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Error-correcting codes with feedback

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considered error correcting codes with noiseless feedback. In Berlekamp's scenario, the receiver chose a subset of possible messages and asked the sender whether the given message was in this subset, a 'yes' or 'no' answer. Based on this answer, the receiver then chose a new subset and repeated the
130:, the feedback received by the sender is always free of errors. In an error-correcting code with noisy feedback, errors can occur in the feedback, as well as in the message. 40: 114:
as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is
339: 295: 175:), with a given percentage of wrong answers, and calculated the minimum number of randomly chosen questions to determine the answer. 320: 35: 192: 95:
to Bob (the receiver). The communication channel between Alice and Bob is imperfect, and can introduce errors.
315:, London Mathematical Society Lecture Note Series, vol. 218, Cambridge University Press, pp. 41–70, 80: 261: 115: 138: 68: 275: 164: 306: 316: 291: 64: 30: 310: 283: 172: 141: 72: 60: 183:
process. The game is further complicated due to noise; some of the answers will be wrong.
179: 168: 157: 153: 333: 104: 287: 56: 282:, Bolyai Society Mathematical Studies, vol. 16, Springer, pp. 27–70, 160: 83:
designed to work in the presence of feedback from the receiver to the sender.
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as a message such that Bob will successfully understand the value
118:: Bob can send feedback to Alice about the message he received. 15: 278:, in Imre Csiszár; Gyula O.H. Katona; Gabor Tardos (eds.), 276:"Coding with Feedback and Searching with Lies" 269:(PhD). Massachusetts Institute of Technology. 8: 163:channel with noiseless feedback. In 1961, 29:It has been suggested that this article be 210: 208: 91:Alice (the sender) wishes to send a value 231: 204: 243: 215: 103:An error-correcting code is a way of 7: 263:Block coding with noiseless feedback 219: 126:In an error-correcting code without 77:error-correcting codes with feedback 14: 20: 36:Hybrid automatic repeat request 340:Error detection and correction 133:An error-correcting code with 1: 260:Berlekamp, Elwyn R. (1964). 193:Noisy channel coding theorem 46:Proposed since October 2024. 288:10.1007/978-3-540-32777-6_2 280:Entropy, Search, Complexity 356: 178:In his 1964 dissertation, 274:Deppe, Christian (2007), 312:Surveys in Combinatorics 144:strategy with errors. 81:error correcting codes 307:"Searching with lies" 137:is equivalent to an 305:Hill, Ray (1995), 135:noiseless feedback 69:information theory 297:978-3-540-32573-4 65:telecommunication 53: 52: 48: 347: 325: 300: 270: 268: 247: 241: 235: 229: 223: 212: 173:Twenty questions 73:searching theory 61:computer science 44: 24: 23: 16: 355: 354: 350: 349: 348: 346: 345: 344: 330: 329: 323: 304: 298: 273: 266: 259: 256: 251: 250: 242: 238: 230: 226: 213: 206: 201: 189: 180:Elwyn Berlekamp 171:(also known as 169:Bar-Kochba game 167:introduced the 156:introduced the 150: 124: 101: 89: 49: 25: 21: 12: 11: 5: 353: 351: 343: 342: 332: 331: 328: 327: 321: 302: 296: 271: 255: 252: 249: 248: 236: 232:Berlekamp 1964 224: 203: 202: 200: 197: 196: 195: 188: 185: 154:Claude Shannon 149: 146: 128:noisy feedback 123: 122:Noisy feedback 120: 100: 97: 88: 85: 51: 50: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 352: 341: 338: 337: 335: 324: 322:0-521-49797-3 318: 314: 313: 308: 303: 299: 293: 289: 285: 281: 277: 272: 265: 264: 258: 257: 253: 245: 240: 237: 233: 228: 225: 221: 217: 211: 209: 205: 198: 194: 191: 190: 186: 184: 181: 176: 174: 170: 166: 162: 159: 155: 147: 145: 143: 140: 136: 131: 129: 121: 119: 117: 113: 109: 106: 98: 96: 94: 86: 84: 82: 78: 74: 70: 66: 62: 58: 47: 42: 38: 37: 32: 27: 18: 17: 311: 279: 262: 239: 227: 177: 165:Alfréd Rényi 151: 134: 132: 127: 125: 111: 107: 102: 92: 90: 76: 54: 45: 34: 57:mathematics 244:Deppe 2007 216:Deppe 2007 199:References 161:memoryless 220:Hill 1995 152:In 1956, 334:Category 187:See also 158:discrete 139:adaptive 105:encoding 99:Solution 254:Sources 148:History 116:two-way 87:Problem 41:Discuss 319:  294:  142:search 71:, and 31:merged 267:(PDF) 33:with 317:ISBN 292:ISBN 218:and 214:See 79:are 284:doi 55:In 39:. ( 336:: 309:, 290:, 207:^ 75:, 67:, 63:, 59:, 326:. 301:. 286:: 246:. 234:. 222:. 112:x 108:x 93:x 43:)

Index

merged
Hybrid automatic repeat request
Discuss
mathematics
computer science
telecommunication
information theory
searching theory
error correcting codes
encoding
two-way
adaptive
search
Claude Shannon
discrete
memoryless
Alfréd Rényi
Bar-Kochba game
Twenty questions
Elwyn Berlekamp
Noisy channel coding theorem


Deppe 2007
Hill 1995
Berlekamp 1964
Deppe 2007
Block coding with noiseless feedback
"Coding with Feedback and Searching with Lies"
doi

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