{"id":2152,"date":"2025-04-19T09:41:44","date_gmt":"2025-04-19T07:41:44","guid":{"rendered":"https:\/\/localdab.org\/?page_id=2152"},"modified":"2026-01-04T09:30:43","modified_gmt":"2026-01-04T08:30:43","slug":"reverse-bit-law","status":"publish","type":"page","link":"https:\/\/localdab.org\/index.php\/glossary\/q-t\/reverse-bit-law\/","title":{"rendered":"Reverse bit law"},"content":{"rendered":"\n<p>It is a specific combination of a fixed number of bits. The rule is used in DAB and DAB+ for time interleaving of the CIFS (Common Interleave Frames) in the MSC (Main Service Channel). It recombines 4 bits or 16 numbers (0 to 15).<\/p>\n\n\n\n<p>A permutation is a specific combination of several possible combinations. And the reverse bit law is nothing but an algorithm that results in one specific combination.&nbsp; Or a permutation of the 16 digits (0 to 15).<\/p>\n\n\n\n<p>It is simple to understand because the binary number corresponding to its number in the inverse bit law permutation is the inverse bit number.<\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<p>In binary, the number <strong><u>12<\/u><\/strong> corresponds to <strong>1100<\/strong>. The inverse of 1100 is <strong><u>0011<\/u><\/strong> and corresponds to <strong>3<\/strong> (the inverse is rearranging the order of bits from the least significant to the most significant bit).<\/p>\n\n\n\n<p>For each number from 0 to 15, we find the corresponding number by using the binary value and reverse it.<\/p>\n\n\n\n<p>So, if you want to scramble bits by using the reverse bit law, the sequence of numbers 0 to 15 can be permuted as follows.<\/p>\n\n\n\n<p>Reverse bit law results in the following permutation table:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"447\" src=\"https:\/\/localdab.org\/wp-content\/uploads\/2025\/04\/Tabel-1-Reverse-Bit-Law.png\" alt=\"\" class=\"wp-image-2153\" srcset=\"https:\/\/localdab.org\/wp-content\/uploads\/2025\/04\/Tabel-1-Reverse-Bit-Law.png 622w, https:\/\/localdab.org\/wp-content\/uploads\/2025\/04\/Tabel-1-Reverse-Bit-Law-300x216.png 300w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/figure>\n\n\n\n<p>Remark that some bit combinations, such as 0, 6, 9 and 15, don\u2019t change in case of bit reversal.<\/p>\n\n\n\n<p>Another way to present the above scrambling is the following table.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"610\" height=\"61\" src=\"https:\/\/localdab.org\/wp-content\/uploads\/2025\/04\/Tabel-2-Reverse-Bit-Law.png\" alt=\"\" class=\"wp-image-2154\" srcset=\"https:\/\/localdab.org\/wp-content\/uploads\/2025\/04\/Tabel-2-Reverse-Bit-Law.png 610w, https:\/\/localdab.org\/wp-content\/uploads\/2025\/04\/Tabel-2-Reverse-Bit-Law-300x30.png 300w\" sizes=\"auto, (max-width: 610px) 100vw, 610px\" \/><\/figure>\n\n\n\n<p class=\"has-small-font-size\">This operation separates the input samples into even- and odd-indexed samples, precisely as described by the radix-2 IFFT algorithm. The samples are first split into two groups\u2014 even and odd \u2014 which forms the initial step of the IFFT computation. This separation is performed internally within the IFFT function used in DAB\/DAB+, with even and odd input samples processed separately.<\/p>\n\n\n\n<p>Understanding the \u201cInverse Bit Law\u201d principle to understand \u201ctime Interleaving\u201d is essential.<\/p>\n\n\n\n<p><a href=\"https:\/\/localdab.org\/index.php\/glossary\/\" data-type=\"page\" data-id=\"15\">Back<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is a specific combination of a fixed number of bits. The rule is used in DAB and DAB+ for time interleaving of the CIFS (Common Interleave Frames) in the MSC (Main Service Channel). It recombines 4 bits or 16 numbers (0 to 15). A permutation is a specific combination of several possible combinations. And [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1266,"menu_order":25,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2152","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/2152","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/comments?post=2152"}],"version-history":[{"count":3,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/2152\/revisions"}],"predecessor-version":[{"id":2323,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/2152\/revisions\/2323"}],"up":[{"embeddable":true,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/1266"}],"wp:attachment":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/media?parent=2152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}