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International Conference on Communications

Low complexity decoding of finite geometry LDPC codes

Zhenyu Liu, Dimitris A. Pados

Published Mar 30, 2004• 16 citations
Publisher

Abstract

We develop a new low complexity algorithm for decoding low-density parity-check (LDPC) codes. The developments are oriented specifically toward the low cost-yet effective-decoding of (high rate) finite geometry LDPC codes. The decoding procedure updates the hard-decision received vector iteratively in search of a valid codeword in the vector space. Only one bit is changed in each iteration and the bit selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optimal mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing performance versus complexity trade-off for finite geometry LDPC codes.

DOI
10.1109/icc.2003.1204470

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We develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low cost, yet effective, decoding of (high-rate) finite-geometry LDPC codes. The decoding procedure iteratively updates the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for finite-geometry LDPC codes.
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In this paper, a new low-complexity symbol-flipping algorithm to decode nonbinary low-density parity-check (LDPC) codes is proposed. The decoding procedure updates iteratively the hard-decision received symbol vector in search of a valid codeword in the symbol vector space. Only one symbol is changed in each iteration, and symbol flipping function combines the number of failed checks and reliability of the received bits and calculated symbols. An optional mechanism to avoid infinite loops in high Galois field search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity over relatively low Galois field for short to medium code length.
Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.
In this paper, we propose a binary message-passing algorithm for decoding low-density parity-check (LDPC) codes. The algorithm substantially improves the performance of purely hard-decision iterative algorithms with a small increase in the memory requirements and the computational complexity. We associate a reliability value to each nonzero element of the code's parity-check matrix, and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes. For the tested random and finite-geometry LDPC codes, the proposed algorithm can achieve performance as close as 1.3 dB and 0.7 dB to that of belief propagation (BP) at the error rates of interest, respectively. This is while, unlike BP, the algorithm does not require the estimation of channel signal to noise ratio. Low memory and computational requirements and binary message-passing make the proposed algorithm attractive for high-speed low-power applications.