Optimum Decoding Characteristics Achievement on the Basis of Multithreshold Algorithms (for ISCTA’07) Space Research Institute RAS United Radioelectronic Technologies V.V.Zolotarev, S.V.Averin, I.V.Chulkov

35 years MTD2 Application of noiseproof coding is necessary, because: 1. The large code gain can be received! 1. The large code gain can be received! Thus: 2. Distance of communication increases. 2. Distance of communication increases. 3. Data transmission reliability and speed increases. 3. Data transmission reliability and speed increases. 4. The sizes of aerials considerably decrease. 4. The sizes of aerials considerably decrease. 6. Work of a communication system is provided at essential higher noise levels. 6. Work of a communication system is provided at essential higher noise levels.

35 years MTD3 The lower estimations for error probabilities of an optimum decoding block codes with R=1/2 in BSC. Even codes of length n=1000 are inefficient at probability of an error Ро~0.08 in the channel. The lower estimations for error probabilities of an optimum decoding block codes with R=1/2 in BSC. Even codes of length n=1000 are inefficient at probability of an error Ро~0.08 in the channel. But the theory states, that it is possible to work successfully if P 0 R n=24 C=R 0,11

35 years MTD4 Threshold repeated short convolutional code decoding R=1/2 d=5 But it was a weak result!Thresholdelement Information Syndrome Syndrome Out Out

35 years MTD5 Repeated Application Efficiency of the Threshold Algorithm Very good! Why is it much more than d/2? d=11 R=1/2 n=1000 N errors in code block Part of gooddecodedblocks 1 2

35 years MTD6 Рис. 1. Многопороговый декодер сверточного СОК с R=1/2, d=5 и n A =14 The Convolutional Multithreshold Decoder for a Code with R=1/2, d=5 and 3 iterations It is - discovery!

35 years MTD7 The Block Multithreshold Decoder for Code with R=1/2 and d=5

35 years MTD8 SOFTWARE IMPLEMENTATION OF MULTITHRESHOLD DECODER 1. The complexity of software implementation: N MTD1 =(I+1)(d+2) additive equivalent operations on an information bit, where I is number of iterations and d is a minimal code distance. 2. MTD is applicable for codes with d<20 and needs about decoding iterations. 3. It’s possible to decrease number of operations to N MTD2 ~4d+3I operations. It is much less than turbo codes decoder complexity! - -In ~100 times more quickly, than for turbo codes!

35 years MTD9 Chipset MTD Decoder at PLIS Xilinx

35 years MTD10 NEW DECODER IN ALTERA PLIS FOR SPEED 600Mb/s AND MORE IN THE SPACE CHANNEL Декодер МПД на ПЛИС ALTERA, 640 Мб/с P b (e)~ Created – Создано - in 2007

35 years MTD11 HARDWARE IMPLEMENTATION OF MULTITHRESHOLD DECODER 1. MTD consists of shift registers. They are the fastest elements in PLIS or BIS. The part of other elements in MTD is less than 1%. 2. MTD consists of parallel shift registers and one-step threshold elements. That’s why the complexity of MTD implemented on PLIS is in 100 and more times faster than other decoder 3. Characteristics of MTD PLIS codec : - speed is about Mbps and more, - coding gain is about 6,5 - 9,5 dB. So, decoding speed is as for single 2 bit adder!

35 years MTD12

35 years MTD13 - Most simple and effective !!! Which decoder must be used? - Most simple and effective !!!

35 years MTD14 Welcome for everybody! Visitors of our site in November, ~5 Gbytes asked data from us for more than 8000 site visitors of 60 countries in Russia ???? 240 data units USA

35 years MTD15 Гости двуязычного специализированного сайта ИКИ РАН в декабре 2006г. Свыше 8000 посетителей нашего веб-сайта из 46 стран переписали более 2 Гбайт данных об алгоритмах МПД в 2006 г. Свыше 8000 посетителей нашего веб-сайта из 60 стран переписали более 5 Гбайт данных об алгоритмах МПД в 2006 г. USA Россия Более 240 блоков данных! Статистика за 2006 год, декабрь ????

35 years MTD16 Reference book «Помехоустойчивое кодирование. Методы и алгоритмы» под редакцией Ю.Б.Зубарева Авторы: В.В.Золотарёв, Г.В.Овечкин Издательство «Горячая линия - Телеком», 2004г. Издательство «Горячая линия - Телеком», 2004г.

35 years MTD17 В.В.Золотарёв Теория и алгоритмы многопорогового декодирования Под редакцией члена-корреспондента РАН Ю.Б.Зубарева Издательства «Радио и связь», «Горячая линия - Телеком» 2006 г. Издательства «Радио и связь», «Горячая линия - Телеком» 2006 г.

35 years MTD18Conclusions 1. We have invented effective iterative MTD algorithms 35 years ago. 2. Complexity of program versions MTD - for today an absolute minimum of calculations. A difference from a turbo codes on number of operations at comparable efficiency of ~100 times! 3. Hardware MTD can be faster than a turbo decoders up to 1000 times! 4. Decisions MTD quickly aspire to decisions of the optimum decoder (OD) even for large noise level 5. MTD – is the absolute leader by criteria "speed" and "complexity-efficiency". 6. MTD – is one of the leading algorithms! WE SUGGEST TO WORK TOGETHER!

35 years MTD In Russia: In Russia: Work ph.: , mоb.: , V.V.Zolotarev, S.V.Averin, I.V.Chulkov SRI RAS, URT

35 years MTD г. Space Research Institute RAS т.+7-(495) моб.: