Virtual Labs

Message Passing Decoding of LDPC Codes on Erasure Channel

1. Which statement is true regarding the complete decoding of the codeword using the peeling decoder occur, given that at least one erasure occured?

a: The number of rounds to complete the decoding will be even. Explanation

Explanation

b: The number of rounds will always be odd, to complete the decoding. Explanation

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c: At most two rounds are required. Explanation

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d: At least four rounds are required to complete the decoding. Explanation

Explanation

2. Assume that for a code with minimum distance

>=2

, we transmitted a codeword which was received with a single erasure. How many rounds may be required to correct this erasure using peeling decoding?

a: 1 Explanation

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b: 3 Explanation

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c: 4 Explanation

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d: 2 Explanation

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3. Does the peeling decoder perform block-wise MAP decoding? Select the most correct option

a: No, because the peeling decoder is a non-linear decoder. Explanation

Explanation

b: Yes, because bit-wise MAP is the same as block-wise MAP, in erasure channels, and the peeling decoder indeed implements bit-wise MAP decoding. Explanation

Explanation

c: No, because the peeling decoder decodes a bit

x_i

only if there is a check of the form

x_i+\sum_{j\neq i}x_j

where

x_j

are known already. However, block-wise MAP can be more complicated. Explanation

Explanation

d: Yes, because the peeling decoder is just solving linear equations, which is exactly the same as block-wise MAP. Explanation

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4. The peeling decoder is called a message-passing decoder because

a: Messages are passed between check nodes and other check nodes in each round. Explanation

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b: Messages are passed between check nodes and other check nodes in the odd rounds, and between variable nodes in the even rounds. Explanation

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c: Message are passed from check to variable nodes in odd rounds, and variable to check nodes in even rounds. Explanation

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d: Messages are passed from variable to check nodes in odd rounds, and from check to variable nodes in even rounds. Explanation

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5. Select the best option regarding the following statement: 'Peeling decoders are useful to decode only LDPC codes, not general block codes.'

a: This is true. Peeling decoders need a sparse parity check matrix. Explanation

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b: This is not true. Peeling decoders can be useful for any block codes. Explanation

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c: This is not true. Peeling decoders need a sparse generator matrix, not a sparse parity check. Explanation

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d: This is true, because peeling decoders can only be used with codes of specific codelengths satisfied by LDPC codes, and not on arbitrary codes. Explanation

Explanation