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Table 1 Graph-based distributed parameter coordination algorithm

From: A distributed approach to precoder selection using factor graphs for wireless communication networks

Steps Description
Step 0 For all communication nodes, initialize all messages to zero (or close to zero at random), in particular, those from variable nodes to factor
  nodes to zero, i.e.,
  μ p k M i ( 0 ) p k =0
  for all i and k, and set iteration index n=0
Step 1 At each communication node i, receive μ p k M i ( n ) p k from (the variable node of) each neighbor communication nodek N i
Step 2 At each communication node i, compute summary messages
  μ M i p k ( n + 1 ) p k = min p A i { k } M i p A i + j A i { k } μ p j M i ( n ) p j ,
  for each neighbor communication node k A i , by hypothesizing each possible value of p k in P k and finding the best corresponding set of
  parameters p A i { k } that minimizes the quantity in brackets above
Step 3 At each communication node i, send a table of values representing μ M i p k ( n + 1 ) p k to (the variable node of) each neighbor communication
  nodek N i
Step 4 At each communication node i, receive a table of values representing μ M k p i p i from (the factor node of) each neighbor communication
  nodek N i
Step 5 At each communication node i, generate aggregated messages
  μ p i M k ( n + 1 ) p i = μ M i p i ( n + 1 ) p i + j N i { k } μ M j p i ( n + 1 ) p i
  for each neighbor communication node k A i by adding up multiple received tables representing μ M j p i ( n + 1 ) p i j N i
Step 6 At each communication node i, send a table of values representing μ p i M k ( n + 1 ) p i to (the factor node of) each neighbor communication node
  k N i
Step 7 Increment iteration index n and go back to step 1 unless a certain stopping criterion, such as reaching a maximum number of iteration, is
  satisfied
Step 8 At each communication node i, compute the optimal parameter p i as
  p i = arg min p i j A i μ M j p i ( n f ) p i ,
  where n f denotes the final value of the iteration index