Conference Paper

On the Design of DC-Free K-Constrained LDPC Codes

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... Multilevel pulse amplitude modulation (PAM) is one modulation scheme to consider, if high speed digital transmissions, like the optical fiber channel and LAN systems are desired [12], [13]. This is because it is capable of reducing the symbol rate and bandwidth of the modulated signal since it requires lower switching rate [14], [15]. ...
... This implies that the summation of each codeword, after being mapped to the PAM symbol will yield zero. As an example, let us consider the PC-tochannel symbols mapping for (10) from Example 1, which is (13) According to (13), column = 0 is the complement of column = 3, and column = 1 is the complement of column = 4. The same thing applies to columns = 2 and = 5. ...
... This implies that the summation of each codeword, after being mapped to the PAM symbol will yield zero. As an example, let us consider the PC-tochannel symbols mapping for (10) from Example 1, which is (13) According to (13), column = 0 is the complement of column = 3, and column = 1 is the complement of column = 4. The same thing applies to columns = 2 and = 5. ...
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... According to (15), the mapping is done by deriving the first M/2 columns (i.e., first half) of the channel symbols from (11) and the remaining M/2 columns (i.e., second half) are constructed such that, for every column in the first half, there exists an exact complement in the second half. That is, column i = 0 is the complement of column i = 2, and column i = 1 is the complement of column i = 3. ...
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In digital transmission systems that involve pulse amplitude modulation (PAM), channel coding is useful for spectral shaping by concentrating the frequency energy of the transmitted information towards a predetermined range of the frequency spectrum, or making it have low power content at such frequencies, so as to suit the frequency characteristics of the communication channel. We thus present a permutation coding system with injections that can exhibit spectral shaping at rational sub-multiples of the symbol frequency. We also present a mathematical expression that allows for the prediction of low energy positions in the codebook’s spectrum. Upper and lower bounds for the low energy spectrum were also determined. Due to the way the injections are introduced, it gives the scheme an advantage of achieving higher symbol rate, when compared with conventional permutation coding systems.
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