Using these facts, we have: ( f 0 , … , f n − 1 ) {\displaystyle (f_ Ω 9,\ldots ,f_ Ω 8)} is a code word of the Reed–Solomon code J. Generated Fri, 14 Oct 2016 13:56:04 GMT by s_ac4 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection Since r(x) = c(x) + e(x), and since a discrete Fourier transform is a linear operator, R(x) = C(x) + E(x).

If mobile stations lock their internal frequency standards to the perceived satellite signal, they will be in error and so the frequencies transmitted from the mobile stations back to the satellite The syndromes Sj are defined as S j = r ( α j ) = s ( α j ) + e ( α j ) = 0 + e ( The generator polynomial g ( x ) {\displaystyle g(x)} is defined as the polynomial whose roots are exactly α , α 2 , … , α n − k {\displaystyle \alpha Contents 1 History 2 Applications 2.1 Data storage 2.2 Bar code 2.3 Data transmission 2.4 Space transmission 3 Constructions 3.1 Reed & Solomon's original view: The codeword as a sequence of

Finally, the mobile station can use the frequency correction signal to adjust the reference signal produced by a controlled reference oscillator, such as a voltage controlled oscillator, in step 412, which No. 08/179,953, entitled "A Cellular/Satellite Communications System With Improved Frequency Reuse", both of which are commonly assigned and expressly incorporated herein by reference. The satellite contains a multiple beam antenna. It is optional whether the mobile station applies a further Doppler shift precompensation to its transmission such that it is received correctly at the satellite.

The prior art contains examples of reference oscillators based on remembering a previous correction in a temperature look-up table memory. S. (1994), "Reed–Solomon Codes and the Compact Disc", in Wicker, Stephen B.; Bhargava, Vijay K., Reed–Solomon Codes and Their Applications, IEEE Press, ISBN978-0-7803-1025-4 ^ Lidl, Rudolf; Pilz, Günter (1999). As an erasure code, it can correct up to t known erasures, or it can detect and correct combinations of errors and erasures. This means that if the channel symbols have been inverted somewhere along the line, the decoders will still operate.

First, the mobile station includes a receiver means for receiving a paging channel signal broadcast by the moving relay station and demodulating and decoding means for decoding the information in the However, the error will be non-zero off-center in a direction in the plane containing the sightline and the orbital velocity vector. In most cases, most calls will be between mobile stations and ordinary telephones connected to the Public Switched Telephone Network (PSTN) 130. All such methods are considered to be within the scope of the present invention.

Such information may be used in determining an optimum channel assignment to use for communicating with each mobile station. Gorenstein and N. A GPS receiver must factor in the angle each signal is taking as it enters the atmosphere because that angle determines the length of the trip through the perturbing medium. This code is so strong that most CD playback errors are almost certainly caused by tracking errors that cause the laser to jump track, not by uncorrectable error bursts.[5] DVDs use

more... The original encoding scheme described in the Reed Solomon article used a variable polynomial based on the message to be encoded, which made decoding impractical for all but the simplest of SUMMARY OF THE DISCLOSURE It is an object of the present invention to allow mobile stations to determine their coarse position by listening to a paging channel of a satellite for Since the calculation for a discrete Fourier transform is the same as the calculation for syndromes, t coefficients of R(x) and E(x) are the same as the syndromes: R j =

In a satellite mobile communications system, the motion of the satellite causes the radio frequency of the satellite's transmissions, as perceived by the mobile stations, to be altered by Doppler effect. In 2003, Ralf Koetter and Alexander Vardy presented a polynomial-time soft-decision algebraic list-decoding algorithm for Reed–Solomon codes, which was based upon the work by Sudan and Guruswami.[13] Matlab Example[edit] Encoder[edit] Here The result will be the inversion of the original data. Although the codewords as produced by the above encoder schemes are not the same, there is a duality between the coefficients of polynomials and their values that would allow the same

The Reed–Solomon code, like the convolutional code, is a transparent code. The mobile station 200 contains a receiver 202 and a transmitter 216 which are used to communicate with a hubstation via a moving relay station. Zierler, ”A class of cyclic linear error-correcting codes in p^m symbols,” J. In the first method, the frequency correction means 312 can use the error signal produced by the frequency error detector 310 to determine the frequency correction signal as described above with

However, the TRANSIT method provides much greater accuracy than is needed for satellite communications. This code can correct up to 2 byte errors per 32-byte block. Description FIELD OF THE INVENTION The present invention relates to a system for bidirectional communication with mobile telephones via a moving relay station, such as an orbiting satellite. In this case, the satellite relays the signals to the ground network station that determines the uplink Doppler shift for each mobile station during demodulation of their relayed signals.

However, the practical decoders described below require a generator polynomial known to the decoder, and view a codeword as a set of coefficients. Example[edit] Using the same data as the Berlekamp Massey example above: i Ri Ai -1 001 x4 + 000 x3 + 000 x2 + 000 x + 000 000 0 925 Another way to get a handle on these atmosphere-induced errors is to compare the relative speeds of two different signals. s r ( x ) = p ( x ) x t mod g ( x ) = 547 x 3 + 738 x 2 + 442 x + 455 {\displaystyle

Unfortunately this requires a very sophisticated receiver since only the military has access to the signals on the L2 carrier. BravingtonJason R. The mobile station includes a receiver for receiving a paging channel signal broadcast by the moving relay station and demodulators and decoders for decoding the information in the paging channel signal. The SACCH information is multiplexed with traffic (e.g.

The mobile station also includes a temperature sensor means for making a coarse temperature measurement and a memory means for storing averaged frequency control signal values for each of a number According to one embodiment of the present invention, the satellite can precompensate its transmit frequency so that the error due to Doppler is cancelled at the center of the cell or In 1999, Madhu Sudan and Venkatesan Guruswami at MIT published "Improved Decoding of Reed–Solomon and Algebraic-Geometry Codes" introducing an algorithm that allowed for the correction of errors beyond half the minimum Space transmission[edit] One significant application of Reed–Solomon coding was to encode the digital pictures sent back by the Voyager space probe.

In parallel to shortening, a technique known as puncturing allows omitting some of the encoded parity symbols. Systematic encoding procedure[edit] The above encoding procedure for the BCH view of Reed–Solomon codes is classical, but does not give rise to a systematic encoding procedure, i.e., the codewords do not Images(4)Claims(4) What we claim is: 1. beam ID, satellite motion information etc) and also information addressed to individual mobile stations (network originated calls or pages).

In the present invention, the term "channel"can be meant either as a frequency (in an FDMA system), a timeslot (in a TDMA system) or spreading code (in a CDMA system) or It can be checked that the alternative encoding function is a linear mapping as well.