A Unifying Approach to Determine the Necessary and Sufficient Conditions for Nonblocking Multicast Three-Stage Clos Networks

Abstract

A parallel between Reed-Solomon codes in the complex field and multicarrier transmission using orthogonal frequency-division multi- plexing (OFDM) is first presented. This shows that when the signal is sent over some channel composed of Gaussian plus impulse noise, the impulse noise can be removed by a procedure similar to channel coding decoding, using information carried by the syndrome. The result is first derived in a simple situation (oversampled discrete multitone, additive channel), which is merely of theoretical interest. In any case, consecutive zeros, in the output of the OFDM modulator, do not correspond to real subcarriers. Pilot tones are emitted for synchronization or channel-estimation purposes. These pilot tones are generally scattered among the information ones. Our approach is to see these pilot tones as syndromes, in order to correct impulse noise. We show that the correction capacity is conditioned by the position of these pilot tones in the emitted sequence. A protection subsystem is in- troduced after the decoding operation in order to detect malfunction of this decoder. Efficiency of this technique is corroborated with simulations in the slightly modified Hiperlan2 context. Other extensions are then provided in order to increase the practical usefulness of the method. Abstract—In this paper, we propose a serial concatenated trellis-coded modulation system using one or more inner rate-1 accumulate codes and a mapping to a higher order, Gray-labeled signal constellation. As outer codes, we consider repeat codes, single parity-check codes, and convolu- tional codes. We show that under maximum-likelihood decoding, there ex- ists a signal-to-noise ratio threshold beyond which the bit-error probability goes to zero as the blocklength goes to infinity. We then evaluate the perfor- mance for finite blocklengths using a modified union bound. Computer sim- ulations demonstrate that the proposed system, despite its use of a simple rate-1 inner code, achieves performance in additive white Gaussian noise and Rayleigh fading that is comparable to, or better than, that of more complex systems suggested in the literature.