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The construction method proposed by Gallager consists of forming a sparse parity check matrix H by randomly determining the positions of 1 s, with a xed number of ones 1 s per column and per row, thus creating a regular LDPC code The condition on the number of 1 s per column and per row can be relaxed, provided that the number of 1 s per column s satis es s > 2 In this case, the LDPC code is said to be irregular The conditions to be satis ed in the construction of the parity check matrix H of a binary regular LDPC code are [9] r The corresponding parity check matrix H should have a xed number v of 1 s per row r The corresponding parity check matrix H should have a xed number s of 1 s per column.

Figure 3-8 An architecture for a packet-based global network for advanced or enhanced VoIP services.

r The overlapping of 1 s per column and per row should be at most equal to one This is a necessary condition for avoiding the presence of cycles in the corresponding bipartite graph r The parameters s and v should be small numbers compared with the code length It is however very dif cult to satisfy the third condition if the intention is to construct good LDPC codes, because cycles are unavoidable in the bipartite graph of an ef cient LDPC code [18] The above construction does not normally lead to the design of a sparse parity check matrix H of systematic form, and so it is usually necessary to utilize Gaussian elimination to convert this resulting matrix into a systematic parity check matrix H = [I n k P T ], where I n k is the identity submatrix of dimension (n k) (n k).

We all face choices every day like David Toms does, several times a day. To build long-term sustained success we too must learn to take the paths that reduce distraction and dissonance and keep our interpersonal synapses clear. Rules keepers are not always there and the rules don t always keep us clear. We can seek our advisors and mentors, and they can guide us, but at the end of the day, we are all metaphorically left in that lonely hotel room late at night, with nothing but ourselves to depend on to do the right thing. It is there that we must seek consonance between the various voices in our heads, be guided by those that help us, and turn away from those that pull our heads out of the game. The guidance we need in that moment is not circumstantial (what can I do now ) but rather foundational (what do I believe ), and that foundational knowledge ows from values, connection, and the pursuit of something larger than immediate success. The ability to keep your head in the game is closely married to the ability to get your HOWs right, to build strong synapses between yourself and others, and to keep them clear and unpolluted in everything you do. If the challenge of living in a connected world requires us to make strong connections with others, we can only do so if we rst accept the challenge of making strong connections within ourselves.

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The initially designed sparse parity check matrix H is the parity check matrix of the LDPC code, whose generator matrix G is of the form G = [ P I k ] Summarizing the design method for an LDPC code, a sparse parity check matrix H = [A B] is constructed rst, obeying the corresponding construction conditions In general, this initial matrix is not in systematic form Submatrices A and B are sparse Submatrix A is a square matrix of dimension (n k) (n k) that is non-singular, and so it has an inverse matrix A 1 Submatrix B is of dimension (n k) k The Gaussian elimination method, operating over the binary eld, modi es the matrix H = [A B ] into the form H = [ I k A 1 B ] = [ I k P T ].