{"id":160511,"date":"2023-09-28T15:02:14","date_gmt":"2023-09-28T09:32:14","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160511"},"modified":"2023-09-28T15:02:16","modified_gmt":"2023-09-28T09:32:16","slug":"a-binary-source-generates-symbols-%f0%9d%91%8b-%e2%88%88-%e2%88%9211-which-are-transmitted-over-a-noisy-channel","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-binary-source-generates-symbols-%f0%9d%91%8b-%e2%88%88-%e2%88%9211-which-are-transmitted-over-a-noisy-channel\/","title":{"rendered":"A binary source generates symbols \ud835\udc4b \u2208 {\u22121,1} which are transmitted over a noisy channel"},"content":{"rendered":"\n<p>Q. A binary source generates symbols \ud835\udc4b \u2208 {\u22121,1} which are transmitted over a noisy channel. The probability of transmitting \ud835\udc4b = 1 is 0.5. Input to the threshold detector is \ud835\udc45 = \ud835\udc4b + \ud835\udc41. The probability density function \ud835\udc53<sub>\ud835\udc41<\/sub>(\ud835\udc5b) of the noise \ud835\udc41 is shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"479\" height=\"155\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-970.png\" alt=\"\" class=\"wp-image-160512\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-970.png 479w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-970-300x97.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/figure>\n\n\n\n<p>If the detection threshold is zero, then the probability of error (correct to two decimal places) is\u00a0<\/p>\n\n\n\n<p>Ans: 0.12 &#8211; 0.14<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A binary source generates symbols \ud835\udc4b \u2208 {\u22121,1} which are transmitted over a noisy channel. The probability of transmitting \ud835\udc4b = 1 is 0.5. Input to the threshold detector is \ud835\udc45 = \ud835\udc4b + \ud835\udc41. The probability density function \ud835\udc53\ud835\udc41(\ud835\udc5b) of the noise \ud835\udc41 is shown below. If the detection threshold is zero, then [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":160513,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-160511","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160511","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=160511"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160511\/revisions"}],"predecessor-version":[{"id":160514,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160511\/revisions\/160514"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160513"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}