This paper overviews and connects together recent results by the authors regarding the weight and stopping set size distributions of generalizations of low-density parity-check (LDPC) codes. We begin by reviewing a result which allows for evaluation of the growth rate of the weight distribution for codewords of any weight (linear in the codeword length). We then show how asymptotic analysis of this general result can lead to a result which encapsulates the behaviour of the growth rate of the weight distribution for the case of small linear-weight codewords. We then show that many existing results in the literature along this line may be viewed as special cases of this general result.
On the Weight and Stopping Set Size Distributions of LDPC Codes and Their Generalizations / M. Flanagan; E. Paolini. - STAMPA. - (2009), pp. 1-6. (Intervento presentato al convegno 2nd International Symposium on Applied Sciences in Biomedical and Communication Technologies, ISABEL 2009 tenutosi a Bratislava, Slovak Republic nel Nov. 2009).
On the Weight and Stopping Set Size Distributions of LDPC Codes and Their Generalizations
PAOLINI, ENRICO
2009
Abstract
This paper overviews and connects together recent results by the authors regarding the weight and stopping set size distributions of generalizations of low-density parity-check (LDPC) codes. We begin by reviewing a result which allows for evaluation of the growth rate of the weight distribution for codewords of any weight (linear in the codeword length). We then show how asymptotic analysis of this general result can lead to a result which encapsulates the behaviour of the growth rate of the weight distribution for the case of small linear-weight codewords. We then show that many existing results in the literature along this line may be viewed as special cases of this general result.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
