes. RRNS code is maximum-minimum distance block codes. RRNS has found wider applications in the field of signal processing especially for error control. The essence of this modification is to reduce the required computation overhead and speed up operation. The proposed method involves conversion of received residues into mixed radix form. Based on the error detecting capability of RRNS code under study, moduli projection is carried out iteratively to determine the corre-sponding integers. The proposed algorithm considerably reduces the number of required iterations involved in the recovery process, therefore improving the speed of decoding operation.

Performance of Systematic RRNS Based Space-Time Block Codes with Probability-Aware Adaptive Demapping

In this paper, we propose a novel design of concatenated Space-Time Block Codes (STBCs) using Systematic Redundant Residue Number System (RRNS) codes. The link between residues and complex signal constellations is optimized by incorporating the Direct Prior probability based Distance Aware and schemes. We analytically quantify the upper bounds on the codeword and bit error probabilities of Systematic RRNS-STBC and characterize the achievable coding and diversity gains assuming maximum likelihood decoding (MLD). We propose an Adaptive M-ary Demapping scheme for ML decoding, which exploits the RRNS code structure to decrease complexity and provide further performance improvement over the Distance Aware Mapping scheme. It is shown that Indirect Mapping, when used for RRNS coding schemes can offer more efficient transmission and performance than naive M-ary mapping. It is also seen that Systematic RRNS-STBC codes provide superior performance compared to Non-systematic RRNS-STBC, for the same code parameters, owing to more efficient binary to residue mapping.

Systematic Redundant Residue Number System Codes: Analytical Upper Bound and Iterative Decoding Performance Over AWGN and Rayleigh Channels

The novel family of redundant residue number system (RRNS) codes is studied. RRNS codes constitute maximum-minimum distance block codes, exhibiting identical distance properties to Reed-Solomon codes. Binary to RRNS symbol-mapping methods are proposed, in order to implement both systematic and nonsystematic RRNS codes. Furthermore, the upper-bound performance of systematic RRNS codes is investigated, when maximum-likelihood (ML) soft decoding is invoked. The classic Chase algorithm achieving near-ML soft decoding is introduced for the first time for RRNS codes, in order to decrease the complexity of the ML soft decoding. Furthermore, the modified Chase algorithm is employed to accept soft inputs, as well as to provide soft outputs, assisting in the turbo decoding of RRNS codes by using the soft-input/soft-output Chase algorithm

A residue number system based parallel communication scheme using orthogonal signaling. I. System outline

A novel signaling scheme is presented, where a set of orthogonal signals is transmitted in parallel. The signals are selected according to the so-called residue number system (RNS). Hence the system is essentially a multiple code parallel communication scheme using high modulation alphabets. It is demonstrated that the system's performance can be substantially improved by exploiting a number of advantageous properties of the RNS arithmetic. We focus our attention on the system's description and on the associated background of the RNS arithmetic, as well as on the performance evaluation of the residue number system arithmetic, using both nonredundant and redundant moduli based orthogonal signaling schemes, over an additive white Gaussian noise (AWGN) channel. Redundant RNS codes are introduced in order to protect the transmitted information. The detection techniques used in this novel system are different from conventional detectors. Specifically, a novel decision algorithm, referred to as a ratio statistic test, is designed, which implies dropping some of the lowest reliability demodulation outputs before the residue digits are transformed back to binary symbols. This improves the system's performance. This dropping technique is different from the conventional errors and erasures decoding, where the erased symbols (or bits) should be computed and filled during decoding. We argue that the demodulated/decoded information can be obtained by decoding the retained or undiscarded symbols upon exploiting the properties of the RNS arithmetic. Our numerical results show that the proposed scheme constitutes a high-efficiency parallel transmission method for high-bit-rate communication, achieving a coding gain of 2 dB at a bit error rate of 10/sup -6/ over AWGN channels.

A residue number system based parallel communication scheme using orthogonal signaling. II. Multipath fading channels

For pt.I see ibid., vol.51, no.6, p.1534-46 (2002). A novel signaling scheme is presented, where a set of orthogonal signals is transmitted in parallel. The signals are selected according to the so-called residue number system (RNS). Hence the system is essentially a multiple code parallel communication scheme using high-modulation alphabets. It is demonstrated that the system performance can be substantially improved by exploiting a number of advantageous properties of the RNS arithmetic. The model treated in part I of this paper is extended here to account for the effects of the multipath Rayleigh fading channel when using noncoherent demodulation. Diversity reception techniques with equal gain combining (EGC) or selection combining (SC) are concerned. The related performance is evaluated for both nonredundant and redundant RNS-based orthogonal signaling. Interleaving and forward error-correction techniques are introduced for enhancing the system's bit error rate (BER) performance. The concept of concatenated coding with a Reed-Solomon (RS) code as the outer code and a redundant RNS code as the inner code is presented, and the performance of the proposed concatenated code is evaluated. Expressions of the error probability for the above-mentioned scenarios are presented, and the associated BER performance is evaluated numerically with respect to specific system parameters. Without concatenated coding, coding gains up to 8.5 or 11 dB are achieved at a BER of 10/sup -6/ using the lowest reliability dropping technique of part I and one or two redundant moduli, respectively. The BER is substantially higher than that over the additive white Gaussian noise channel reported in part I. With the aid of RS coding, an additional 7.5-dB coding gain is achieved.

Performance analysis of coded M-ary orthogonal signaling using errors-and-erasures decoding over frequency-selective fading channels

The performance of M-ary orthogonal signaling schemes employing Reed-Solomon (RS) codes and redundant residue number system (RRNS) codes is investigated over frequency-selective Rayleigh fading channels. Errors-and-erasures decoding is considered, where erasures are judged based on two low-complexity, low-delay erasure insertion schemes-Viterbi's ratio threshold test (RTT) and the proposed output threshold test (OTT). The probability density functions (PDF) of the ratio associated with the RTT and that of the demodulation output in the OTT conditioned on both the correct detection and erroneous detection of M-ary signals are derived, and the characteristics of the RTT and OTT are investigated. Furthermore, expressions are derived for computing the codeword decoding error probability of RS codes or RRNS codes based on the above PDFs, The OTT technique is compared to Viterbi's RTT, and both of these are compared to receivers using error-correction only decoding over frequency-selective Rayleigh-fading channels. The numerical results show that by using errors-and-erasures decoding, RS or RRNS codes of a given code rate can achieve higher coding gain than that without erasure information, and that the OTT technique outperforms the RTT, provided that both schemes are operated at the optimum decision thresholds.