### Abstract

In this paper, we consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter p and (b) the process which adds the errors can be described by a sufficiently "simple" circuit. Codes for such channel models are attractive since, like codes for standard adversarial errors, they can handle channels whose true behavior is unknown or varying over time. For three classes of channels, we provide explicit, efficiently encodable/decodable codes of optimal rate where only inefficiently decodable codes were previously known. In each case, we provide one encoder/decoder that works for every channel in the class. Unique decoding for additive errors: We give the first construction of a poly-time encodable/decodable code for additive (a.k.a. oblivious) channels that achieve the Shannon capacity 1 - H(p). List-decoding for online log-space channels: We give an efficient code with optimal rate (arbitrarily close to 1 - H(p)) that recovers a short list containing the correct message with high probability for channels which read and modify the transmitted codeword as a stream, using at most O(log N) bits of workspace on transmissions of N bits. List-decoding for poly-time channels: For any constant c we give a similar list-decoding result for channels describable by circuits of size at most N^{c}, assuming the existence of pseudorandom generators.

Original language | English (US) |
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Title of host publication | Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |

Pages | 723-732 |

Number of pages | 10 |

DOIs | |

State | Published - Dec 1 2010 |

Event | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 - Las Vegas, NV, United States Duration: Oct 23 2010 → Oct 26 2010 |

### Other

Other | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |
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Country | United States |

City | Las Vegas, NV |

Period | 10/23/10 → 10/26/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science(all)

### Cite this

*Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010*(pp. 723-732). [5671339] https://doi.org/10.1109/FOCS.2010.74

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*Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010.*, 5671339, pp. 723-732, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010, Las Vegas, NV, United States, 10/23/10. https://doi.org/10.1109/FOCS.2010.74

**Codes for computationally simple channels : Explicit constructions with optimal rate venkatesan guruswami.** / Guruswami, Venkatesan; Smith, Adam Davison.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Codes for computationally simple channels

T2 - Explicit constructions with optimal rate venkatesan guruswami

AU - Guruswami, Venkatesan

AU - Smith, Adam Davison

PY - 2010/12/1

Y1 - 2010/12/1

N2 - In this paper, we consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter p and (b) the process which adds the errors can be described by a sufficiently "simple" circuit. Codes for such channel models are attractive since, like codes for standard adversarial errors, they can handle channels whose true behavior is unknown or varying over time. For three classes of channels, we provide explicit, efficiently encodable/decodable codes of optimal rate where only inefficiently decodable codes were previously known. In each case, we provide one encoder/decoder that works for every channel in the class. Unique decoding for additive errors: We give the first construction of a poly-time encodable/decodable code for additive (a.k.a. oblivious) channels that achieve the Shannon capacity 1 - H(p). List-decoding for online log-space channels: We give an efficient code with optimal rate (arbitrarily close to 1 - H(p)) that recovers a short list containing the correct message with high probability for channels which read and modify the transmitted codeword as a stream, using at most O(log N) bits of workspace on transmissions of N bits. List-decoding for poly-time channels: For any constant c we give a similar list-decoding result for channels describable by circuits of size at most Nc, assuming the existence of pseudorandom generators.

AB - In this paper, we consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter p and (b) the process which adds the errors can be described by a sufficiently "simple" circuit. Codes for such channel models are attractive since, like codes for standard adversarial errors, they can handle channels whose true behavior is unknown or varying over time. For three classes of channels, we provide explicit, efficiently encodable/decodable codes of optimal rate where only inefficiently decodable codes were previously known. In each case, we provide one encoder/decoder that works for every channel in the class. Unique decoding for additive errors: We give the first construction of a poly-time encodable/decodable code for additive (a.k.a. oblivious) channels that achieve the Shannon capacity 1 - H(p). List-decoding for online log-space channels: We give an efficient code with optimal rate (arbitrarily close to 1 - H(p)) that recovers a short list containing the correct message with high probability for channels which read and modify the transmitted codeword as a stream, using at most O(log N) bits of workspace on transmissions of N bits. List-decoding for poly-time channels: For any constant c we give a similar list-decoding result for channels describable by circuits of size at most Nc, assuming the existence of pseudorandom generators.

UR - http://www.scopus.com/inward/record.url?scp=78751551195&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78751551195&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2010.74

DO - 10.1109/FOCS.2010.74

M3 - Conference contribution

AN - SCOPUS:78751551195

SN - 9780769542447

SP - 723

EP - 732

BT - Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010

ER -