{"id":238,"date":"2015-08-29T15:48:00","date_gmt":"2015-08-29T15:48:00","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/video-equipment\/uncategorized\/channel-encodingerror-correction\/"},"modified":"2015-08-29T15:48:00","modified_gmt":"2015-08-29T15:48:00","slug":"channel-encodingerror-correction","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/video-equipment\/channel-encodingerror-correction\/","title":{"rendered":"Channel encoding:Error correction"},"content":{"rendered":"<div class=\"jirnc6a0dbd9937902\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '61e5902552e2353963d8d2f1bd1f4a8f',\n\t\t'format' : 'iframe',\n\t\t'height' : 250,\n\t\t'width' : 300,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/61e5902552e2353963d8d2f1bd1f4a8f\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.jirnc6a0dbd9937902 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.jirnc6a0dbd9937902 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.jirnc6a0dbd9937902 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.jirnc6a0dbd9937902 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.jirnc6a0dbd9937902 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<h3 align=\"justify\">Error correction<\/h3>\n<p align=\"justify\">The introduction of redundancy bits to a package of data increases the data length and with it the number of possible combinations. Consider a 6-bit package consisting of 4 bits of useful data and 2 redundancy bits.  <\/p>\n<p align=\"justify\"><a href=\"http:\/\/lh3.googleusercontent.com\/-jmyjL5mbcx4\/VeHUKRtkPaI\/AAAAAAAB39s\/vm0XyQDpeoE\/s1600-h\/Channel-encoding-05662.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"Channel encoding-0566\" border=\"0\" alt=\"Channel encoding-0566\" src=\"http:\/\/lh3.googleusercontent.com\/-ZzqQ7LAeOt0\/VeHURSOrBiI\/AAAAAAAB3-Y\/xlB40DFpz_0\/Channel-encoding-0566_thumb.jpg?imgmax=800\" width=\"366\" height=\"281\" \/><\/a>  <\/p>\n<p align=\"justify\">The 4 bits of useful data contain 24 = 16 different valid messages. At the receiving end, however, a set of 26 = 64 different messages may be received, of which only a sub-set contains the 16 valid messages. This sub-set is called a <i>cod<\/i><i>e <\/i>and the valid messages are called <i>cod<\/i><i>e words <\/i>or <i>cod<\/i><i>e vectors <\/i>(vectors for short). When a message is received that does not correspond to any of the valid codes, the receiver finds a valid code word \u2018nearest\u2019 to the received message, on the assumption that the nearest is the most likely correct mes- sage in the same way as the corrupted word in the sentence \u2018the fishing boat <i>saike<\/i><i>d <\/i>in the morning\u2019 is easily deduced to be \u2018<i>saile<\/i><i>d<\/i>\u2019 being the nearest valid replacement. This technique is known as forward error correction (FEC).  <\/p><div class=\"mgfvk6a0dbd9937ae8\" ><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-0778475562755157\"\n     crossorigin=\"anonymous\"><\/script>\n<!-- 300x600 television-and-video -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:600px\"\n     data-ad-client=\"ca-pub-0778475562755157\"\n     data-ad-slot=\"6549443290\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.mgfvk6a0dbd9937ae8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.mgfvk6a0dbd9937ae8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.mgfvk6a0dbd9937ae8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.mgfvk6a0dbd9937ae8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.mgfvk6a0dbd9937ae8 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"kmtvi6a0dbd9937a0a\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '0c1eb4c533eaedb7b996f49a5a4983a9',\n\t\t'format' : 'iframe',\n\t\t'height' : 300,\n\t\t'width' : 160,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/0c1eb4c533eaedb7b996f49a5a4983a9\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.kmtvi6a0dbd9937a0a {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.kmtvi6a0dbd9937a0a {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.kmtvi6a0dbd9937a0a {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.kmtvi6a0dbd9937a0a {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.kmtvi6a0dbd9937a0a {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\">In practice, real codes contain very long strings of binary bits with thousands of valid code words requiring carefully designed coding tech- niques to produce code words which are well structured into sets and sub-sets. The process of correction is then carried out by advanced and sophisticated mathematics. There are two coding techniques: <i>block coding <\/i>and <i>convolutional coding<\/i>. In block coding, such as Hamming or Reed\u2013Solomon codes, a block of <i>k <\/i>data digits is encoded by a code gener- ator into a code word of <i>n <\/i>digits where <i>n <\/i>is larger than <i>k<\/i>. The number of redundancy bits is therefore (<i>n <\/i>&#8211; <i>k<\/i>). The ratio <i>k<\/i>\/<i>n <\/i>represents the efficiency of the code and is normally known as the <i>code rate<\/i>. In convolutional codes, the coded sequence from the encoder depends not only on the sequence of the incoming block of <i>k <\/i>bits, but also on the sequence of data bits that preceded it. Unlike block codes, the code word of a convolutional code is not unique to the incoming <i>k <\/i>bits, but depends on earlier data as well.  <\/p>\n<p align=\"justify\">For convolutional codes, <i>k <\/i>and <i>n <\/i>are usually small, giving small code rates such as 1\/2, 2\/3, 3\/4 and 7\/8.  <\/p>\n<p align=\"justify\">Convolutional codes invariably outperform block codes, especially for correcting random and burst errors. One of the more efficient algorithms for decoding convolutional codes was devised by <i>V<\/i><i>iterb<\/i><i>i <\/i>with especially good results in correcting random channel errors. DTV uses both block coding (Hamming and Reed\u2013Solomon) and convolutional coding.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Error correction The introduction of redundancy bits to a package of data increases the data length and with it the number of possible combinations. Consider a 6-bit package consisting of 4 bits of useful data and 2 redundancy bits. The 4 bits of useful data contain 24 = 16 different valid messages. At the receiving [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/video-equipment\/channel-encodingerror-correction\/\" class=\"more-link\" >Continue reading&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"aioseo_notices":[],"views":678,"_links":{"self":[{"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/posts\/238"}],"collection":[{"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/comments?post=238"}],"version-history":[{"count":0,"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/posts\/238\/revisions"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/media?parent=238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/categories?post=238"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/video-equipment\/wp-json\/wp\/v2\/tags?post=238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}