Technique to prove the channel coding theorem for a reduced class of codes and its applications

Nadav Shulman*, Meir Feder

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

Abstract

The channel coding theorem for DMCs is proved using random coding. The standard proofs [1],[2]. are strongly using the property of total randomness of the ensemble of codes. For a more restricted ensemble of codes a specific proof is needed. This was done, for example, for linear codes, time-varying convolutional codes, see [3, pages 189 and 301], and for constant composition (constant type) codes, see [4]. In this work we show that weaker demands on the ensembles of codes, than independency of the code words, are needed. As a result, we get simple proofs of the channel coding theorem for interesting restricted ensembles of codes. As an example we can prove the channel coding theorem for the ensembles of codes based on the output of an LF-SR (linear feedback shift register). A particularly interesting application of our technique is a proof that fixed (time-invariant) convolutional codes attain capacity.

Original languageEnglish
Pages1.1.3/1-5
StatePublished - 1995
EventProceedings of the 18th Convention of Electrical and Electronics Engineers in Israel - Tel Aviv, Isr
Duration: 7 Mar 19958 Mar 1995

Conference

ConferenceProceedings of the 18th Convention of Electrical and Electronics Engineers in Israel
CityTel Aviv, Isr
Period7/03/958/03/95

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