第七章：限失真编码2(英文).ppt

§7.4: Limited loss source encoding theorem－1 Limited loss source encoding theorem Authentication Practical significance §7.4: Limited loss source encoding theorem－2 Limited loss source encoding theorem Assume R(D) is a distortion function of discrete non-memory steady source, and it has limited infidelity measure. For any D≥0，ε＞0，δ＞0 and any enough code length n，there will inevitably exist a kind of source encoding C，which code number is: M=exp{n［R(D)+ε］} its average infidelity after encoding: d(C)≤D+δ if used dual encoding，the unit of R(D) is bit，then the previous expression M can be : M=2{n［R(D)+ε］} §7.4: Limited loss source encoding theorem－3 Explanation： For any infidelity D≥0，if the code length n is enough，we can always find a kind of encoding C to make the info. transmit rate of each source signal be after encoding: R′=logM/n=R(D)+ε namely: R′≥R(D) its code average infidelity d(C)≤D。 With permitted distortion D, the least and available info. transmit rate is R(D) of the source. §7.4: Limited loss source encoding theorem－4 Authentication problem： 设有达到R(D)的试验信道p(v|u),要证明对于任意的R‘R(D)时，存在一种信息传输率为R’的信源编码，其平均失真度≤D+δ train of thought： 产生码书 选取编译码方法 计算失真度 method： 产生码书：在Vn空间随机抽取M=2nR’个随机序列v 编码方法：若存在与信源序列u构成失真典型序列对的序列v(ω),则编码u?v(ω),否则编码u?v(1) 译码：再现v(ω) 失真度计算：在所有随机码书和Un空间统计平均的基础上计算平均失真度 §7.4: Limited loss source encoding theorem－5 Several statements It is only a existence theorem, doesnt has construct methods. Problem existed： It is difficult to calculate the function R(D) of practical source It is difficult to get accurate mathematic description of the source statistic characteristics It is difficult to get the infidelity measure of the practical source R(D) itself is difficult to calculate Even if we have got R(D)，we still research the best encoding method to get the limit value of R(D). §7.4: Limited loss source encoding theorem－6 Practical significance How to encoding？ Example： Practical significance of R（D） Source function R(D) can be a