Entanglement-assisted quantum turbo codes

An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin et al., in order to have the constituent decoders pass along only "extrinsic information" to each other rather than a posteriori probabilities as in the decoder of Poulin et al., and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.Comment: 31 pages, software for simulating EA turbo codes is available at http://code.google.com/p/ea-turbo/ and a presentation is available at http://markwilde.com/publications/10-10-EA-Turbo.ppt ; v2, revisions based on feedback from journal; v3, modification of the quantum turbo decoding algorithm that leads to improved performance over results in v2 and the results of Poulin et al. in arXiv:0712.288

PENGARUH PENGUNAAN MODEL PEMBELAJARAN JOGYUKENYU (LESSON STUDY) TERHADAP PRESTASI BELAJAR MATEMATIKA PADA SEGIEMPAT DITINJAU DARI MINAT BELAJAR (Eksperiment Pembelajaran Pada Siwa Kelas VII Semester 1 SMP N 2 Gatak )

Penelitian ini bertujuan untuk : 1) Menganalisis dan menguji pengaruh model pembelajaran jogyukenyu (lesson study) terhadap prestasi belajar. 2) Menganalisis dan menguji pengaruh minat belajar siswa terhadap prestasi belajar siswa. 3) Menganalisis dan menguji interaksi antara pendekatan pembelajaran dengan minat belajar siswa terhadap prestasi belajar matematika. Populasi penelitian adalah semua kelas VII yang terdidri dari delapan kelas dan sampel sebanyak dua kelas yaitu kelompok eksperimen siswa kelas VII G dengan jumlah 38 siswa, sedangkan kelompok kontrol siswa kelas VIIH dengan jumlah 38 siswa teknik sampling menggunakan cluster random. Metode pengumpulan data adalah metode tes, dokumentasi dan observasi. Teknik analisis data yang digunakan analisis variansi dua jalan dengan frekuensi sel tak sama yang sebelumya dilakukan uji prasyarat yaitu uji normalitas dan uji homogenitas. Hasil pengujian hipotesis menggunakan α = 5 % menunjukan : (1) FA = 7,15 berarti ada pengaruh yang signifikan antara model pembelajaran terhadap prestasi belajar matematika, (ii) FB = 90, 75 berarti ada pengaruh yang signifikan antara minat belajar terhadap prestasi belajar matematika, dan (iii) FAB = 0,14 berarti tidak terdapat interaksi yang signifikan antara model pembelajaran dan minat belajar siswa terhadap prestasi belajar. Penelitian ini menyimpulkan bahwa prestasi belajar menggunakan model pembelajaran jogyukenyu lebih baik dari pada prestasi belajar mengunakan model pembelajaran konvesional. Demikian pula jika ditinjau dari minat belajar siswa, bahwa minat belajar yang lebih tinggi memberikan prestasi belajar lebih baik dari prestasi belajar dari minat sedang maupun rendah

Turbo Decoding and Detection for Wireless Applications

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Concatenated Space Time Block Codes and TCM, Turbo TCM Convolutional as well as Turbo Codes

Space-time block codes provide substantial diversity advantages for multiple transmit antenna systems at a low decoding complexity. In this paper, we concatenate space-time codes with Convolutional Codes (CC), Turbo Convolutional codes (TC), Turbo BCH codes (TBCH), Trellis Coded Modulation (TCM) and Turbo Trellis Coded Modulation (TTCM) schemes for achieving a high coding gain. The associated performance and complexity of the coding schemes is compared