Low Power Decoding of LDPC Codes

Algorithm 1

Gallager bit flipping.

(1) For  j = 1 : N,

   𝑥_𝑗=sign(𝑦_𝑗)

(2) Let  𝑠_𝑗=∑_{𝑖∈𝑁(𝑗)}𝑥_𝑖 over 𝔽² for all 𝑗∈{1,…,𝑀}.

(3) If  ∑_𝑗𝑠_𝑗=0 for all 𝑗∈{1,…,𝑀},

   output x and stop.

(4) Form a count, 𝑓_𝑗, of the number of failed parity checks for all 𝑗∈{1,…,𝑀}.

(5) If the count 𝑓_𝑗 for any bit 𝑗 exceeds a threshold 𝑡,

   change the sign of the bit 𝑗.

(6) If the maximum number of iterations is reached

   output x and stop.

  otherwise

   go to step 2.