Method for optimizing protograph-based LDPC code over underwater acoustic channel

(Current amended) A method for optimizing a protograph-based low-density parity-check (LDPC) code over an underwater acoustic (UWA) channel, comprising:

• step (1):
• constructing an UWA channel transfer function based on an eigenray model:
• a channel is represented by a linear time-invariant finite impulse response filter, and z-transform for finite impulse response is:
• H(z)=Σi=1LAl×z−τl, wherein L denotes the number of multipaths of the channel in a symbol duration, Al is a signal amplitude of the l-th multipath, τl is a relative signal delay of the l-th multipath, and l=1, 2, . . . , L;
• and
• determining, based on a basic protograph B and an LDPC code length N, first-extension times T1 and second-extension times T2 of the protograph, wherein
• the basic protograph B is an m×n matrix, and
• B
• =
• [
• B
• 1
• ,
• 1
• B
• 1
• ,
• 2
• …
• B
• 1
• ,
• n
• B
• 2
• ,
• 1
• B
• 2
• ,
• 2
• …
• B
• 2
• ,
• n
• ⋮
• ⋮
• ⋱
• ⋮
• B
• m
• ,
• 1
• B
• m
• ,
• 2
• …
• B
• m
• ,
• n
• ]
• ;
• each row of the matrix corresponds to one check node, and there are a total of m check nodes;
• each column of matrix B corresponds to one variable node, and there are a total of n variable nodes;
• element Bi,j represents a quantity of edges between the i-th check node and the j-th variable node, i=1,2, . . . , m and j=1,2, . . . , n;
• a value of T1 is set to be greater than or equal to a maximum value of elements in the matrix of the basic protograph
• N
• T
• 1
• ×
• n
• is set to a minimum value among integers;
• and
• T
• 2
• =
• N
• T
• 1
• ×
• n
• ;
• wherein
• the eigenray model takes propagation of sound waves as propagation of countless rays perpendicular to an isophase plane, wherein each ray is perpendicular to the isophase plane, and the ray is an eigenray;
• it is assumed that a sound velocity and an refractive index do not change horizontally, but are only a function of sea depth;
• sea surface and seabed interfaces are assumed to be flat interfaces;
• positions of a sound source and a reception point are static and unchanged;
• a sound field is determined by the eigenray;
• and an entire UWA channel is taken as a network system;
• step (2):
• selecting two variable nodes for the first optimization:
• rearranging n variable nodes in the basic protograph B in descending order of column weights, to obtain a rearranged protograph B, wherein the column weight is the sum of values of m elements constituting a variable node;
• one of the variable nodes to be optimized is a variable node with a largest column weight in B, and a sequence number of the variable node is ja=1;
• the other variable node to be optimized is a variable node with the smallest column weight among variable nodes with a column weight greater than 2, and a sequence number of the variable node is jb;
• and jb>ja;
• step (3):
• among m elements of the variable node numbered jb subtracting 1 from a value of element Bi,jb with a maximum value, to reduce the column weight of the variable node numbered jb wherein iε(1, m);
• among m elements of the variable node numbered ja, adding 1 to a value of element Bi,ja, to keep a row weight of the i-th check node ci unchanged and increase the column weight of the variable node numbered ja, wherein the row weight is the sum of values of n elements constituting a check node;
• and a matrix with the values of the element Bi,jb and the element Bi,ja changed is an optimized protograph {tilde over (B)};
• step (4):
• if ja+1≥jb−1, rearranging n variable nodes in the optimized protograph {tilde over (B)} in descending order of column weights, repeating steps (2) and (3) until ja+1<jb−1, and then performing step (5);
• step (5):
• replicating check nodes and variable nodes in the optimized protograph {tilde over (B)} in step (4) for T1 times, and generating a transition graph B′ by using a traditional progressive edge growth (PEG) algorithm, wherein the transition graph B′ is an m′×n′ matrix, m′=T1×m, and n′=T1×n,
• step (6):
• replicating check nodes and variable nodes in the transition graph B′ for T2 times, to obtain a derived graph matrix H;
• and interleaving all edges of H by using a UWA channel-based traditional PEG/approximate cycle extrinsic message degree (ACE) hybrid construction algorithm, to generate a parity check matrix H′;
• step (7):
• performing ACE check on rings in which all variable nodes vj′in the parity check matrix H′ are located:
• if H′ does not pass the ACE check, using variable nodes numbered j′a and j′b in B′ as two variable nodes for the next optimization, and performing step (3), wherein j′a=ja+1, and j′b=jb−1;
• if H′ passes ACE check, performing step (8);
• step (8):
• calculating a decoding threshold γ′ for an optimized codeword by using an extrinsic information transfer chart algorithm of a finite-length protograph-based LDPC code over the UWA channel:
• if |γ−γ′|≥η, using the variable nodes numbered j′a and j′b in B′ as two variable nodes for the next optimization, and performing step (3), wherein γ is a target decoding threshold, η is a threshold adjustment factor, j′a=ja+1, and j′b=jb−1;
• if |γ−γ′|<η, performing step (9);
• step (9):
• obtaining a final optimized parity check matrix H=H′;
• and
• step (10):
• transmitting a transmission signal comprising an optimized encoded data using the final optimized parity check matrix H.