Analsis Performansi Sistem Multiband OFDM UWB Menggunakan Pengkodean Reed Solomon Dan Turbo Code Pada Kanal Saleh Valenzuela

ABSTRAKSI: Ultrawideband (UWB) merupakan teknologi aplikasi wireless yang beroperasi pada frekuensi 3.1 GHz – 10.6 GHz dan memiliki bandwith transmisi lebih besar dari 500 MHz. UWB dapat diterapkan di lingkungan indoor dengan sangat baik karena keuntungan dari UWB adalah kecepatan transmisi data yang sangat tinggi dengan daya transmit yang sangat rendah. Di sisi lain, pengunaan teknik Orthogonal Frequency Division Multiplexing (OFDM) yang sangat populer dalam komunikasi wireless dengan data-rate yang tinggi, mampu mengarungi kondisi kanal yang bersifat frequency selective fading dengan mengubahnya menjadi kumpulan kanal yang bersifat flat fading. Untuk mendapatkan bandwidth yang efisien dan ketahanan terhadap interferensi narrowband maka dapat digunakan teknik pendekatan multiband OFDM UWB. Multiband OFDM UWB membagi spektrum frekuensi UWB menjadi 13 subband, masing-masing subband menduduki spektrum sebesar 528 MHz sesuai dengan minimum bandwidth yang telah ditetapkan oleh FCC. Sedangkan pemodelan kanal indoor Saleh-Valenzuela merupakan salah satu model kanal yang tepat untuk komunikasi menggunakan UWB menurut 802.15.3a dan didalamnya terdiri dari 4 model kanal (SV1, SV2, SV3, dan SV4). Reed-Solomon (RS) codes menggunakan teknik Forward Error Correction (FEC) yang mampu memperbaiki burst error. FEC digunakan untuk mengkoreksi error yang terjadi akibat gangguan selama proses transmisi pada komunikasi indoor. Sedangkan Turbo codes diharapkan dapat menghasilkan probabilitas error yang kecil dengan daya yang kecil. Hasil simulasi menunjukkan untuk semua model kanal Saleh Valenzuela, model kanal SV1 merupakan model kanal yang memiliki performansi paling baik dibandingkan dengan ketiga model kanal lainnya pada sistem multiband OFDM UWB dengan Reed-Solomon codes dan Turbo codes. Hal ini dibuktikan dengan simulasi multiband OFDM UWB pada SV1 untuk target BER 10-3 dengan Turbo code dengan g = [1 0 1; 1 1 1] memberikan perbaikan gain sebesar 3.5 dB dan dengan RS (127,107,8) memberikan perbaikan gain sebesar 2.1 dB.Kata Kunci : Ultra Wideband (UWB), Multiband OFDM, Reed-Solomon codes, Turbo codes, SNR, BERABSTRACT: Ultra Wideband (UWB) is a wireless application technology that has operation frequency within 3.1 GHz – 10.6 GHz and its transmission bandwidth is more than 500 MHz. UWB can been applied in indoor environment with very good performance because the benefit of UWB is providing very high data transmission rate with low transmission power. In other side, using Orthogonal Frequency Division Multiplexing (OFDM) technique that is very popular in wireless communication with high data-rate that could change frequency selective fading channel into flat fading channel. To get bandwidth efficiency and durability towards narrowband interference, then multiband OFDM UWB approaching technique can be used. Multiband OFDM UWB divides UWB frequency spectrum into 13 subbands, each subband has bandwidth operation about 528 MHz according to minimum bandwidth that had been decided by FCC. Though indoor channel model named Saleh-Valenzuela is one kind of channel model that has suitable for UWB communication according to IEEE 802.15.3a and Saleh-Valenzuela has 4 channel model (SV1, SV2, SV3, and SV4). Reed-Solomon (RS) codes is using Forward Error Correction (FEC) technique that can fix and repair burst error. FEC is used for correcting error that established because of noise in indoor communication transmission process. Turbo codes is error correction codes can make small probability of error with low power. Simulation results show for all Saleh-Valenzuela channel model, SV1 has the best performance from other three channel model in multiband OFDM UWB system with each Reed- Solomon codes and Turbo codes. It can be proven in multiband OFDM UWB simulation for SV1 with the BER 10-3 target, Turbo codes g=[1 0 1;1 1 1] is resulting gain as much as 3.5 dB and RS(63,43,6) is resulting gain as much as 2.1 dB.Keyword: Ultra Wideband (UWB), Multiband OFDM, Reed-Solomon codes, Turbo codes, SNR, BE

Error correction based on partial information

We consider the decoding of linear and array codes from errors when we are only allowed to download a part of the codeword. More specifically, suppose that we have encoded $k$ data symbols using an $(n,k)$ code with code length $n$ and dimension $k.$ During storage, some of the codeword coordinates might be corrupted by errors. We aim to recover the original data by reading the corrupted codeword with a limit on the transmitting bandwidth, namely, we can only download an $\alpha$ proportion of the corrupted codeword. For a given $\alpha,$ our objective is to design a code and a decoding scheme such that we can recover the original data from the largest possible number of errors. A naive scheme is to read $\alpha n$ coordinates of the codeword. This method used in conjunction with MDS codes guarantees recovery from any $\lfloor(\alpha n-k)/2\rfloor$ errors. In this paper we show that we can instead read an $\alpha$ proportion from each of the codeword's coordinates. For a well-designed MDS code, this method can guarantee recovery from $\lfloor (n-k/\alpha)/2 \rfloor$ errors, which is $1/\alpha$ times more than the naive method, and is also the maximum number of errors that an $(n,k)$ code can correct by downloading only an $\alpha$ proportion of the codeword. We present two families of such optimal constructions and decoding schemes. One is a Reed-Solomon code with evaluation points in a subfield and the other is based on Folded Reed-Solomon codes. We further show that both code constructions attain asymptotically optimal list decoding radius when downloading only a part of the corrupted codeword. We also construct an ensemble of random codes that with high probability approaches the upper bound on the number of correctable errors when the decoder downloads an $\alpha$ proportion of the corrupted codeword.Comment: Extended version of the conference paper in ISIT 201