This repository gives the following converse bounds under addtive Gausian white noise (AWGN) channel:
- Shannon's 1959 Sphere Packing Bound
- Gonzela's Converse bound for power-constrained AWGN channel.
The use of this function is:
[FER] = Shannon_SP59(n,k,snr)
[FER] = pc_awgn_lower_bound(n,rate,snr_val);Input arguments:
| Input argument | meaning | valid value |
|---|---|---|
| n | blocklength (real-valued channel) | integer scalar |
| k | input bit number | integer scalar |
| rate | transmission rate k/n [bit/real channel use] | real scalr |
| SNR | 10log10(Es/sigma2) | real scalar or vector |
output
| output value | meaning |
|---|---|
| FER | column 1: SNR=10log10(Es/sigma2) column 2: EbN0(dB)=10log10(Eb/N0) column 3: EsN0(dB)=10log10(Es/N0) column 4: Block (frame) error rate |
Run:
demo.m will give you the Shannon'59 SPB and Gonzalo k=64 n=128 snr=0-3dB.
[1] C. E. Shannon, "Probability of error for optimal codes in a Gaussian channel," in The Bell System Technical Journal, vol. 38, no. 3, pp. 611-656, May 1959, doi: 10.1002/j.1538-7305.1959.tb03905.x.
[2] G. Wiechman and I. Sason, "An Improved Sphere-Packing Bound for Finite-Length Codes Over Symmetric Memoryless Channels," in IEEE Transactions on Information Theory, vol. 54, no. 5, pp. 1962-1990, May 2008, doi: 10.1109/TIT.2008.920216.
[3] I. Sason and G. Wiechman, "Log-Domain Calculation of the 1959 Sphere-Packing Bound with Application to M-ary PSK Block Coded Modulation," 2006 IEEE 24th Convention of Electrical & Electronics Engineers in Israel, 2006, pp. 344-348, doi: 10.1109/EEEI.2006.321097.
[4] G. Vazquez-Vilar, "Error Probability Bounds for Gaussian Channels Under Maximal and Average Power Constraints," in IEEE Transactions on Information Theory, vol. 67, no. 6, pp. 3965-3985, June 2021, doi: 10.1109/TIT.2021.3063311.