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- | === The football match problem === | ||

- | |||

- | In a football match problem with n games there are n pairs of teams playing playing | ||

- | against one another. The outcome of every game is given by the numbers 0, 1, and 2, | ||

- | according to whether the game was a draw, whether the home team won, or whether | ||

- | the home team lost. It is possible to bet on the outcomes of these games. A series of n | ||

- | bets gives a win if at most 2 of the games in the series were predicted in error. | ||

- | The classical problem asks for the smallest number of bets such that, no matter the | ||

- | outcome, there is a winning bet. | ||

- | |||

- | This problem can be solved with coding theory. We can identify the possible outcomes | ||

- | of the games by a vector of length n over the field GF(3). The task is to find the smallest | ||

- | number of vectors (=bets) such that any vector in GF(3)^n (=outcome of the games) has | ||

- | Hamming distance at most 2 from a bet. | ||

- | |||

- | In this project we are interested in a soft version of this problem in which there are prior | ||

- | probabilities for the outcome of each game, and there is a confidence level, P; the task is | ||

- | to find the smallest number of bets such that, given the prior probabilities, with probability | ||

- | at most P none of the bets wins. The student should study optimization techniques for | ||

- | finding a good set of bets. | ||

- | |||

- | |||

---- dataentry project ---- | ---- dataentry project ---- | ||

- | title : The football match problem | + | title : Joint Source Channel Coding for Image Transmission |

contactname: Harm Cronie | contactname: Harm Cronie | ||

contactmail_mail: harm.cronie@epfl.ch | contactmail_mail: harm.cronie@epfl.ch | ||

- | contacttel: 021 6931205 | + | contacttel: 021 6936793 |

- | contactroom: BC 150 | + | contactroom: BC150 |

- | type : bachelor semester | + | type : master semester |

status : available | status : available | ||

+ | created_dt : 2009-06-05 | ||

+ | taken_dt : YYYY-MM-DD | ||

+ | completed_dt : YYYY-MM-DD | ||

+ | by : STUDENT_NAME | ||

+ | output_media : MEDIA_ADDRESS_TO_FINAL_REPORT | ||

table : projects | table : projects | ||

- | created_dt : 2009-01-01 | ||

- | taken_dt : | ||

- | completed_dt : | ||

- | by : | ||

- | output_media : | ||

====== | ====== | ||

template:datatemplates:project | template:datatemplates:project | ||

---- | ---- | ||

+ | |||

+ | In this assignment we consider the efficient transmission of images | ||

+ | over a noisy channel. On one hand we would like to represent the image | ||

+ | with as less bits as possible. This is done by image compression | ||

+ | methods such as jpeg compression. On the other hand we need some | ||

+ | redundancy in the form of an error-correcting code to ensure reliable | ||

+ | transmission over the channel. Traditionally, these two tasks are | ||

+ | solved separately. One of the disadvantages of this approach is that a | ||

+ | few residual errors after decoding the error-correcting code usually | ||

+ | lead to a very large error in image reconstruction. | ||

+ | |||

+ | Joint source channel coding methods can provide a finer trade-off | ||

+ | between the image reconstruction quality and the amount of noise the | ||

+ | system can deal with. In this assignment you will implement signal | ||

+ | processing algorithms to represent an image efficiently. These methods | ||

+ | include image transforms such as the discrete cosine transform and | ||

+ | quantization. After this signal processing stage, a Raptor code can be | ||

+ | applied to allow for reliable transmission over the channel. The goal | ||

+ | is to reconstruct the image at the receiver side with as less | ||

+ | distortion as possible given the signal to noise ratio of the channel. | ||

+ |