Ua hana mākou!
"ʻO ke kumu o kēia papa ʻo ka hoʻomākaukau ʻana iā ʻoe no kou wā e hiki mai ana."
Aloha, Habr. E hoʻomanaʻo i ka ʻatikala weliweli (+219, 2588 bookmarks, 429k heluhelu)?
No laila ʻo Hamming (ʻae, ʻae, nānā pono a hoʻoponopono iā ʻoe iho ) aia kahi holoʻokoʻa , kākau ʻia ma muli o kāna mau haʻiʻōlelo. Unuhi mākou, no ka mea, ʻōlelo ke kanaka i kona manaʻo.
He puke kēia ʻaʻole e pili ana i ka IT wale nō, he puke e pili ana i ke ʻano noʻonoʻo o ka poʻe ʻoluʻolu. "ʻAʻole ia he mea hoʻoikaika i ka noʻonoʻo maikaʻi; wehewehe ia i nā kūlana e hoʻonui ai i ka manawa e hana ai i ka hana nui. "
Mahalo iā Andrey Pakhomov no ka unuhi.
Ua hoʻomohala ʻia ka Information Theory e CE Shannon i ka hopena o 1940s. Ua koi ʻo Bell Labs e kapa ʻia ʻo ia ʻo "Communication Theory" no ka mea ... he inoa pololei loa keia. No nā kumu maopopo, ʻoi aku ka nui o ka hopena o ka inoa "Information Theory" i ka lehulehu, ʻo ia ke kumu i koho ai ʻo Shannon, a ʻo ia ka inoa a mākou i ʻike ai a hiki i kēia lā. Hōʻike ka inoa ponoʻī e pili ana ke kumumanaʻo i ka ʻike, a he mea nui ia i ko mākou neʻe hohonu ʻana i ka makahiki ʻike. Ma kēia mokuna, e hoʻopā wau i kekahi mau manaʻo manaʻo nui mai kēia kumumanaʻo, ʻaʻole wau e hāʻawi i nā hōʻike koʻikoʻi, akā naʻe i nā hōʻike intuitive o kekahi mau mea hoʻolako o kēia kumumanaʻo, i maopopo ai iā ʻoe ke ʻano o ka "Information Theory", kahi āu e hoʻohana ai. a ma kahi ʻaʻole .
ʻO ka mea mua, he aha ka "ʻike"? Hoʻohālikelike ʻo Shannon i ka ʻike me ka maopopo ʻole. Ua koho ʻo ia i ka logarithm maikaʻi ʻole o ka likelika o kahi hanana ma ke ʻano he ana nui o ka ʻike i loaʻa iā ʻoe i ka wā e hiki mai ai kahi hanana me ka probability p. No ka laʻana, inā e haʻi aku au iā ʻoe he pohu ka lewa ma Los Angeles, a laila kokoke p i ka 1, ʻaʻole ia e hāʻawi i ka ʻike nui. Akā inā e ʻōlelo wau ua ua ma Monterey i Iune, e ʻike ʻole ʻia ka ʻōlelo a loaʻa ka ʻike hou aʻe. ʻAʻole loaʻa i kahi hanana hilinaʻi kekahi ʻike, no ka mea, log 1 = 0.
E nānā hou kākou i kēia. Manaʻo ʻo Shannon ʻo ke ana nui o ka ʻike he hana mau ia o ka probability o kahi hanana p, a no nā hanana kūʻokoʻa pono ia e hoʻohui - ʻo ka nui o ka ʻike i loaʻa ma muli o ka hiki ʻana o nā hanana kūʻokoʻa ʻelua e like me ka ka nui o ka ʻike i loaʻa ma muli o ka loaʻa ʻana o kahi hanana hui. Eia kekahi laʻana,ʻo ka hopena o ka'ōwili dice a me ka'ōwili kālā e mālama mauʻia e like me nā hanana kūʻokoʻa. E unuhi kākou i ka ʻōlelo o ka makemakika. Inā 'o I (p) ka nui o ka 'ike i loko o kekahi hanana me ka p, a laila, no ka hanana hui 'ana o 'elua hanana kū'oko'a x me ka p1 a me y me ka p2 hiki ke loa'a.
(x a me y nā hanana kūʻokoʻa)
ʻO kēia ka hoʻohālikelike Cauchy hana, ʻoiaʻiʻo no ka p1 a me ka p2 a pau. No ka hoʻoponopono ʻana i kēia haʻihaʻi hana, e noʻonoʻo i kēlā
p1 = p2 = p,
hāʻawi kēia
Ina p1 = p2 a p2 = p alaila
etc. ʻO ka hoʻonui ʻana i kēia kaʻina hana me ka hoʻohana ʻana i ke ʻano maʻamau no nā exponentials, no nā helu rational a pau m/n he ʻoiaʻiʻo kēia
Mai ka manaʻo hoʻomau o ke ana ʻike, ʻike ʻia ʻo ka hana logarithmic wale nō ka hopena hoʻomau i ka hoʻohālikelike hana Cauchy.
Ma ka ʻikepili ʻike, he mea maʻamau ka lawe ʻana i ke kumu logarithm he 2, no laila, aia i kahi koho binary he 1 kikoʻī o ka ʻike. No laila, ana ʻia ka ʻike e ke ʻano
E hoʻomaha a hoʻomaopopo i ka mea i hana ʻia ma luna. ʻO ka mea mua, ʻaʻole mākou i wehewehe i ka manaʻo o ka "ʻike"; wehewehe wale mākou i ke ʻano no kāna ana quantitative.
ʻO ka lua, pili kēia ana i ka maopopo ʻole, a ʻoiai he kūpono kūpono ia no nā mīkini-e like me nā ʻōnaehana kelepona, lekiō, televise, kamepiula, a me nā mea ʻē aʻe.
ʻO ke kolu, he ana pili kēia, pili ia i ke kūlana o kou ʻike i kēia manawa. Inā ʻoe e nānā i ke kahawai o nā "huahelu lauwili" mai kahi mea hoʻoheheʻe helu maʻamau, manaʻo ʻoe ʻaʻole maopopo kēlā me kēia helu aʻe, akā inā ʻoe e ʻike i ke ʻano o ka helu ʻana i nā "helu helu", e ʻike ʻia ka helu aʻe, a no laila ʻaʻole e ʻike ʻia. loaʻa ka ʻike.
No laila, kūpono ka wehewehe ʻana o Shannon no nā mīkini i nā manawa he nui, akā ʻaʻole i kūpono i ka ʻike kanaka o ka huaʻōlelo. ʻO ia ke kumu i kapa ʻia ai ʻo "Information Theory" he "Communication Theory." Eia nō naʻe, ua lōʻihi loa ka hoʻololi ʻana i nā wehewehe (nāna i hāʻawi i ka manaʻo i kona kaulana mua, a ʻo ia ka mea e manaʻo ai ka poʻe e pili ana kēia kumumanaʻo i ka "ʻike"), no laila pono mākou e noho pū me lākou, akā i ka manawa like ʻoe e pono ai. ʻike maopopo i ka mamao o ka wehewehe ʻana o Shannon i ka ʻike mai kona manaʻo maʻamau. Pili ka ʻike a Shannon i kekahi mea ʻokoʻa loa, ʻo ia hoʻi ka maopopo ʻole.
Eia kekahi mea e noʻonoʻo ai ke kau ʻoe i kekahi huaʻōlelo. Pehea e ʻae ai kahi wehewehe i manaʻo ʻia, e like me ka wehewehe ʻana o Shannon no ka ʻike, me kou manaʻo kumu a pehea ka ʻokoʻa? Aneane ʻaʻohe huaʻōlelo e hōʻike pono ana i kāu ʻike mua o kahi manaʻo, akā ʻo ka hopena, ʻo ka huaʻōlelo i hoʻohana ʻia e hōʻike ana i ke ʻano o ka manaʻo, no laila, ʻo ka hoʻomaʻamaʻa ʻana i kekahi mea ma o nā wehewehe wehewehe e hoʻopuka mau i kahi walaʻau.
E noʻonoʻo i kahi ʻōnaehana i loaʻa nā hōʻailona q me nā mea like pi. Ma keia hihia ka nui o ka ike i loko o ka ʻōnaehana (kona waiwai i manaʻo ʻia) ua like me:
Kapa ʻia kēia ʻo ka entropy o ka ʻōnaehana me ka puunaue likelika {pi}. Hoʻohana mākou i ka huaʻōlelo "entropy" no ka mea ua ʻike ʻia ke ʻano makemakika like i ka thermodynamics a me ka mechanics helu. ʻO ia ke kumu i hoʻokumu ai ka huaʻōlelo "entropy" i kekahi aura koʻikoʻi a puni iā ia iho, ʻaʻole i ʻāpono ʻia. ʻAʻole like ke ʻano makemakika o ka notation i ka wehewehe like o nā hōʻailona!
He kuleana nui ka entropy o ka puunaue likelika i ke kumumanaʻo coding. ʻO ka like ʻole o Gibbs no nā puʻunaue like ʻole ʻelua pi a me qi kekahi o nā hopena koʻikoʻi o kēia manaʻo. No laila pono mākou e hōʻoia i kēlā
Hoʻokumu ʻia ka hōʻike ma kahi pakuhi maopopo, Fig. 13.I, e hoike ana i kela
a loaʻa ke kaulike inā wale nō ka x = 1. E hoʻopili kākou i ka like ʻole i kēlā me kēia huahelu o ka huina mai ka ʻaoʻao hema.
Inā loaʻa i ka alphabet o kahi ʻōnaehana kamaʻilio nā hōʻailona q, a laila e lawe i ka likelika o ka lawe ʻana i kēlā me kēia hōʻailona qi = 1/q a hoʻololi i q, loaʻa iā mākou mai ka like ʻole o Gibbs.
Helu 13.I
'O ia ho'i, inā like ka like 'ana o ka ho'oili 'ana i nā hō'ailona q a pau me - 1 / q, a laila ua like ka entropy ki'eki'e me ln q, i 'ole e pa'a ka like 'ole.
I ka hihia o kahi code decodable kū hoʻokahi, loaʻa iā mākou ka like ʻole o Kraft
I kēia manawa inā wehewehe mākou i nā pseudo-probability
kahi o ka oiaio = 1, e hahai ana mai ka like ole o Gibbs,
a hoʻopili i kahi algebra liʻiliʻi (e hoʻomanaʻo ʻo K ≤ 1, no laila hiki iā mākou ke hoʻokuʻu i ka huaʻōlelo logarithmic, a hoʻoikaika paha i ka like ʻole ma hope), loaʻa iā mākou.
ʻo L ka lōʻihi o ke code maʻamau.
No laila, ʻo ka entropy ka palena liʻiliʻi loa no kēlā me kēia pāʻālua ʻano-ma-hōʻailona me ka lōʻihi o ka huaʻōlelo code L. ʻO kēia ka manaʻo kumu a Shannon no kahi kaha ʻole keakea.
E noʻonoʻo i ka manaʻo nui e pili ana i nā palena o nā ʻōnaehana kamaʻilio kahi e hoʻouna ʻia ai ka ʻike ma ke ʻano he kahawai o nā bits kūʻokoʻa a me ka walaʻau. Ua hoʻomaopopo ʻia ʻo ka likelika o ka hoʻouna pololei ʻana o hoʻokahi bit he P > 1/2, a ʻo ka likelika e hoʻohuli ʻia ka waiwai bit i ka wā o ka lawe ʻana (e loaʻa kahi hewa) ua like ia me Q = 1 - P. No ka maʻalahi, mākou e noʻonoʻo he kūʻokoʻa nā hewa a ua like ka like o ka hewa no kēlā me kēia bit i hoʻouna ʻia - ʻo ia hoʻi, aia ka "wīwī keʻokeʻo" ma ke kahawai kamaʻilio.
ʻO ke ala i loaʻa iā mākou kahi kahawai lōʻihi o nā n bits i hoʻopaʻa ʻia i hoʻokahi memo, ʻo ia ka n - dimensional extension o ka code one-bit. E hoʻoholo mākou i ka waiwai o n ma hope. E noʻonoʻo i kahi memo i loaʻa i nā n-bits ma ke ʻano he kiko ma ke ākea n-dimensional. No ka mea he wahi n-dimensional kā mākou - a no ka maʻalahi e manaʻo mākou ua like ka like o kēlā me kēia memo - aia nā M memo (e wehewehe pū ʻia ʻo M ma hope), no laila ʻo ka likelika o kekahi memo i hoʻouna ʻia.
(mea hoʻouna)
Papa 13.II
A laila, e noʻonoʻo i ka manaʻo o ka mana channel. Me ka ʻole o ka hele ʻana i nā kikoʻī, ua wehewehe ʻia ka mana o ke kahawai ʻo ia ka nui o ka ʻike i hiki ke hilinaʻi ʻia ma luna o kahi ala kamaʻilio, me ka noʻonoʻo ʻana i ka hoʻohana ʻana i ka coding kūpono loa. ʻAʻohe manaʻo hoʻopaʻapaʻa e hiki ke hoʻouna ʻia ka ʻike hou aʻe ma o ke ala kamaʻilio ma mua o kona hiki. Hiki ke hōʻoia ʻia kēia no kahi kahawai symmetric binary (a mākou e hoʻohana ai i kā mākou hihia). Ua kuhikuhi ʻia ka mana o ke kahawai, i ka wā e hoʻouna ai i nā bits
kahi, e like me ka wā ma mua, ʻo P ka mea hiki ʻole ke kuhi hewa i kekahi bit i hoʻouna ʻia. I ka hoʻouna ʻana i nā bits kūʻokoʻa, hāʻawi ʻia ka hiki ke kahawai e
Inā kokoke mākou i ke kaha kaha, a laila pono mākou e hoʻouna kokoke i kēia nui o ka ʻike no kēlā me kēia hōʻailona ai, i = 1, ..., M. E noʻonoʻo ana i ka hiki ʻana o kēlā me kēia hōʻailona ai he 1 / M, loaʻa iā mākou
ke hoʻouna aku mākou i kekahi o nā memo M like probable ai, loaʻa iā mākou
Ke hoʻouna ʻia nā n bits, manaʻo mākou e hiki mai nā hewa nQ. I ka hoʻomaʻamaʻa, no ka memo i loaʻa i nā n-bits, e loaʻa iā mākou nā hewa nQ i ka memo i loaʻa. No ka n nui, ka hoʻololi pili (ka hoʻololi = ka laula mahele, )
e piʻi aʻe ka puʻunaue o ka heluna hewa i ka piʻi ʻana o n.
No laila, mai ka ʻaoʻao transmitter, lawe au i ka leka ai e hoʻouna a huki i kahi pōʻai a puni me kahi radius
ʻoi aku ka nui iki ma ka huina like me ka e2 ma mua o ka helu i manaʻo ʻia o nā hewa Q, (Figure 13.II). Inā nui ka nui o n, a laila, aia ka liʻiliʻi liʻiliʻi o kahi kiko memo bj e ʻike ʻia ana ma ka ʻaoʻao hoʻokipa e hoʻolōʻihi i waho o kēia pōʻai. E kiʻi i ke kūlana e like me kaʻu e ʻike ai mai ka ʻike o ka mea hoʻouna: loaʻa iā mākou kekahi radii mai ka leka i hoʻouna ʻia ai i ka leka i loaʻa bj me ka likelika o ka hewa e like (a i ʻole like paha) i ka puʻunaue maʻamau, hiki i ka palena kiʻekiʻe. i nQ. No kēlā me kēia e2 i hāʻawi ʻia, aia kahi n nui loa i hiki i ka liʻiliʻi o ka liʻiliʻi o ke kiko o ka hopena bj ma waho o koʻu pōʻai.
I kēia manawa, e nānā kāua i ke kūlana like mai kou ʻaoʻao (Fig. 13.III). Aia ma ka ʻaoʻao hoʻokipa he pōʻai S(r) o ka radius like r a puni ke kiko i loaʻa bj ma ke ākea n-dimensional, ʻo ia hoʻi inā i loko o koʻu pōʻai ka leka i loaʻa, a laila aia ka leka i hoʻouna ʻia e aʻu i loko o kāu. pōʻai.
Pehea e hiki mai ai ka hewa? Hiki ke kuhi hewa i nā hihia i wehewehe ʻia ma ka papa ma lalo:
Helu 13.III
Maanei mākou e ʻike ai inā i loko o ka pōʻai i kūkulu ʻia a puni ka wahi i loaʻa ma kahi o hoʻokahi kikoʻī e pili ana i kahi memo i hoʻouna ʻole ʻia, a laila ua loaʻa kahi hewa i ka wā o ka hoʻouna ʻana, no ka mea ʻaʻole hiki iā ʻoe ke hoʻoholo i ka mea o kēia mau memo i hoʻouna ʻia. ʻAʻole hewa ka memo i hoʻouna ʻia inā aia ka kiko e pili ana iā ia i loko o ka pōʻai, a ʻaʻohe wahi ʻē aʻe i hiki i ke code i hāʻawi ʻia ma ka pōʻai like.
Loaʻa iā mākou kahi helu makemakika no ka hewa Pe inā hoʻouna ʻia ka leka ai
Hiki iā mākou ke hoʻolei i ka helu mua i ka huaʻōlelo ʻelua, e lawe ana i ka helu 1. Pēlā e loaʻa ai ka like ʻole
ʻIke pololei
No laila
e noi hou i ka huaolelo hope ma ka akau
ʻO ka lawe ʻana i ka nui nui, hiki ke lawe ʻia ka huaʻōlelo mua e like me ka liʻiliʻi e like me ka makemake, e haʻi aku ma mua o kekahi helu d. No laila ua loaʻa iā mākou
I kēia manawa, e nānā kākou pehea e hiki ai iā mākou ke kūkulu i kahi code hoʻololi maʻalahi e hoʻopili i nā memo M me nā n bits. Me ka ʻike ʻole pehea e hana pono ai i kahi code (ʻaʻole i hana ʻia nā code hoʻoponopono hewa), ua koho ʻo Shannon i ka coding random. E hoʻohuli i ke kālā no kēlā me kēia n bit i ka memo a hana hou i ke kaʻina hana no nā memo M. I ka huina, pono e hana ʻia nā ʻāpana kālā nM, no laila hiki
nā puke wehewehe ʻōlelo helu like ½nM. ʻOiaʻiʻo, ʻo ke kaʻina hana maʻamau o ka hana ʻana i kahi codebook ʻo ia ka mea hiki ke hoʻopaʻa ʻia, a me nā helu code e pili kokoke ana kekahi i kekahi a no laila ke kumu o nā hewa. Pono kekahi e hōʻoia inā ʻaʻole hiki kēia me ka ʻoi aku ka nui ma mua o nā pae hewa liʻiliʻi i koho ʻia, a laila lawa ka nui o ka n i hāʻawi ʻia.
ʻO ka mea koʻikoʻi, ʻo Shannon i ʻawelika i nā codebook hiki ke loaʻa i ka hapa awelika! E hoʻohana mākou i ka hōʻailona Av[.] e hōʻike i ka waiwai awelika ma luna o ka pūʻulu o nā puke code random āpau. ʻO ka awelika ʻana ma luna o ka d mau, ʻoiaʻiʻo, hāʻawi i kahi mau, no ka mea, no ka ʻawelika ʻana o kēlā me kēia huaʻōlelo ua like ia me kēlā me kēia huaʻōlelo i ka huina,
hiki ke hoʻonui ʻia (M–1 hele i M)
No kēlā me kēia memo i hāʻawi ʻia, i ka wā e kau ana ma waena o nā puke code a pau, e holo ana ka hoʻopili ʻana i nā waiwai kūpono a pau, no laila, ʻo ka awelika hiki ke loaʻa kahi kiko i loko o kahi pōʻai, ʻo ia ka ratio o ka nui o ka pōʻai me ka nui o ka lewa. ʻO ka nui o ka pōʻai
ma kahi o s=Q+e2 <1/2 a me ns he helu helu.
ʻO ka huaʻōlelo hope ma ka ʻākau ka mea nui loa i kēia huina. ʻO ka mea mua, e hoʻohālikelike i kona waiwai me ka hoʻohana ʻana i ka formula Stirling no nā factorial. A laila, e nānā kākou i ka helu emi o ka huaʻōlelo i mua ona, e hoʻomaopopo i ka piʻi ʻana o kēia helu i ko mākou neʻe ʻana i ka hema, a no laila hiki iā mākou ke: (1) kaohi i ka waiwai o ka huina i ka huina o ka holomua geometric me keia helu helu mua, (2) e hoonui i ka holomua geometric mai na huaolelo ns a i ka helu pau ole o na huaolelo, (3) e helu i ka huina o ka holomua geometric palena ole (algebra ma'amau, aohe mea nui) a loaa ka waiwai palena (no ka huina nui. n):
E nānā i ka ʻike ʻana o ka entropy H(s) i ka ʻike binomial. E hoʻomanaʻo i ka hoʻonui ʻana o ka moʻo Taylor H(s)=H(Q+e2) hāʻawi i kahi kuhi i loaʻa me ka noʻonoʻo ʻana i ka derivative mua wale nō a me ka nānā ʻole ʻana i nā mea ʻē aʻe. I kēia manawa e hui pū kākou i ka ʻōlelo hope loa:
kahi
ʻO kā mākou mea e hana ai, ʻo ke koho ʻana i ka e2 e like me ka e3 < e1, a laila e liʻiliʻi ka huaʻōlelo hope, ʻoiai ka nui o n. No laila, hiki ke loaʻa ka hewa PE awelika me ka liʻiliʻi e like me ka makemake me ka hiki o ke kahawai kokoke i C.
Inā he hapa liʻiliʻi ka awelika o nā code a pau, a laila pono ke kūpono i hoʻokahi code, no laila aia hoʻokahi ʻōnaehana coding kūpono. He hopena koʻikoʻi kēia i loaʻa iā Shannon - "Shannon's theorem for a sound channel", akā naʻe e hoʻomaopopo ʻia ua hōʻoia ʻo ia i kēia no kahi hihia nui loa ma mua o ke kahawai symmetric binary maʻalahi aʻu i hoʻohana ai. No ka hihia maʻamau, ʻoi aku ka paʻakikī o nā helu makemakika, akā ʻaʻole ʻokoʻa nā manaʻo, no laila, pinepine, me ka hoʻohana ʻana i ka laʻana o kekahi hihia, hiki iā ʻoe ke hōʻike i ke ʻano maoli o ka theorem.
E hoʻohewa kākou i ka hopena. Ua ʻōlelo pinepine mākou: "No ka nui n." Pehea ka nui o n? Nui, nui loa inā makemake ʻoe e pili kokoke i ka hiki o ke kahawai a e hōʻoia i ka hoʻoili ʻikepili pololei! Nui loa, ʻoiaʻiʻo, pono ʻoe e kali i kahi manawa lōʻihi e hōʻiliʻili i kahi leka i lawa nā bits e hoʻopili ai ma hope. I kēia hihia, ʻoi aku ka nui o ka puke wehewehe ʻōlelo random code (ma hope o nā mea a pau, ʻaʻole hiki ke hōʻike ʻia kēlā puke wehewehe i kahi ʻano pōkole ma mua o ka papa inoa piha o nā ʻāpana Mn āpau, ʻoiai ʻo ka nui o n a me M)!
Hōʻalo nā code hoʻoponopono hewa i ke kali ʻana i kahi leka lōʻihi loa a laila hoʻopaʻa a hoʻokaʻawale iā ia ma o nā codebook nui loa no ka mea e pale lākou i nā codebook a hoʻohana i ka helu helu maʻamau. Ma ke kumumanaʻo maʻalahi, ʻo ia mau code e nalowale i ka hiki ke hoʻokokoke i ke kahawai a mālama mau i ka hapa haʻahaʻa haʻahaʻa, akā ke hoʻoponopono ke code i ka nui o nā hewa, hana maikaʻi lākou. I nā huaʻōlelo ʻē aʻe, inā ʻoe e hoʻokaʻawale i kahi kaha kahawai i ka hoʻoponopono hewa, a laila pono ʻoe e hoʻohana i ka hiki ke hoʻoponopono hewa i ka hapa nui o ka manawa, ʻo ia hoʻi, pono e hoʻoponopono ʻia ka nui o nā hewa i kēlā me kēia memo i hoʻouna ʻia, i ʻole e hoʻopau ʻoe i kēia hiki.
I ka manawa like, ʻaʻole he mea ʻole ka theorem i hōʻike ʻia ma luna! Hōʻike ia e pono e hoʻohana nā ʻōnaehana hoʻouna maikaʻi i nā hoʻolālā hoʻopili akamai no nā kaula bit lōʻihi loa. ʻO kahi laʻana, ʻo ia nā satelite i lele ma waho o nā hōkū o waho; Ke neʻe nei lākou mai ka Honua a me ka Lā, ua koi ʻia lākou e hoʻoponopono i nā hewa hou aʻe i ka poloka ʻikepili: hoʻohana kekahi mau satellite i nā panela lā, e hāʻawi ana ma kahi o 5 W, hoʻohana kekahi i nā kumu mana nuklea, e hāʻawi ana e pili ana i ka mana like. ʻO ka mana haʻahaʻa o ka lako mana, ka liʻiliʻi o nā kīʻaha transmitter a me ka palena palena o nā kīʻaha hoʻokipa ma ka Honua, ka mamao nui e hele ai ka hōʻailona - pono kēia mau mea i ka hoʻohana ʻana i nā code me kahi kiʻekiʻe o ka hoʻoponopono hewa e kūkulu i kahi ʻōnaehana kamaʻilio kūpono.
E hoʻi kāua i ka n-dimensional space a mākou i hoʻohana ai i ka hōʻoia ma luna. Ma ke kamaʻilio ʻana, ua hōʻike mākou ua kokoke ka leo holoʻokoʻa o ka pōʻai ma kahi kokoke i ka ʻili o waho - no laila, ʻaneʻane maopopo loa ka hōʻailona hoʻouna ʻia ma kahi kokoke i ka ʻili o ka pōʻai i kūkulu ʻia a puni ka hōʻailona i loaʻa, ʻoiai me kahi hōʻailona koʻikoʻi. radius liʻiliʻi o ia pōʻai. No laila, ʻaʻole ia he mea kupanaha ka loaʻa ʻana o ka hōʻailona, ma hope o ka hoʻoponopono ʻana i kahi helu nui o nā hewa, nQ, huli i kahi kokoke i kahi hōʻailona me ka hewa ʻole. ʻO ka mana loulou a mākou i kūkākūkā ai ma mua ke kī e hoʻomaopopo ai i kēia ʻano. E hoʻomanaʻo ʻaʻole e uhi ʻia nā ʻāpana like i kūkulu ʻia no ka hoʻoponopono hewa ʻana i nā code Hamming. ʻO ka heluna nui o nā anana orthogonal i loko o ke ākea n-dimensional e hōʻike ana i ke kumu e hiki ai iā mākou ke hoʻokomo i nā pōʻai M ma ke ākea me ka liʻiliʻi o ka uhi. Inā ʻae mākou i kahi liʻiliʻi liʻiliʻi liʻiliʻi liʻiliʻi, hiki ke alakaʻi i kahi helu liʻiliʻi o nā hewa i ka wā decoding, hiki iā mākou ke loaʻa kahi hoʻonohonoho paʻa o nā spheres i ka lewa. Ua hōʻoia ʻo Hamming i kahi pae o ka hoʻoponopono hewa, ʻo Shannon - kahi haʻahaʻa haʻahaʻa o ka hewa, akā i ka manawa like e mālama i ka throughput maoli arbitrarily kokoke i ka hiki o ke ala kamaʻilio, ʻaʻole hiki i nā code Hamming ke hana.
ʻAʻole haʻi mai ka ʻikepili ʻikepili iā mākou pehea e hoʻolālā ai i kahi ʻōnaehana kūpono, akā kuhikuhi ia i ke ala e hiki ai i nā ʻōnaehana kamaʻilio kūpono. He mea hana waiwai ia no ke kūkulu ʻana i nā ʻōnaehana kamaʻilio me ka mīkini, akā, e like me ka mea i hōʻike mua ʻia, ʻaʻohe mea pili i ke ʻano o ke kamaʻilio ʻana o ke kanaka me kekahi. ʻAʻole ʻike ʻia ka nui o ka hoʻoilina olaola e like me nā ʻōnaehana kamaʻilio ʻenehana, no laila ʻaʻole maopopo i kēia manawa pehea e pili ai ka ʻikepili ʻike i nā genes. ʻAʻohe o mākou koho akā e hoʻāʻo, a inā hōʻike ka kūleʻa iā mākou i ke ʻano like me ka mīkini o kēia ʻano, a laila e kuhikuhi ka hemahema i nā ʻano koʻikoʻi ʻē aʻe o ke ʻano o ka ʻike.
Mai haʻalele nui kākou. Ua ʻike mākou ʻo nā wehewehe kumu a pau, i ka nui a i ʻole ka liʻiliʻi, pono e hōʻike i ke ʻano o kā mākou mau manaʻoʻiʻo mua, akā ua ʻike ʻia lākou e kekahi ʻano o ka distortion a no laila ʻaʻole pili. Ua ʻae ʻia ʻo ia, ma ka hopena, ʻo ka wehewehe a mākou e hoʻohana ai e wehewehe maoli i ke ʻano; akā, haʻi wale kēia iā mākou pehea e hoʻoponopono ai i nā mea a ʻaʻohe ala e hōʻike i kekahi manaʻo iā mākou. ʻO ke ʻano postulational, makemake nui ʻia i nā pōʻai makemakika, waiho nui i ka makemake i ka hana.
I kēia manawa e nānā mākou i kahi laʻana o nā hoʻāʻo IQ kahi i hoʻohālikelike ʻia ka wehewehe ʻana e like me kou makemake a, ma muli o ka hoʻopunipuni. Hana ʻia kahi hoʻāʻo i manaʻo ʻia e ana i ka naʻauao. Hoʻoponopono hou ʻia e hana like me ka hiki, a laila paʻi ʻia a, ma ke ʻano maʻalahi, calibrated i hiki ke hoʻohele ʻia ka "naʻauao" i ana ma ke ʻano maʻamau (ma ka pihi calibration, ʻoiaʻiʻo). Pono e nānā hou ʻia nā wehewehe ʻana a pau, ʻaʻole wale i ka wā i manaʻo mua ʻia ai, akā ma hope loa, i ka wā e hoʻohana ʻia ai i nā hopena i huki ʻia. Pehea ka nui o nā palena wehewehe i kūpono i ka pilikia e hoʻoholo ʻia? ʻEhia mau manawa e hoʻohana ʻia ai nā wehewehe i hāʻawi ʻia ma kahi hoʻonohonoho hoʻokahi i nā hoʻonohonoho ʻokoʻa? Hiki pinepine kēia! I loko o nā humanities, kahi āu e hālāwai ai i kou ola, hiki pinepine kēia.
No laila, ʻo kekahi o nā kumu o kēia hōʻike ʻana i ke kumumanaʻo ʻike, ma waho aʻe o ka hōʻike ʻana i kona pono, ʻo ia ke aʻo iā ʻoe no kēia pilikia, a i ʻole e hōʻike pololei iā ʻoe pehea e hoʻohana ai i ka hopena i makemake ʻia. Ua ʻike lōʻihi ʻia ʻo nā wehewehe mua e hoʻoholo i ka mea āu e ʻike ai i ka hopena, i kahi ʻoi aku ka nui ma mua o ka mea i manaʻo ʻia. ʻO nā wehewehe mua e pono ai ka nānā nui ʻana mai iā ʻoe, ʻaʻole wale ma kahi kūlana hou, akā ma nā wahi āu i hana ai no ka manawa lōʻihi. E ʻae kēia iā ʻoe e hoʻomaopopo i ka nui o nā hopena i loaʻa he tautology a ʻaʻole he mea pono.
Hōʻike ka moʻolelo kaulana o Eddington i ka poʻe lawaiʻa i ke kai me ka ʻupena. Ma hope o ke aʻo ʻana i ka nui o nā iʻa i loaʻa iā lākou, ua hoʻoholo lākou i ka liʻiliʻi o nā iʻa i loaʻa i ke kai! Ua alakaʻi ʻia kā lākou hopena e ka mea hana i hoʻohana ʻia, ʻaʻole ma ka ʻoiaʻiʻo.
E hoʻomau 'ia…
ʻO wai ka mea makemake e kōkua i ka unuhi ʻana, ka hoʻonohonoho ʻana a me ka hoʻolaha ʻana o ka puke - e kākau i kahi leka pilikino a i ʻole leka uila [pale ʻia ka leka uila]
Ma ke ala, ua hoʻomaka pū mākou i ka unuhi ʻana o kekahi puke maikaʻi - )
Ke ʻimi nui nei mākou ka poe kokua i ka unuhi . (hoʻololi no 10 mau minuke, ua lawe mua ʻia nā 20 mua)
Ma loko o ka puke a me nā mokuna unuhi
- Intro to The Art of Doing Science and Engineering: Learning to Learn (Malaki 28, 1995)
- "Nā Kumu o ka Digital (Discrete) Revolution" (Malaki 30, 1995)
- "History of Computers - Hardware" (Malaki 31, 1995)
- "History of Computers - Software" (ʻApelila 4, 1995)
- "History of Computers - Applications" (ʻApelila 6, 1995)
- "Naʻauao Artificial - Māhele I" (ʻApelila 7, 1995)
- "Naʻauao Artificial - Māhele II" (ʻApelila 11, 1995)
- "Naʻauao Artificial III" (ʻApelila 13, 1995)
- "N-Dimensional Space" (ʻApelila 14, 1995)
- "Coding Theory - The Representation of Information, Part I" (ʻApelila 18, 1995)
- "Coding Theory - The Representation of Information, Part II" (ʻApelila 20, 1995)
- "Nā Palapala Hoʻoponopono Haʻihaʻi" (ʻApelila 21, 1995)
- "Ka Manaʻo ʻIke" (ʻApelila 25, 1995)
- "Nā kānana kikohoʻe, Māhele I" (ʻApelila 27, 1995)
- "Nā kānana kikohoʻe, Mahele II" (ʻApelila 28, 1995)
- "Nā kānana kikohoʻe, Māhele III" (Mei 2, 1995)
- "Nā kānana kikohoʻe, Mahele IV" (Mei 4, 1995)
- "Simulation, Māhele I" (Mei 5, 1995)
- "Simulation, Part II" (Mei 9, 1995)
- "Simulation, Part III" (Mei 11, 1995)
- "Fiber Optics" (Mei 12, 1995)
- "Aʻoaʻo kōkua kamepiula" (Mei 16, 1995)
- "Mathematics" (Mei 18, 1995)
- "Quantum Mechanics" (Mei 19, 1995)
- "Creativity" (Mei 23, 1995). Unuhi:
- "Nā Kauka" (Mei 25, 1995)
- "ʻIkepili hikiʻole ke hilinaʻi" (Mei 26, 1995)
- "Systems Engineering" (Mei 30, 1995)
- "Loaʻa iā ʻoe ka mea āu e ana" (Iune 1, 1995)
- (Iune 2, 1995) unuhi i loko o 10 mau ʻāpana minuke
- Hamming, “You and Your Research” (Iune 6, 1995).
ʻO wai ka mea makemake e kōkua i ka unuhi ʻana, ka hoʻonohonoho ʻana a me ka hoʻolaha ʻana o ka puke - e kākau i kahi leka pilikino a i ʻole leka uila [pale ʻia ka leka uila]
Source: www.habr.com